From d8a0afc55065467bc642fca181c6560565cb0247 Mon Sep 17 00:00:00 2001 From: Rafael Date: Fri, 7 Jul 2017 19:08:04 +0200 Subject: [PATCH 01/73] fix error in preshow --- data_structures/Binary Tree/binary_seach_tree.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/data_structures/Binary Tree/binary_seach_tree.py b/data_structures/Binary Tree/binary_seach_tree.py index 1dac948ae..7840b2a32 100644 --- a/data_structures/Binary Tree/binary_seach_tree.py +++ b/data_structures/Binary Tree/binary_seach_tree.py @@ -68,7 +68,7 @@ class BinarySearchTree: return False def preShow(self, curr_node): - if curr_node is None: + if curr_node is not None: print(curr_node.getLabel(), end=" ") self.preShow(curr_node.getLeft()) From 8384cbb8792cade306b630b56917e9ee41b4ba55 Mon Sep 17 00:00:00 2001 From: Rafael Date: Fri, 7 Jul 2017 20:06:33 +0200 Subject: [PATCH 02/73] finish AVL --- data_structures/AVL/AVL.py | 82 ++++++++++++++++++++++++++------------ 1 file changed, 56 insertions(+), 26 deletions(-) diff --git a/data_structures/AVL/AVL.py b/data_structures/AVL/AVL.py index 0e3008dc1..ad8458365 100644 --- a/data_structures/AVL/AVL.py +++ b/data_structures/AVL/AVL.py @@ -39,7 +39,7 @@ class Node: def setHeight(self, height): self.height = height - def getHeight(self, height): + def getHeight(self): return self.height @@ -72,38 +72,36 @@ class AVL: if node.getLabel() < dad_node.getLabel(): dad_node.setLeft(node) dad_node.setHeight(dad_node.getHeight() + 1) - - if (dad_node.getRight().getHeight() - - dad_node.getLeft.getHeight() > 1): - self.rebalance(dad_node) - else: dad_node.setRight(node) dad_node.setHeight(dad_node.getHeight() + 1) - - if (dad_node.getRight().getHeight() - - dad_node.getLeft.getHeight() > 1): - self.rebalance(dad_node) break def rebalance(self, node): - if (node.getRight().getHeight() - - node.getLeft.getHeight() > 1): - if (node.getRight().getHeight() > - node.getLeft.getHeight()): - pass + height_right = 0 + height_left = 0 + + if node.getRight() is not None: + height_right = node.getRight().getHeight() + + if node.getLeft() is not None: + height_left = node.getLeft().getHeight() + + if abs(height_left - height_right) > 1: + if height_left > height_right: + right_child = node.getRight() + if (right_child.getLeft().getHeight() > + right_child.getRight().getHeight()): + self.rotate_left(node) + else: + self.double_rotate_right(node) else: - pass - pass - elif (node.getRight().getHeight() - - node.getLeft.getHeight() > 2): - if (node.getRight().getHeight() > - node.getLeft.getHeight()): - pass - else: - pass - pass - pass + left_child = node.getLeft() + if (left_child.getLeft().getHeight() > + left_child.getRight().getHeight()): + self.double_rotate_left(node) + else: + self.rotate_right(node) def rotate_left(self, node): # TODO: is this pythonic enought? @@ -129,3 +127,35 @@ class AVL: def double_rotate_right(self, node): self.rotate_left(node.getLeft().getLeft()) self.rotate_right(node) + + def empty(self): + if self.root is None: + return True + return False + + def preShow(self, curr_node): + if curr_node is not None: + self.preShow(curr_node.getLeft()) + print(curr_node.getLabel(), end=" ") + self.preShow(curr_node.getRight()) + + def getRoot(self): + return self.root + +t = AVL() +t.insert(11) +t.insert(14) +t.insert(3) +t.insert(4) +t.insert(5) +t.insert(6) +t.insert(7) +t.insert(8) +t.insert(9) +t.insert(10) +t.insert(1) +t.insert(12) +t.insert(13) +t.insert(2) +t.insert(15) +t.preShow(t.getRoot()) From 67f23f59b15581be38c5d630018e590148928384 Mon Sep 17 00:00:00 2001 From: Rafael Date: Sat, 8 Jul 2017 01:26:49 +0200 Subject: [PATCH 03/73] rotate left almost working --- data_structures/AVL/AVL.py | 177 +++++++++++++++++++++++++++---------- 1 file changed, 129 insertions(+), 48 deletions(-) diff --git a/data_structures/AVL/AVL.py b/data_structures/AVL/AVL.py index ad8458365..4a360fee5 100644 --- a/data_structures/AVL/AVL.py +++ b/data_structures/AVL/AVL.py @@ -23,18 +23,24 @@ class Node: def setLeft(self, left): self.left = left - + self.left.setParent(self) + self.left.setHeight(self.height + 1) + def getRight(self): return self.rigt def setRight(self, right): self.rigt = right + self.rigt.setParent(self) + self.rigt.setHeight(self.height + 1) def getParent(self): return self.parent def setParent(self, parent): self.parent = parent + self.height = (self.parent.getHeight() + 1 if + (self.parent is not None) else 0) def setHeight(self, height): self.height = height @@ -53,6 +59,7 @@ class AVL: node = Node(value) if self.root is None: self.root = node + self.root.setHeight(0) self.size = 1 else: # Same as Binary Tree @@ -71,54 +78,59 @@ class AVL: else: if node.getLabel() < dad_node.getLabel(): dad_node.setLeft(node) - dad_node.setHeight(dad_node.getHeight() + 1) else: dad_node.setRight(node) - dad_node.setHeight(dad_node.getHeight() + 1) + self.rebalance(dad_node) break def rebalance(self, node): height_right = 0 height_left = 0 + n = node + while n is not None: + height_right = 0 + height_left = 0 - if node.getRight() is not None: - height_right = node.getRight().getHeight() + if node.getRight() is not None: + height_right = node.getRight().getHeight() - if node.getLeft() is not None: - height_left = node.getLeft().getHeight() + if node.getLeft() is not None: + height_left = node.getLeft().getHeight() - if abs(height_left - height_right) > 1: - if height_left > height_right: - right_child = node.getRight() - if (right_child.getLeft().getHeight() > - right_child.getRight().getHeight()): - self.rotate_left(node) + if abs(height_left - height_right) > 1: + if height_left > height_right: + left_child = node.getRight() + if (): + self.rotate_left(n) + break + else: + self.double_rotate_right(n) + break else: - self.double_rotate_right(node) - else: - left_child = node.getLeft() - if (left_child.getLeft().getHeight() > - left_child.getRight().getHeight()): - self.double_rotate_left(node) - else: - self.rotate_right(node) + right_child = node.getRight() + if right_child is not None: + h_right = (right_child.getRight().getHeight() + if (right_child.getRight() is not None) else 0) + h_left = (right_child.getLeft().getHeight() + if (right_child.getLeft() is not None) else 0) + + if (h_left > h_right): + self.double_rotate_left(n) + break + else: + self.rotate_right(n) + print(n.getLabel()) + break + n = n.getParent() def rotate_left(self, node): - # TODO: is this pythonic enought? - aux = node.getLabel() - node = aux.getRight() - node.setHeight(node.getHeight() - 1) - node.setLeft(Node(aux)) - node.getLeft().setHeight(node.getHeight() + 1) - node.getRight().setHeight(node.getRight().getHeight() - 1) + pass def rotate_right(self, node): - aux = node.getLabel() - node = aux.getLeft() - node.setHeight(node.getHeight() - 1) - node.setRight(Node(aux)) - node.getLeft().setHeight(node.getHeight() + 1) - node.getLeft().setHeight(node.getLeft().getHeight() - 1) + n = Node(node.getLabel()) + n.setRight(node.getRight()) + n.setLeft(Node(node.getParent().getLabel())) + node = n def double_rotate_left(self, node): self.rotate_right(node.getRight().getRight()) @@ -139,23 +151,92 @@ class AVL: print(curr_node.getLabel(), end=" ") self.preShow(curr_node.getRight()) + def preorden(self, curr_node): + if curr_node is not None: + self.preShow(curr_node.getLeft()) + self.preShow(curr_node.getRight()) + print(curr_node.getLabel(), end=" ") + def getRoot(self): return self.root t = AVL() -t.insert(11) -t.insert(14) -t.insert(3) -t.insert(4) -t.insert(5) -t.insert(6) -t.insert(7) -t.insert(8) -t.insert(9) -t.insert(10) +# t.insert(1) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(2) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(3) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# print(t.getRoot().getHeight()) +# print(t.getRoot().getRight().getHeight()) t.insert(1) -t.insert(12) -t.insert(13) t.insert(2) -t.insert(15) -t.preShow(t.getRoot()) +t.insert(3) +# t.insert(4) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(5) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(6) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(7) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(8) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(9) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(10) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(11) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(12) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(13) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(14) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) +# print("\n") +# t.insert(15) +# t.preShow(t.getRoot()) +# print("\n") +# t.preorden(t.getRoot()) From d8cd33add2274af8f8ef6371f2bb019bab734b98 Mon Sep 17 00:00:00 2001 From: Rafael Date: Sat, 8 Jul 2017 20:50:47 +0200 Subject: [PATCH 04/73] using python properties --- data_structures/AVL/AVL.py | 67 +++++++++++++++++--------------------- 1 file changed, 29 insertions(+), 38 deletions(-) diff --git a/data_structures/AVL/AVL.py b/data_structures/AVL/AVL.py index 4a360fee5..f1ac16ef8 100644 --- a/data_structures/AVL/AVL.py +++ b/data_structures/AVL/AVL.py @@ -12,41 +12,32 @@ class Node: self.parent = None self.height = 0 - def getLabel(self): - return self.label + @property + def right(self): + return self.right - def setLabel(self, label): - self.label = label + @right.setter + def right(self, node): + node.parent = self + self.right = node - def getLeft(self): - return self.left - - def setLeft(self, left): - self.left = left - self.left.setParent(self) - self.left.setHeight(self.height + 1) - - def getRight(self): - return self.rigt - - def setRight(self, right): - self.rigt = right - self.rigt.setParent(self) - self.rigt.setHeight(self.height + 1) - - def getParent(self): + @property + def left(self): return self.parent - def setParent(self, parent): - self.parent = parent - self.height = (self.parent.getHeight() + 1 if - (self.parent is not None) else 0) + @left.setter + def left(self, node): + node.parent = self + self.left = node - def setHeight(self, height): - self.height = height + @property + def parent(self): + return self.parent - def getHeight(self): - return self.height + @parent.setter + def parent(self, node): + self.parent = node + self.height = self.parent.height + 1 class AVL: @@ -59,7 +50,7 @@ class AVL: node = Node(value) if self.root is None: self.root = node - self.root.setHeight(0) + self.root.height = 0 self.size = 1 else: # Same as Binary Tree @@ -71,16 +62,18 @@ class AVL: dad_node = curr_node - if node.getLabel() < curr_node.getLabel(): - curr_node = curr_node.getLeft() + if node.label < curr_node.label: + curr_node = curr_node.left else: - curr_node = curr_node.getRight() + curr_node = curr_node.rigt else: - if node.getLabel() < dad_node.getLabel(): - dad_node.setLeft(node) + if node.label < dad_node.label: + dad_node.left = node else: - dad_node.setRight(node) + dad_node.right = node + self.rebalance(dad_node) + self.size += 1 break def rebalance(self, node): @@ -119,7 +112,6 @@ class AVL: break else: self.rotate_right(n) - print(n.getLabel()) break n = n.getParent() @@ -130,7 +122,6 @@ class AVL: n = Node(node.getLabel()) n.setRight(node.getRight()) n.setLeft(Node(node.getParent().getLabel())) - node = n def double_rotate_left(self, node): self.rotate_right(node.getRight().getRight()) From 8e41aca1b943d9bbbd742f57a0aa58cfa5e6c35e Mon Sep 17 00:00:00 2001 From: Rafael Date: Mon, 10 Jul 2017 18:29:45 +0200 Subject: [PATCH 05/73] node now eses pythonproperties --- data_structures/AVL/AVL.py | 30 ++++++++++++++++-------------- 1 file changed, 16 insertions(+), 14 deletions(-) diff --git a/data_structures/AVL/AVL.py b/data_structures/AVL/AVL.py index f1ac16ef8..0c34cb597 100644 --- a/data_structures/AVL/AVL.py +++ b/data_structures/AVL/AVL.py @@ -7,9 +7,6 @@ class Node: def __init__(self, label): self.label = label - self.left = None - self.rigt = None - self.parent = None self.height = 0 @property @@ -23,7 +20,7 @@ class Node: @property def left(self): - return self.parent + return self.left @left.setter def left(self, node): @@ -48,6 +45,7 @@ class AVL: def insert(self, value): node = Node(value) + if self.root is None: self.root = node self.root.height = 0 @@ -65,7 +63,7 @@ class AVL: if node.label < curr_node.label: curr_node = curr_node.left else: - curr_node = curr_node.rigt + curr_node = curr_node.right else: if node.label < dad_node.label: dad_node.left = node @@ -92,7 +90,7 @@ class AVL: if abs(height_left - height_right) > 1: if height_left > height_right: - left_child = node.getRight() + # left_child = node.getRight() if (): self.rotate_left(n) break @@ -100,12 +98,12 @@ class AVL: self.double_rotate_right(n) break else: - right_child = node.getRight() + right_child = node.right if right_child is not None: - h_right = (right_child.getRight().getHeight() - if (right_child.getRight() is not None) else 0) - h_left = (right_child.getLeft().getHeight() - if (right_child.getLeft() is not None) else 0) + h_right = (right_child.right.height + if (right_child.right is not None) else 0) + h_left = (right_child.left.height + if (right_child.left is not None) else 0) if (h_left > h_right): self.double_rotate_left(n) @@ -119,9 +117,13 @@ class AVL: pass def rotate_right(self, node): - n = Node(node.getLabel()) - n.setRight(node.getRight()) - n.setLeft(Node(node.getParent().getLabel())) + aux = node.parent + node.parent = node + node.left = aux + + print(node.parent.label) + print(node.parent.right.label) + print(node.parent.left.label) def double_rotate_left(self, node): self.rotate_right(node.getRight().getRight()) From 52ee9a1e128c137793f08f69f4835b67f3b9c5d1 Mon Sep 17 00:00:00 2001 From: Stephen Lee <245885195@qq.com> Date: Fri, 22 Sep 2017 14:34:28 +0800 Subject: [PATCH 06/73] commit convolution_neural_network.py --- Neural_Network/convolution_neural_network.py | 343 +++++++++++++++++++ 1 file changed, 343 insertions(+) create mode 100644 Neural_Network/convolution_neural_network.py diff --git a/Neural_Network/convolution_neural_network.py b/Neural_Network/convolution_neural_network.py new file mode 100644 index 000000000..539c315a0 --- /dev/null +++ b/Neural_Network/convolution_neural_network.py @@ -0,0 +1,343 @@ +#-*- coding: utf-8 -*- + +''' + - - - - - -- - - - - - - - - - - - - - - - - - - - - - - + Name - - CNN - Convolution Neural Network For Photo Recognizing + Goal - - Recognize Handing Writting Word Photo + Detail：Total 5 layers neural network + * Convolution layer + * Pooling layer + * Input layer layer of BP + * Hiden layer of BP + * Output layer of BP + Author: Stephen Lee + Program: PYTHON + Date: 2017.9.20 + - - - - - -- - - - - - - - - - - - - - - - - - - - - - - + ''' +import numpy as np +import matplotlib.pyplot as plt + + +class CNN(): + conv1 = [] + w_conv1 = [] + thre_conv1 = [] + step_conv1 = 0 + size_pooling1 = 0 + num_bp1 = 0 + num_bp2 = 0 + num_bp3 = 0 + thre_bp1 = [] + thre_bp2 = [] + wkj = np.mat([]) + vji = np.mat([]) + rate_weight = 0 + rate_thre = 0 + + + def __init__(self,conv1_get,size_p1,bp_num1,bp_num2,bp_num3,rate_w=0.2,rate_t=0.2): + ''' + :param conv1_get: [a,c,d]，size, number, step of convolution kernel + :param size_p1: pooling size + :param bp_num1: units number of flatten layer + :param bp_num2: units number of hidden layer + :param bp_num3: units number of output layer + :param rate_w: rate of weight learning + :param rate_t: rate of threshold learning + ''' + self.num_bp1 = bp_num1 + self.num_bp2 = bp_num2 + self.num_bp3 = bp_num3 + self.conv1 = conv1_get[:2] + self.step_conv1 = conv1_get[2] + self.size_pooling1 = size_p1 + self.rate_weight = rate_w + self.rate_thre = rate_t + self.w_conv1 = [np.mat(-1*np.random.rand(self.conv1[0],self.conv1[0])+0.5) for i in range(self.conv1[1])] + self.wkj = np.mat(-1 * np.random.rand(self.num_bp3, self.num_bp2) + 0.5) + self.vji = np.mat(-1*np.random.rand(self.num_bp2, self.num_bp1)+0.5) + self.thre_conv1 = -2*np.random.rand(self.conv1[1])+1 + self.thre_bp2 = -2*np.random.rand(self.num_bp2)+1 + self.thre_bp3 = -2*np.random.rand(self.num_bp3)+1 + + + def save_model(self,save_path): + #将模型保存 + import pickle + model_dic = {'num_bp1':self.num_bp1, + 'num_bp2':self.num_bp2, + 'num_bp3':self.num_bp3, + 'conv1':self.conv1, + 'step_conv1':self.step_conv1, + 'size_pooling1':self.size_pooling1, + 'rate_weight':self.rate_weight, + 'rate_thre':self.rate_thre, + 'w_conv1':self.w_conv1, + 'wkj':self.wkj, + 'vji':self.vji, + 'thre_conv1':self.thre_conv1, + 'thre_bp2':self.thre_bp2, + 'thre_bp3':self.thre_bp3} + with open(save_path, 'wb') as f: + pickle.dump(model_dic, f) + + print('模型已经保存： %s'% save_path) + + + def paste_model(self,save_path): + #实例方法， + #虽然这么写一点也不简洁。。。。 + #卸载这个里面的话，只是用于修改已经存在的模型，要根据读取的数据返回实例的模型，再写一个吧 + import pickle + with open(save_path, 'rb') as f: + model_dic = pickle.load(f) + self.num_bp1 = model_dic.get('num_bp1') + self.num_bp2 = model_dic.get('num_bp2') + self.num_bp3 = model_dic.get('num_bp3') + self.conv1 = model_dic.get('conv1') + self.step_conv1 = model_dic.get('step_conv1') + self.size_pooling1 = model_dic.get('size_pooling1') + self.rate_weight = model_dic.get('rate_weight') + self.rate_thre = model_dic.get('rate_thre') + self.w_conv1 = model_dic.get('w_conv1') + self.wkj = model_dic.get('wkj') + self.vji = model_dic.get('vji') + self.thre_conv1 = model_dic.get('thre_conv1') + self.thre_bp2 = model_dic.get('thre_bp2') + self.thre_bp3 = model_dic.get('thre_bp3') + print('已经成功读取模型') + + @classmethod + def ReadModel(cls,model_path): + #类方法，读取保存的模型，返回一个实例。 + import pickle + with open(model_path, 'rb') as f: + model_dic = pickle.load(f) + + conv_get= model_dic.get('conv1') + conv_get.append(model_dic.get('step_conv1')) + size_p1 = model_dic.get('size_pooling1') + bp1 = model_dic.get('num_bp1') + bp2 = model_dic.get('num_bp2') + bp3 = model_dic.get('num_bp3') + r_w = model_dic.get('rate_weight') + r_t = model_dic.get('rate_thre') + #创建实例 + conv_ins = CNN(conv_get,size_p1,bp1,bp2,bp3,r_w,r_t) + #修改实例的参数 + conv_ins.w_conv1 = model_dic.get('w_conv1') + conv_ins.wkj = model_dic.get('wkj') + conv_ins.vji = model_dic.get('vji') + conv_ins.thre_conv1 = model_dic.get('thre_conv1') + conv_ins.thre_bp2 = model_dic.get('thre_bp2') + conv_ins.thre_bp3 = model_dic.get('thre_bp3') + return conv_ins + + + def sig(self,x): + return 1 / (1 + np.exp(-1*x)) + def do_round(self,x): + return round(x, 3) + #卷积 + def Convolute(self,data,convs,w_convs,thre_convs,conv_step): + size_conv = convs[0] + num_conv =convs[1] + size_data = np.shape(data)[0] + #得到原图像滑动的小图，data_focus + data_focus = [] + for i_focus in range(0, size_data - size_conv + 1, conv_step): + for j_focus in range(0, size_data - size_conv + 1, conv_step): + focus = data[i_focus:i_focus + size_conv, j_focus:j_focus + size_conv] + data_focus.append(focus) + #计算所有卷积核得到的特征图，每个特征图以矩阵形式，存储为一个列表data_featuremap + data_featuremap = [] + Size_FeatureMap = int((size_data - size_conv) / conv_step + 1) + for i_map in range(num_conv): + featuremap = [] + for i_focus in range(len(data_focus)): + net_focus = np.sum(np.multiply(data_focus[i_focus], w_convs[i_map])) - thre_convs[i_map] + featuremap.append(self.sig(net_focus)) + featuremap = np.asmatrix(featuremap).reshape(Size_FeatureMap, Size_FeatureMap) + data_featuremap.append(featuremap) + + #将data_focus中的focus展开为一维 + focus1_list = [] + for each_focus in data_focus: + focus1_list.extend(self.Expand_Mat(each_focus)) + focus_list = np.asarray(focus1_list) + return focus_list,data_featuremap + + # 池化 + def Pooling(self,featuremaps,size_pooling): + size_map = len(featuremaps[0]) + size_pooled = int(size_map/size_pooling) + featuremap_pooled = [] + for i_map in range(len(featuremaps)): + map = featuremaps[i_map] + map_pooled = [] + for i_focus in range(0,size_map,size_pooling): + for j_focus in range(0, size_map, size_pooling): + focus = map[i_focus:i_focus + size_pooling, j_focus:j_focus + size_pooling] + #平均池化 + map_pooled.append(np.average(focus)) + #最大池化 + #map_pooled.append(np.max(focus)) + map_pooled = np.asmatrix(map_pooled).reshape(size_pooled,size_pooled) + featuremap_pooled.append(map_pooled) + return featuremap_pooled + + def Expand(self,datas): + #将三元的数据展开为1为的list + data_expanded = [] + for i in range(len(datas)): + shapes = np.shape(datas[i]) + data_listed = datas[i].reshape(1,shapes[0]*shapes[1]) + data_listed = data_listed.getA().tolist()[0] + data_expanded.extend(data_listed) + #连接所有数据 + data_expanded = np.asarray(data_expanded) + return data_expanded + + def Expand_Mat(self,data_mat): + #用来展开矩阵为一维的list + data_mat = np.asarray(data_mat) + shapes = np.shape(data_mat) + data_expanded = data_mat.reshape(1,shapes[0]*shapes[1]) + return data_expanded + + def Getpd_From_Pool(self,out_map,pd_pool,num_map,size_map,size_pooling): + ''' + 误差反传，从pooled到前一个map, 例如将池化层6*6的误差矩阵扩大为12*12的误差矩阵 + pd_pool: 是采样层的误差，list形式。。。。要改要改 + out_map: 前面特征图的输出，数量*size*size的列表形式 + return: pd_all:前面层所有的特征图的pd， num*size_map*size_map的列表形式 + ''' + pd_all = [] + i_pool = 0 + for i_map in range(num_map): + pd_conv1 = np.ones((size_map, size_map)) + for i in range(0, size_map, size_pooling): + for j in range(0, size_map, size_pooling): + pd_conv1[i:i + size_pooling, j:j + size_pooling] = pd_pool[i_pool] + i_pool = i_pool + 1 + pd_conv2 = np.multiply(pd_conv1,np.multiply(out_map[i_map],(1-out_map[i_map]))) + pd_all.append(pd_conv2) + return pd_all + + def trian(self,patterns,datas_train, datas_teach, n_repeat, error_accuracy,draw_e = bool): + print('----------------------Start Training-------------------------') + print(' - - Shape: Train_Data ',np.shape(datas_train)) + print(' - - Shape: Teach_Data ',np.shape(datas_teach)) + rp = 0 + all_mse = [] + mse = 10000 + while rp < n_repeat and mse >= error_accuracy: + alle = 0 + print('-------------进行第%d次学习--------------'%rp) + for p in range(len(datas_train)): + #print('------------学习第%d个图像--------------'%p) + data_train = np.asmatrix(datas_train[p]) + data_teach = np.asarray(datas_teach[p]) + data_focus1,data_conved1 = self.Convolute(data_train,self.conv1,self.w_conv1, + self.thre_conv1,conv_step=self.step_conv1) + data_pooled1 = self.Pooling(data_conved1,self.size_pooling1) + shape_featuremap1 = np.shape(data_conved1) + ''' + print(' -----original shape ', np.shape(data_train)) + print(' ---- after convolution ',np.shape(data_conv1)) + print(' -----after pooling ',np.shape(data_pooled1)) + ''' + data_bp_input = self.Expand(data_pooled1) + # 计算第一层输入输出 + bp_out1 = data_bp_input + # 计算第二层输入输出 + bp_net_j = np.dot(bp_out1,self.vji.T) - self.thre_bp2 + bp_out2 = self.sig(bp_net_j) + # 计算第三层输入输出 + bp_net_k = np.dot(bp_out2 ,self.wkj.T) - self.thre_bp3 + bp_out3 = self.sig(bp_net_k) + + # 计算一般化误差 + pd_k_all = np.multiply((data_teach - bp_out3), np.multiply(bp_out3, (1 - bp_out3))) + pd_j_all = np.multiply(np.dot(pd_k_all,self.wkj), np.multiply(bp_out2, (1 - bp_out2))) + pd_i_all = np.dot(pd_j_all,self.vji) + + pd_conv1_pooled = pd_i_all / (self.size_pooling1*self.size_pooling1) + pd_conv1_pooled = pd_conv1_pooled.T.getA().tolist() + pd_conv1_all = self.Getpd_From_Pool(data_conved1,pd_conv1_pooled,shape_featuremap1[0], + shape_featuremap1[1],self.size_pooling1) + + #卷积层1的权重和阈值修正，每个卷积核的权重需要修正 12*12(map) 次 + #修正量为featuremap中点的偏导值 乘以 前一层图像focus， 整个权重模板一起更新 + for k_conv in range(self.conv1[1]): + pd_conv_list = self.Expand_Mat(pd_conv1_all[k_conv]) + delta_w = self.rate_weight * np.dot(pd_conv_list,data_focus1) + + self.w_conv1[k_conv] = self.w_conv1[k_conv] + delta_w.reshape((self.conv1[0],self.conv1[0])) + + self.thre_conv1[k_conv] = self.thre_conv1[k_conv] - np.sum(pd_conv1_all[k_conv]) * self.rate_thre + # 更新kj层的权重 + + self.wkj = self.wkj + pd_k_all.T * bp_out2 * self.rate_weight + # 更新ji层的权重 + self.vji = self.vji + pd_j_all.T * bp_out1 * self.rate_weight + # 更新阈值 + self.thre_bp3 = self.thre_bp3 - pd_k_all * self.rate_thre + self.thre_bp2 = self.thre_bp2 - pd_j_all * self.rate_thre + # 计算总误差 + errors = np.sum(abs((data_teach - bp_out3))) + alle = alle + errors + #print(' ----Teach ',data_teach) + #print(' ----BP_output ',bp_out3) + rp = rp + 1 + mse = alle/patterns + all_mse.append(mse) + def draw_error(): + yplot = [error_accuracy for i in range(int(n_repeat * 1.2))] + plt.plot(all_mse, '+-') + plt.plot(yplot, 'r--') + plt.xlabel('Learning Times') + plt.ylabel('All_mse') + plt.grid(True, alpha=0.5) + plt.show() + print('------------------Training Complished---------------------') + print(' - - Training epoch: ', rp, ' - - Mse: %.6f' % mse) + if draw_e: + draw_error() + return mse + + def produce(self,datas_test): + #对验证和测试数据集进行输出 + produce_out = [] + print('-------------------Start Testing-------------------------') + print(' - - Shape: Test_Data ',np.shape(datas_test)) + for p in range(len(datas_test)): + print('--------测试第%d个图像----------' % p) + data_test = np.asmatrix(datas_test[p]) + data_focus1, data_conved1 = self.Convolute(data_test, self.conv1, self.w_conv1, + self.thre_conv1, conv_step=self.step_conv1) + data_pooled1 = self.Pooling(data_conved1, self.size_pooling1) + data_bp_input = self.Expand(data_pooled1) + # 计算第一层输入输出 + bp_out1 = data_bp_input + # 计算第二层输入输出 + bp_net_j = bp_out1 * self.vji.T - self.thre_bp2 + bp_out2 = self.sig(bp_net_j) + # 计算第三层输入输出 + bp_net_k = bp_out2 * self.wkj.T - self.thre_bp3 + bp_out3 = self.sig(bp_net_k) + produce_out.extend(bp_out3.getA().tolist()) + res = [list(map(self.do_round,each)) for each in produce_out] + return np.asarray(res) + + def convolution(self,data): + #返回卷积和池化后的数据,用于查看图像 + data_test = np.asmatrix(data) + data_focus1, data_conved1 = self.Convolute(data_test, self.conv1, self.w_conv1, + self.thre_conv1, conv_step=self.step_conv1) + data_pooled1 = self.Pooling(data_conved1, self.size_pooling1) + + return data_conved1,data_pooled1 + + From 6e61ac19cd50288175b7b2c94d93133adc69492d Mon Sep 17 00:00:00 2001 From: Stephen Lee <245885195@qq.com> Date: Fri, 22 Sep 2017 14:56:20 +0800 Subject: [PATCH 07/73] commit convolution_neural_network.py --- Neural_Network/convolution_neural_network.py | 158 +++++++------------ 1 file changed, 60 insertions(+), 98 deletions(-) diff --git a/Neural_Network/convolution_neural_network.py b/Neural_Network/convolution_neural_network.py index 539c315a0..d8ab0d2e5 100644 --- a/Neural_Network/convolution_neural_network.py +++ b/Neural_Network/convolution_neural_network.py @@ -11,30 +11,15 @@ * Hiden layer of BP * Output layer of BP Author: Stephen Lee - Program: PYTHON + Github: 245885195@qq.com Date: 2017.9.20 - - - - - -- - - - - - - - - - - - - - - - - - - - - - - ''' + import numpy as np import matplotlib.pyplot as plt - class CNN(): - conv1 = [] - w_conv1 = [] - thre_conv1 = [] - step_conv1 = 0 - size_pooling1 = 0 - num_bp1 = 0 - num_bp2 = 0 - num_bp3 = 0 - thre_bp1 = [] - thre_bp2 = [] - wkj = np.mat([]) - vji = np.mat([]) - rate_weight = 0 - rate_thre = 0 - def __init__(self,conv1_get,size_p1,bp_num1,bp_num2,bp_num3,rate_w=0.2,rate_t=0.2): ''' @@ -63,7 +48,7 @@ class CNN(): def save_model(self,save_path): - #将模型保存 + #save model dict with pickle import pickle model_dic = {'num_bp1':self.num_bp1, 'num_bp2':self.num_bp2, @@ -82,35 +67,11 @@ class CNN(): with open(save_path, 'wb') as f: pickle.dump(model_dic, f) - print('模型已经保存： %s'% save_path) - - - def paste_model(self,save_path): - #实例方法， - #虽然这么写一点也不简洁。。。。 - #卸载这个里面的话，只是用于修改已经存在的模型，要根据读取的数据返回实例的模型，再写一个吧 - import pickle - with open(save_path, 'rb') as f: - model_dic = pickle.load(f) - self.num_bp1 = model_dic.get('num_bp1') - self.num_bp2 = model_dic.get('num_bp2') - self.num_bp3 = model_dic.get('num_bp3') - self.conv1 = model_dic.get('conv1') - self.step_conv1 = model_dic.get('step_conv1') - self.size_pooling1 = model_dic.get('size_pooling1') - self.rate_weight = model_dic.get('rate_weight') - self.rate_thre = model_dic.get('rate_thre') - self.w_conv1 = model_dic.get('w_conv1') - self.wkj = model_dic.get('wkj') - self.vji = model_dic.get('vji') - self.thre_conv1 = model_dic.get('thre_conv1') - self.thre_bp2 = model_dic.get('thre_bp2') - self.thre_bp3 = model_dic.get('thre_bp3') - print('已经成功读取模型') + print('Model saved： %s'% save_path) @classmethod def ReadModel(cls,model_path): - #类方法，读取保存的模型，返回一个实例。 + #read saved model import pickle with open(model_path, 'rb') as f: model_dic = pickle.load(f) @@ -123,9 +84,9 @@ class CNN(): bp3 = model_dic.get('num_bp3') r_w = model_dic.get('rate_weight') r_t = model_dic.get('rate_thre') - #创建实例 + #create model instance conv_ins = CNN(conv_get,size_p1,bp1,bp2,bp3,r_w,r_t) - #修改实例的参数 + #modify model parameter conv_ins.w_conv1 = model_dic.get('w_conv1') conv_ins.wkj = model_dic.get('wkj') conv_ins.vji = model_dic.get('vji') @@ -137,20 +98,22 @@ class CNN(): def sig(self,x): return 1 / (1 + np.exp(-1*x)) + def do_round(self,x): return round(x, 3) - #卷积 - def Convolute(self,data,convs,w_convs,thre_convs,conv_step): + + def convolute(self,data,convs,w_convs,thre_convs,conv_step): + #convolution process size_conv = convs[0] num_conv =convs[1] size_data = np.shape(data)[0] - #得到原图像滑动的小图，data_focus + #get the data slice of original image data, data_focus data_focus = [] for i_focus in range(0, size_data - size_conv + 1, conv_step): for j_focus in range(0, size_data - size_conv + 1, conv_step): focus = data[i_focus:i_focus + size_conv, j_focus:j_focus + size_conv] data_focus.append(focus) - #计算所有卷积核得到的特征图，每个特征图以矩阵形式，存储为一个列表data_featuremap + #caculate the feature map of every single kernel, and saved as list of matrix data_featuremap = [] Size_FeatureMap = int((size_data - size_conv) / conv_step + 1) for i_map in range(num_conv): @@ -161,15 +124,15 @@ class CNN(): featuremap = np.asmatrix(featuremap).reshape(Size_FeatureMap, Size_FeatureMap) data_featuremap.append(featuremap) - #将data_focus中的focus展开为一维 + #expanding the data slice to One dimenssion focus1_list = [] for each_focus in data_focus: focus1_list.extend(self.Expand_Mat(each_focus)) focus_list = np.asarray(focus1_list) return focus_list,data_featuremap - # 池化 - def Pooling(self,featuremaps,size_pooling): + def pooling(self,featuremaps,size_pooling,type='average_pool'): + #pooling process size_map = len(featuremaps[0]) size_pooled = int(size_map/size_pooling) featuremap_pooled = [] @@ -179,39 +142,40 @@ class CNN(): for i_focus in range(0,size_map,size_pooling): for j_focus in range(0, size_map, size_pooling): focus = map[i_focus:i_focus + size_pooling, j_focus:j_focus + size_pooling] - #平均池化 - map_pooled.append(np.average(focus)) - #最大池化 - #map_pooled.append(np.max(focus)) + if type == 'average_pool': + #average pooling + map_pooled.append(np.average(focus)) + elif type == 'max_pooling': + #max pooling + map_pooled.append(np.max(focus)) map_pooled = np.asmatrix(map_pooled).reshape(size_pooled,size_pooled) featuremap_pooled.append(map_pooled) return featuremap_pooled - def Expand(self,datas): - #将三元的数据展开为1为的list + def _expand(self,datas): + #expanding three dimension data to one dimension list data_expanded = [] for i in range(len(datas)): shapes = np.shape(datas[i]) data_listed = datas[i].reshape(1,shapes[0]*shapes[1]) data_listed = data_listed.getA().tolist()[0] data_expanded.extend(data_listed) - #连接所有数据 data_expanded = np.asarray(data_expanded) return data_expanded - def Expand_Mat(self,data_mat): - #用来展开矩阵为一维的list + def _expand_mat(self,data_mat): + #expanding matrix to one dimension list data_mat = np.asarray(data_mat) shapes = np.shape(data_mat) data_expanded = data_mat.reshape(1,shapes[0]*shapes[1]) return data_expanded - def Getpd_From_Pool(self,out_map,pd_pool,num_map,size_map,size_pooling): + def _calculate_gradient_from_pool(self,out_map,pd_pool,num_map,size_map,size_pooling): ''' - 误差反传，从pooled到前一个map, 例如将池化层6*6的误差矩阵扩大为12*12的误差矩阵 - pd_pool: 是采样层的误差，list形式。。。。要改要改 - out_map: 前面特征图的输出，数量*size*size的列表形式 - return: pd_all:前面层所有的特征图的pd， num*size_map*size_map的列表形式 + calcluate the gradient from the data slice of pool layer + pd_pool: list of matrix + out_map: the shape of data slice(size_map*size_map) + return: pd_all: list of matrix, [num, size_map, size_map] ''' pd_all = [] i_pool = 0 @@ -226,6 +190,7 @@ class CNN(): return pd_all def trian(self,patterns,datas_train, datas_teach, n_repeat, error_accuracy,draw_e = bool): + #model traning print('----------------------Start Training-------------------------') print(' - - Shape: Train_Data ',np.shape(datas_train)) print(' - - Shape: Teach_Data ',np.shape(datas_teach)) @@ -234,58 +199,53 @@ class CNN(): mse = 10000 while rp < n_repeat and mse >= error_accuracy: alle = 0 - print('-------------进行第%d次学习--------------'%rp) + print('-------------Learning Time %d--------------'%rp) for p in range(len(datas_train)): - #print('------------学习第%d个图像--------------'%p) + #print('------------Learning Image: %d--------------'%p) data_train = np.asmatrix(datas_train[p]) data_teach = np.asarray(datas_teach[p]) - data_focus1,data_conved1 = self.Convolute(data_train,self.conv1,self.w_conv1, + data_focus1,data_conved1 = self.convolute(data_train,self.conv1,self.w_conv1, self.thre_conv1,conv_step=self.step_conv1) - data_pooled1 = self.Pooling(data_conved1,self.size_pooling1) + data_pooled1 = self.pooling(data_conved1,self.size_pooling1) shape_featuremap1 = np.shape(data_conved1) ''' print(' -----original shape ', np.shape(data_train)) print(' ---- after convolution ',np.shape(data_conv1)) print(' -----after pooling ',np.shape(data_pooled1)) ''' - data_bp_input = self.Expand(data_pooled1) - # 计算第一层输入输出 + data_bp_input = self._expand(data_pooled1) bp_out1 = data_bp_input - # 计算第二层输入输出 + bp_net_j = np.dot(bp_out1,self.vji.T) - self.thre_bp2 bp_out2 = self.sig(bp_net_j) - # 计算第三层输入输出 bp_net_k = np.dot(bp_out2 ,self.wkj.T) - self.thre_bp3 bp_out3 = self.sig(bp_net_k) - # 计算一般化误差 + #--------------Model Leaning ------------------------ + # calcluate error and gradient--------------- pd_k_all = np.multiply((data_teach - bp_out3), np.multiply(bp_out3, (1 - bp_out3))) pd_j_all = np.multiply(np.dot(pd_k_all,self.wkj), np.multiply(bp_out2, (1 - bp_out2))) pd_i_all = np.dot(pd_j_all,self.vji) pd_conv1_pooled = pd_i_all / (self.size_pooling1*self.size_pooling1) pd_conv1_pooled = pd_conv1_pooled.T.getA().tolist() - pd_conv1_all = self.Getpd_From_Pool(data_conved1,pd_conv1_pooled,shape_featuremap1[0], + pd_conv1_all = self._calculate_gradient_from_pool(data_conved1,pd_conv1_pooled,shape_featuremap1[0], shape_featuremap1[1],self.size_pooling1) - - #卷积层1的权重和阈值修正，每个卷积核的权重需要修正 12*12(map) 次 - #修正量为featuremap中点的偏导值 乘以 前一层图像focus， 整个权重模板一起更新 + #weight and threshold learning process--------- + #convolution layer for k_conv in range(self.conv1[1]): - pd_conv_list = self.Expand_Mat(pd_conv1_all[k_conv]) + pd_conv_list = self._expand_mat(pd_conv1_all[k_conv]) delta_w = self.rate_weight * np.dot(pd_conv_list,data_focus1) self.w_conv1[k_conv] = self.w_conv1[k_conv] + delta_w.reshape((self.conv1[0],self.conv1[0])) self.thre_conv1[k_conv] = self.thre_conv1[k_conv] - np.sum(pd_conv1_all[k_conv]) * self.rate_thre - # 更新kj层的权重 - + #all connected layer self.wkj = self.wkj + pd_k_all.T * bp_out2 * self.rate_weight - # 更新ji层的权重 self.vji = self.vji + pd_j_all.T * bp_out1 * self.rate_weight - # 更新阈值 self.thre_bp3 = self.thre_bp3 - pd_k_all * self.rate_thre self.thre_bp2 = self.thre_bp2 - pd_j_all * self.rate_thre - # 计算总误差 + # calculate the sum error of all single image errors = np.sum(abs((data_teach - bp_out3))) alle = alle + errors #print(' ----Teach ',data_teach) @@ -307,24 +267,21 @@ class CNN(): draw_error() return mse - def produce(self,datas_test): - #对验证和测试数据集进行输出 + def predict(self,datas_test): + #model predict produce_out = [] print('-------------------Start Testing-------------------------') print(' - - Shape: Test_Data ',np.shape(datas_test)) for p in range(len(datas_test)): - print('--------测试第%d个图像----------' % p) data_test = np.asmatrix(datas_test[p]) - data_focus1, data_conved1 = self.Convolute(data_test, self.conv1, self.w_conv1, + data_focus1, data_conved1 = self.convolute(data_test, self.conv1, self.w_conv1, self.thre_conv1, conv_step=self.step_conv1) - data_pooled1 = self.Pooling(data_conved1, self.size_pooling1) - data_bp_input = self.Expand(data_pooled1) - # 计算第一层输入输出 + data_pooled1 = self.pooling(data_conved1, self.size_pooling1) + data_bp_input = self._expand(data_pooled1) + bp_out1 = data_bp_input - # 计算第二层输入输出 bp_net_j = bp_out1 * self.vji.T - self.thre_bp2 bp_out2 = self.sig(bp_net_j) - # 计算第三层输入输出 bp_net_k = bp_out2 * self.wkj.T - self.thre_bp3 bp_out3 = self.sig(bp_net_k) produce_out.extend(bp_out3.getA().tolist()) @@ -332,12 +289,17 @@ class CNN(): return np.asarray(res) def convolution(self,data): - #返回卷积和池化后的数据,用于查看图像 + #return the data of image after convoluting process so we can check it out data_test = np.asmatrix(data) - data_focus1, data_conved1 = self.Convolute(data_test, self.conv1, self.w_conv1, + data_focus1, data_conved1 = self.convolute(data_test, self.conv1, self.w_conv1, self.thre_conv1, conv_step=self.step_conv1) - data_pooled1 = self.Pooling(data_conved1, self.size_pooling1) + data_pooled1 = self.pooling(data_conved1, self.size_pooling1) return data_conved1,data_pooled1 +if __name__ == '__main__': + pass + ''' + I will put the example on other file + ''' \ No newline at end of file From 1958cf25c5e636e695a7cbed529a013f3a4704cd Mon Sep 17 00:00:00 2001 From: theycallmemac Date: Thu, 28 Sep 2017 20:54:15 +0100 Subject: [PATCH 08/73] added timsort.py --- sorts/timsort.py | 68 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 68 insertions(+) create mode 100644 sorts/timsort.py diff --git a/sorts/timsort.py b/sorts/timsort.py new file mode 100644 index 000000000..04360e256 --- /dev/null +++ b/sorts/timsort.py @@ -0,0 +1,68 @@ +def binary_search(the_array, item, start, end): + if start == end: + if the_array[start] > item: + return start + else: + return start + 1 + if start > end: + return start + + mid = (start + end)/ 2 + if the_array[mid] < item: + return binary_search(the_array, item, mid + 1, end) + elif the_array[mid] > item: + return binary_search(the_array, item, start, mid - 1) + else: + return mid + + +""" +Insertion sort that the heap sort uses if the array size is small or if +the size of the "run" is small +""" +def insertion_sort(the_array): + l = len(the_array) + for index in range(1, l): + value = the_array[index] + pos = binary_search(the_array, value, 0, index - 1) + the_array = the_array[:pos] + [value] + the_array[pos:index] + the_array[index+1:] + return the_array + +def merge(left, right): + """Takes two sorted lists and returns a single sorted list by comparing the + elements one at a time. + [1, 2, 3, 4, 5, 6] + """ + if not left: + return right + if not right: + return left + if left[0] < right[0]: + return [left[0]] + merge(left[1:], right) + return [right[0]] + merge(left, right[1:]) + + +def timsort(the_array): + runs, sorted_runs = [], [] + l = len(the_array) + new_run = [the_array[0]] + for i in range(1, l): + if i == l-1: + new_run.append(the_array[i]) + runs.append(new_run) + break + if the_array[i] < the_array[i-1]: + if not new_run: + runs.append([the_array[i-1]]) + new_run.append(the_array[i]) + else: + runs.append(new_run) + new_run = [] + else: + new_run.append(the_array[i]) + for each in runs: + sorted_runs.append(insertion_sort(each)) + sorted_array = [] + for run in sorted_runs: + sorted_array = merge(sorted_array, run) +print(sorted_array) From edcf6d54b6304d3e3bead3b1d2d7d14d04b70aab Mon Sep 17 00:00:00 2001 From: KuLi Date: Fri, 29 Sep 2017 23:47:24 +0200 Subject: [PATCH 09/73] #130 fixed radix sort for python 3 --- sorts/radix_sort.py | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/sorts/radix_sort.py b/sorts/radix_sort.py index 82f8a38b4..f19bc10e8 100644 --- a/sorts/radix_sort.py +++ b/sorts/radix_sort.py @@ -2,19 +2,19 @@ def radixsort(lst): RADIX = 10 maxLength = False tmp , placement = -1, 1 - + while not maxLength: maxLength = True # declare and initialize buckets buckets = [list() for _ in range( RADIX )] - + # split lst between lists for i in lst: - tmp = i / placement + tmp = i // placement buckets[tmp % RADIX].append( i ) if maxLength and tmp > 0: maxLength = False - + # empty lists into lst array a = 0 for b in range( RADIX ): @@ -22,6 +22,6 @@ def radixsort(lst): for i in buck: lst[a] = i a += 1 - + # move to next placement *= RADIX From 4d4b0ff31a88d13e42021687b8a0cd3e5db09d78 Mon Sep 17 00:00:00 2001 From: malikshubham827 Date: Sun, 1 Oct 2017 00:06:03 +0530 Subject: [PATCH 10/73] Added Dijkstra Algorithm --- data_structures/Graph/dijkstra_algorithm.py | 211 ++++++++++++++++++++ 1 file changed, 211 insertions(+) create mode 100644 data_structures/Graph/dijkstra_algorithm.py diff --git a/data_structures/Graph/dijkstra_algorithm.py b/data_structures/Graph/dijkstra_algorithm.py new file mode 100644 index 000000000..c43ff37f5 --- /dev/null +++ b/data_structures/Graph/dijkstra_algorithm.py @@ -0,0 +1,211 @@ +# Title: Dijkstra's Algorithm for finding single source shortest path from scratch +# Author: Shubham Malik +# References: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm + +import math +import sys +# For storing the vertex set to retreive node with the lowest distance + + +class PriorityQueue: + # Based on Min Heap + def __init__(self): + self.cur_size = 0 + self.array = [] + self.pos = {} # To store the pos of node in array + + def isEmpty(self): + return self.cur_size == 0 + + def min_heapify(self, idx): + lc = self.left(idx) + rc = self.right(idx) + if lc < self.cur_size and self.array(lc)[0] < self.array(idx)[0]: + smallest = lc + else: + smallest = idx + if rc < self.cur_size and self.array(rc)[0] < self.array(smallest)[0]: + smallest = rc + if smallest != idx: + self.swap(idx, smallest) + self.min_heapify(smallest) + + def insert(self, tup): + # Inserts a node into the Priority Queue + self.pos[tup[1]] = self.cur_size + self.cur_size += 1 + self.array.append((sys.maxsize, tup[1])) + self.decrease_key((sys.maxsize, tup[1]), tup[0]) + + def extract_min(self): + # Removes and returns the min element at top of priority queue + min_node = self.array[0][1] + self.array[0] = self.array[self.cur_size - 1] + self.cur_size -= 1 + self.min_heapify(1) + del self.pos[min_node] + return min_node + + def left(self, i): + # returns the index of left child + return 2 * i + 1 + + def right(self, i): + # returns the index of right child + return 2 * i + 2 + + def par(self, i): + # returns the index of parent + return math.floor(i / 2) + + def swap(self, i, j): + # swaps array elements at indices i and j + # update the pos{} + self.pos[self.array[i][1]] = j + self.pos[self.array[j][1]] = i + temp = self.array[i] + self.array[i] = self.array[j] + self.array[j] = temp + + def decrease_key(self, tup, new_d): + idx = self.pos[tup[1]] + # assuming the new_d is atmost old_d + self.array[idx] = (new_d, tup[1]) + while idx > 0 and self.array[self.par(idx)][0] > self.array[idx][0]: + self.swap(idx, self.par(idx)) + idx = self.par(idx) + + +class Graph: + def __init__(self, num): + self.adjList = {} # To store graph: u -> (v,w) + self.num_nodes = num # Number of nodes in graph + # To store the distance from source vertex + self.dist = [0] * self.num_nodes + self.par = [-1] * self.num_nodes # To store the path + + def add_edge(self, u, v, w): + # Edge going from node u to v and v to u with weight w + # u (w)-> v, v (w) -> u + # Check if u already in graph + if u in self.adjList.keys(): + self.adjList[u].append((v, w)) + else: + self.adjList[u] = [(v, w)] + + # Assuming undirected graph + if v in self.adjList.keys(): + self.adjList[v].append((u, w)) + else: + self.adjList[v] = [(u, w)] + + def show_graph(self): + # u -> v(w) + for u in self.adjList: + print(u, '->', ' -> '.join(str("{}({})".format(v, w)) + for v, w in self.adjList[u])) + + def dijkstra(self, src): + # Flush old junk values in par[] + self.par = [-1] * self.num_nodes + # src is the source node + self.dist[src] = 0 + Q = PriorityQueue() + Q.insert((0, src)) # (dist from src, node) + for u in self.adjList.keys(): + if u != src: + self.dist[u] = sys.maxsize # Infinity + self.par[u] = -1 + + while not Q.isEmpty(): + u = Q.extract_min() # Returns node with the min dist from source + # Update the distance of all the neighbours of u and + # if their prev dist was INFINITY then push them in Q + for v, w in self.adjList[u]: + new_dist = self.dist[u] + w + if self.dist[v] > new_dist: + if self.dist[v] == sys.maxsize: + Q.insert((new_dist, v)) + else: + Q.decrease_key((self.dist[v], v), new_dist) + self.dist[v] = new_dist + self.par[v] = u + + # Show the shortest distances from src + self.show_distances(src) + + def show_distances(self, src): + print("Distance from node: {}".format(src)) + for u in range(self.num_nodes): + print('Node {} has distance: {}'.format(u, self.dist[u])) + + def show_path(self, src, dest): + # To show the shortest path from src to dest + # WARNING: Use it *after* calling dijkstra + path = [] + cost = 0 + temp = dest + # Backtracking from dest to src + while self.par[temp] != -1: + path.append(temp) + if temp != src: + for v, w in self.adjList[temp]: + if v == self.par[temp]: + cost += w + break + temp = self.par[temp] + path.append(src) + path.reverse() + + print('----Path to reach {} from {}----'.format(dest, src)) + for u in path: + print('{}'.format(u), end=' ') + if u != dest: + print('-> ', end='') + + print('\nTotal cost of path: ', cost) + + +if __name__ == '__main__': + graph = Graph(9) + graph.add_edge(0, 1, 4) + graph.add_edge(0, 7, 8) + graph.add_edge(1, 2, 8) + graph.add_edge(1, 7, 11) + graph.add_edge(2, 3, 7) + graph.add_edge(2, 8, 2) + graph.add_edge(2, 5, 4) + graph.add_edge(3, 4, 9) + graph.add_edge(3, 5, 14) + graph.add_edge(4, 5, 10) + graph.add_edge(5, 6, 2) + graph.add_edge(6, 7, 1) + graph.add_edge(6, 8, 6) + graph.add_edge(7, 8, 7) + graph.show_graph() + graph.dijkstra(0) + graph.show_path(0, 4) + +# OUTPUT +# 0 -> 1(4) -> 7(8) +# 1 -> 0(4) -> 2(8) -> 7(11) +# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7) +# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4) +# 3 -> 2(7) -> 4(9) -> 5(14) +# 8 -> 2(2) -> 6(6) -> 7(7) +# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2) +# 4 -> 3(9) -> 5(10) +# 6 -> 5(2) -> 7(1) -> 8(6) +# Distance from node: 0 +# Node 0 has distance: 0 +# Node 1 has distance: 4 +# Node 2 has distance: 12 +# Node 3 has distance: 19 +# Node 4 has distance: 21 +# Node 5 has distance: 11 +# Node 6 has distance: 9 +# Node 7 has distance: 8 +# Node 8 has distance: 14 +# ----Path to reach 4 from 0---- +# 0 -> 7 -> 6 -> 5 -> 4 +# Total cost of path: 21 From 2480eacdcc5927933b9f2d6de8a9f93ecaa6687b Mon Sep 17 00:00:00 2001 From: Juan Antonio Date: Sun, 1 Oct 2017 14:50:45 +0200 Subject: [PATCH 11/73] Adding Euclidean GCD algorithm --- other/euclidean_gcd.py | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) create mode 100644 other/euclidean_gcd.py diff --git a/other/euclidean_gcd.py b/other/euclidean_gcd.py new file mode 100644 index 000000000..13378379f --- /dev/null +++ b/other/euclidean_gcd.py @@ -0,0 +1,18 @@ +# https://en.wikipedia.org/wiki/Euclidean_algorithm + +def euclidean_gcd(a, b): + while b: + t = b + b = a % b + a = t + return a + +def main(): + print("GCD(3, 5) = " + str(euclidean_gcd(3, 5))) + print("GCD(5, 3) = " + str(euclidean_gcd(5, 3))) + print("GCD(1, 3) = " + str(euclidean_gcd(1, 3))) + print("GCD(3, 6) = " + str(euclidean_gcd(3, 6))) + print("GCD(6, 3) = " + str(euclidean_gcd(6, 3))) + +if __name__ == '__main__': + main() From a97ab2f4e433e41a38fd28307a02f412c4fb3a01 Mon Sep 17 00:00:00 2001 From: James Mc Dermott Date: Sun, 1 Oct 2017 22:13:54 +0100 Subject: [PATCH 12/73] Update timsort.py --- sorts/timsort.py | 85 ++++++++++++++++++++++++++++-------------------- 1 file changed, 49 insertions(+), 36 deletions(-) diff --git a/sorts/timsort.py b/sorts/timsort.py index 04360e256..8c75b5191 100644 --- a/sorts/timsort.py +++ b/sorts/timsort.py @@ -1,68 +1,81 @@ -def binary_search(the_array, item, start, end): +def binary_search(lst, item, start, end): if start == end: - if the_array[start] > item: + if lst[start] > item: return start else: return start + 1 if start > end: return start - mid = (start + end)/ 2 - if the_array[mid] < item: - return binary_search(the_array, item, mid + 1, end) - elif the_array[mid] > item: - return binary_search(the_array, item, start, mid - 1) + mid = (start + end) // 2 + if lst[mid] < item: + return binary_search(lst, item, mid + 1, end) + elif lst[mid] > item: + return binary_search(lst, item, start, mid - 1) else: return mid -""" -Insertion sort that the heap sort uses if the array size is small or if -the size of the "run" is small -""" -def insertion_sort(the_array): - l = len(the_array) - for index in range(1, l): - value = the_array[index] - pos = binary_search(the_array, value, 0, index - 1) - the_array = the_array[:pos] + [value] + the_array[pos:index] + the_array[index+1:] - return the_array +def insertion_sort(lst): + length = len(lst) + + for index in range(1, length): + value = lst[index] + pos = binary_search(lst, value, 0, index - 1) + lst = lst[:pos] + [value] + lst[pos:index] + lst[index+1:] + + return lst + def merge(left, right): - """Takes two sorted lists and returns a single sorted list by comparing the - elements one at a time. - [1, 2, 3, 4, 5, 6] - """ if not left: return right + if not right: return left + if left[0] < right[0]: return [left[0]] + merge(left[1:], right) + return [right[0]] + merge(left, right[1:]) -def timsort(the_array): +def timsort(lst): runs, sorted_runs = [], [] - l = len(the_array) - new_run = [the_array[0]] - for i in range(1, l): - if i == l-1: - new_run.append(the_array[i]) + length = len(lst) + new_run = [lst[0]] + sorted_array = [] + + for i in range(1, length): + if i == length - 1: + new_run.append(lst[i]) runs.append(new_run) break - if the_array[i] < the_array[i-1]: + + if lst[i] < lst[i - 1]: if not new_run: - runs.append([the_array[i-1]]) - new_run.append(the_array[i]) + runs.append([lst[i - 1]]) + new_run.append(lst[i]) else: runs.append(new_run) new_run = [] else: - new_run.append(the_array[i]) - for each in runs: - sorted_runs.append(insertion_sort(each)) - sorted_array = [] + new_run.append(lst[i]) + + for run in runs: + sorted_runs.append(insertion_sort(run)) + for run in sorted_runs: sorted_array = merge(sorted_array, run) -print(sorted_array) + + return sorted_array + + +def main(): + + lst = [5,9,10,3,-4,5,178,92,46,-18,0,7] + sorted_lst = timsort(lst) + print(sorted_lst) + +if __name__ == '__main__': + main() From 6903d95b41206d757540f48230e245e7f28b8667 Mon Sep 17 00:00:00 2001 From: Rafael Leyva Ruiz Date: Mon, 2 Oct 2017 16:32:59 +0200 Subject: [PATCH 13/73] AVL done --- data_structures/AVL/AVL.py | 173 +++++++++++++------------------------ 1 file changed, 59 insertions(+), 114 deletions(-) diff --git a/data_structures/AVL/AVL.py b/data_structures/AVL/AVL.py index 0c34cb597..9717f1b6e 100644 --- a/data_structures/AVL/AVL.py +++ b/data_structures/AVL/AVL.py @@ -7,34 +7,42 @@ class Node: def __init__(self, label): self.label = label + self._parent = None + self._left = None + self._right = None self.height = 0 @property def right(self): - return self.right + return self._right @right.setter def right(self, node): - node.parent = self - self.right = node + if node is not None: + node._parent = self + self._right = node @property def left(self): - return self.left + return self._left @left.setter def left(self, node): - node.parent = self - self.left = node + if node is not None: + node._parent = self + self._left = node @property def parent(self): - return self.parent + return self._parent @parent.setter def parent(self, node): - self.parent = node - self.height = self.parent.height + 1 + if node is not None: + self._parent = node + self.height = self.parent.height + 1 + else: + self.height = 0 class AVL: @@ -45,7 +53,7 @@ class AVL: def insert(self, value): node = Node(value) - + if self.root is None: self.root = node self.root.height = 0 @@ -65,65 +73,72 @@ class AVL: else: curr_node = curr_node.right else: + node.height = dad_node.height + dad_node.height += 1 if node.label < dad_node.label: dad_node.left = node else: dad_node.right = node - - self.rebalance(dad_node) + self.rebalance(node) self.size += 1 break def rebalance(self, node): - height_right = 0 - height_left = 0 n = node + while n is not None: - height_right = 0 - height_left = 0 + height_right = n.height + height_left = n.height - if node.getRight() is not None: - height_right = node.getRight().getHeight() + if n.right is not None: + height_right = n.right.height - if node.getLeft() is not None: - height_left = node.getLeft().getHeight() + if n.left is not None: + height_left = n.left.height if abs(height_left - height_right) > 1: if height_left > height_right: - # left_child = node.getRight() - if (): + left_child = n.left + if left_child is not None: + h_right = (right_child.right.height + if (right_child.right is not None) else 0) + h_left = (right_child.left.height + if (right_child.left is not None) else 0) + if (h_left > h_right): self.rotate_left(n) break else: self.double_rotate_right(n) break else: - right_child = node.right + right_child = n.right if right_child is not None: h_right = (right_child.right.height if (right_child.right is not None) else 0) h_left = (right_child.left.height if (right_child.left is not None) else 0) - if (h_left > h_right): self.double_rotate_left(n) break else: self.rotate_right(n) break - n = n.getParent() + n = n.parent def rotate_left(self, node): - pass + aux = node.parent.label + node.parent.label = node.label + node.parent.right = Node(aux) + node.parent.right.height = node.parent.height + 1 + node.parent.left = node.right + def rotate_right(self, node): - aux = node.parent - node.parent = node - node.left = aux - - print(node.parent.label) - print(node.parent.right.label) - print(node.parent.left.label) + aux = node.parent.label + node.parent.label = node.label + node.parent.left = Node(aux) + node.parent.left.height = node.parent.height + 1 + node.parent.right = node.right def double_rotate_left(self, node): self.rotate_right(node.getRight().getRight()) @@ -140,96 +155,26 @@ class AVL: def preShow(self, curr_node): if curr_node is not None: - self.preShow(curr_node.getLeft()) - print(curr_node.getLabel(), end=" ") - self.preShow(curr_node.getRight()) + self.preShow(curr_node.left) + print(curr_node.label, end=" ") + self.preShow(curr_node.right) - def preorden(self, curr_node): + def preorder(self, curr_node): if curr_node is not None: - self.preShow(curr_node.getLeft()) - self.preShow(curr_node.getRight()) - print(curr_node.getLabel(), end=" ") + self.preShow(curr_node.left) + self.preShow(curr_node.right) + print(curr_node.label, end=" ") def getRoot(self): return self.root t = AVL() -# t.insert(1) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(2) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(3) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# print(t.getRoot().getHeight()) -# print(t.getRoot().getRight().getHeight()) t.insert(1) t.insert(2) t.insert(3) +# t.preShow(t.root) +# print("\n") # t.insert(4) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") # t.insert(5) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(6) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(7) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(8) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(9) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(10) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(11) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(12) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(13) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(14) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) -# print("\n") -# t.insert(15) -# t.preShow(t.getRoot()) -# print("\n") -# t.preorden(t.getRoot()) +# t.preShow(t.root) +# t.preorden(t.root) From 07fb7d695ac946ad1de8ebaa12df3c99dec331a8 Mon Sep 17 00:00:00 2001 From: Anurag Kumar Date: Mon, 2 Oct 2017 21:13:43 +0530 Subject: [PATCH 14/73] added k means clustering algorithm, usage doc inside. --- machine_learning/k_means_clust.py | 172 ++++++++++++++++++++++++++++++ 1 file changed, 172 insertions(+) create mode 100644 machine_learning/k_means_clust.py diff --git a/machine_learning/k_means_clust.py b/machine_learning/k_means_clust.py new file mode 100644 index 000000000..c19832726 --- /dev/null +++ b/machine_learning/k_means_clust.py @@ -0,0 +1,172 @@ +'''README, Author - Anurag Kumar(mailto:anuragkumarak95@gmail.com) + +Requirements: + - sklearn + - numpy + - matplotlib + +Python: + - 3.5 + +Inputs: + - X , a 2D numpy array of features. + - k , number of clusters to create. + - initial_centroids , initial centroid values generated by utility function(mentioned in usage). + - maxiter , maximum number of iterations to process. + - heterogeneity , empty list that will be filled with hetrogeneity values if passed to kmeans func. + +Usage: + 1. define 'k' value, 'X' features array and 'hetrogeneity' empty list + + 2. create initial_centroids, + initial_centroids = get_initial_centroids( + X, + k, + seed=0 # seed value for initial centroid generation, None for randomness(default=None) + ) + + 3. find centroids and clusters using kmeans function. + + centroids, cluster_assignment = kmeans( + X, + k, + initial_centroids, + maxiter=400, + record_heterogeneity=heterogeneity, + verbose=True # whether to print logs in console or not.(default=False) + ) + + + 4. Plot the loss function, hetrogeneity values for every iteration saved in hetrogeneity list. + plot_heterogeneity( + heterogeneity, + k + ) + + 5. Have fun.. + +''' +from sklearn.metrics import pairwise_distances +import numpy as np + +TAG = 'K-MEANS-CLUST/ ' + +def get_initial_centroids(data, k, seed=None): + '''Randomly choose k data points as initial centroids''' + if seed is not None: # useful for obtaining consistent results + np.random.seed(seed) + n = data.shape[0] # number of data points + + # Pick K indices from range [0, N). + rand_indices = np.random.randint(0, n, k) + + # Keep centroids as dense format, as many entries will be nonzero due to averaging. + # As long as at least one document in a cluster contains a word, + # it will carry a nonzero weight in the TF-IDF vector of the centroid. + centroids = data[rand_indices,:] + + return centroids + +def centroid_pairwise_dist(X,centroids): + return pairwise_distances(X,centroids,metric='euclidean') + +def assign_clusters(data, centroids): + + # Compute distances between each data point and the set of centroids: + # Fill in the blank (RHS only) + distances_from_centroids = centroid_pairwise_dist(data,centroids) + + # Compute cluster assignments for each data point: + # Fill in the blank (RHS only) + cluster_assignment = np.argmin(distances_from_centroids,axis=1) + + return cluster_assignment + +def revise_centroids(data, k, cluster_assignment): + new_centroids = [] + for i in range(k): + # Select all data points that belong to cluster i. Fill in the blank (RHS only) + member_data_points = data[cluster_assignment==i] + # Compute the mean of the data points. Fill in the blank (RHS only) + centroid = member_data_points.mean(axis=0) + new_centroids.append(centroid) + new_centroids = np.array(new_centroids) + + return new_centroids + +def compute_heterogeneity(data, k, centroids, cluster_assignment): + + heterogeneity = 0.0 + for i in range(k): + + # Select all data points that belong to cluster i. Fill in the blank (RHS only) + member_data_points = data[cluster_assignment==i, :] + + if member_data_points.shape[0] > 0: # check if i-th cluster is non-empty + # Compute distances from centroid to data points (RHS only) + distances = pairwise_distances(member_data_points, [centroids[i]], metric='euclidean') + squared_distances = distances**2 + heterogeneity += np.sum(squared_distances) + + return heterogeneity + +from matplotlib import pyplot as plt +def plot_heterogeneity(heterogeneity, k): + plt.figure(figsize=(7,4)) + plt.plot(heterogeneity, linewidth=4) + plt.xlabel('# Iterations') + plt.ylabel('Heterogeneity') + plt.title('Heterogeneity of clustering over time, K={0:d}'.format(k)) + plt.rcParams.update({'font.size': 16}) + plt.show() + +def kmeans(data, k, initial_centroids, maxiter=500, record_heterogeneity=None, verbose=False): + '''This function runs k-means on given data and initial set of centroids. + maxiter: maximum number of iterations to run.(default=500) + record_heterogeneity: (optional) a list, to store the history of heterogeneity as function of iterations + if None, do not store the history. + verbose: if True, print how many data points changed their cluster labels in each iteration''' + centroids = initial_centroids[:] + prev_cluster_assignment = None + + for itr in range(maxiter): + if verbose: + print(itr, end='') + + # 1. Make cluster assignments using nearest centroids + cluster_assignment = assign_clusters(data,centroids) + + # 2. Compute a new centroid for each of the k clusters, averaging all data points assigned to that cluster. + centroids = revise_centroids(data,k, cluster_assignment) + + # Check for convergence: if none of the assignments changed, stop + if prev_cluster_assignment is not None and \ + (prev_cluster_assignment==cluster_assignment).all(): + break + + # Print number of new assignments + if prev_cluster_assignment is not None: + num_changed = np.sum(prev_cluster_assignment!=cluster_assignment) + if verbose: + print(' {0:5d} elements changed their cluster assignment.'.format(num_changed)) + + # Record heterogeneity convergence metric + if record_heterogeneity is not None: + # YOUR CODE HERE + score = compute_heterogeneity(data,k,centroids,cluster_assignment) + record_heterogeneity.append(score) + + prev_cluster_assignment = cluster_assignment[:] + + return centroids, cluster_assignment + +# Mock test below +if False: # change to true to run this test case. + import sklearn.datasets as ds + dataset = ds.load_iris() + k = 3 + heterogeneity = [] + initial_centroids = get_initial_centroids(dataset['data'], k, seed=0) + centroids, cluster_assignment = kmeans(dataset['data'], k, initial_centroids, maxiter=400, + record_heterogeneity=heterogeneity, verbose=True) + plot_heterogeneity(heterogeneity, k) \ No newline at end of file From 9ba6426aad2fee8b4676da0e04079194d197485c Mon Sep 17 00:00:00 2001 From: rudrasohan Date: Tue, 3 Oct 2017 20:29:29 +0530 Subject: [PATCH 15/73] Added A* Algorithm --- Graphs/A*.py | 101 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 101 insertions(+) create mode 100644 Graphs/A*.py diff --git a/Graphs/A*.py b/Graphs/A*.py new file mode 100644 index 000000000..21f346225 --- /dev/null +++ b/Graphs/A*.py @@ -0,0 +1,101 @@ + +grid = [[0, 1, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0],#0 are free path whereas 1's are obstacles + [0, 1, 0, 0, 0, 0], + [0, 1, 0, 0, 1, 0], + [0, 0, 0, 0, 1, 0]] + +''' +heuristic = [[9, 8, 7, 6, 5, 4], + [8, 7, 6, 5, 4, 3], + [7, 6, 5, 4, 3, 2], + [6, 5, 4, 3, 2, 1], + [5, 4, 3, 2, 1, 0]]''' + +init = [0, 0] +goal = [len(grid)-1, len(grid[0])-1] +cost = 1 + +#the cost map which pushes the path closer to the goal +heuristic = [[0 for row in range(len(grid[0]))] for col in range(len(grid))] +for i in range(len(grid)): + for j in range(len(grid[0])): + heuristic[i][j] = abs(i - goal[0]) + abs(j - goal[1]) + if grid[i][j] == 1: + heuristic[i][j] = 99 #added extra penalty in the heuristic map + + +#the actions we can take +delta = [[-1, 0 ], # go up + [ 0, -1], # go left + [ 1, 0 ], # go down + [ 0, 1 ]] # go right + + +#function to search the path +def search(grid,init,goal,cost,heuristic): + + closed = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]# the referrence grid + closed[init[0]][init[1]] = 1 + action = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]#the action grid + + x = init[0] + y = init[1] + g = 0 + f = g + heuristic[init[0]][init[0]] + cell = [[f, g, x, y]] + + found = False # flag that is set when search is complete + resign = False # flag set if we can't find expand + + while not found and not resign: + if len(cell) == 0: + resign = True + return "FAIL" + else: + cell.sort()#to choose the least costliest action so as to move closer to the goal + cell.reverse() + next = cell.pop() + x = next[2] + y = next[3] + g = next[1] + f = next[0] + + + if x == goal[0] and y == goal[1]: + found = True + else: + for i in range(len(delta)):#to try out different valid actions + x2 = x + delta[i][0] + y2 = y + delta[i][1] + if x2 >= 0 and x2 < len(grid) and y2 >=0 and y2 < len(grid[0]): + if closed[x2][y2] == 0 and grid[x2][y2] == 0: + g2 = g + cost + f2 = g2 + heuristic[x2][y2] + cell.append([f2, g2, x2, y2]) + closed[x2][y2] = 1 + action[x2][y2] = i + invpath = [] + x = goal[0] + y = goal[1] + invpath.append([x, y])#we get the reverse path from here + while x != init[0] or y != init[1]: + x2 = x - delta[action[x][y]][0] + y2 = y - delta[action[x][y]][1] + x = x2 + y = y2 + invpath.append([x, y]) + + path = [] + for i in range(len(invpath)): + path.append(invpath[len(invpath) - 1 - i]) + print "ACTION MAP" + for i in range(len(action)): + print action[i] + + return path + +a = search(grid,init,goal,cost,heuristic) +for i in range(len(a)): + print a[i] + From 271cc48a2bf7057c1aaf24b792691e2d9e4a881e Mon Sep 17 00:00:00 2001 From: Sohan Rudra Date: Tue, 3 Oct 2017 21:10:34 +0530 Subject: [PATCH 16/73] Update A*.py --- Graphs/A*.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Graphs/A*.py b/Graphs/A*.py index 21f346225..2ca9476e5 100644 --- a/Graphs/A*.py +++ b/Graphs/A*.py @@ -13,7 +13,7 @@ heuristic = [[9, 8, 7, 6, 5, 4], [5, 4, 3, 2, 1, 0]]''' init = [0, 0] -goal = [len(grid)-1, len(grid[0])-1] +goal = [len(grid)-1, len(grid[0])-1] #all coordinates are given in format [y,x] cost = 1 #the cost map which pushes the path closer to the goal From 46b82fa249a0cb4811b3bfcbe99b68c32e33181f Mon Sep 17 00:00:00 2001 From: rajnishyadav321 Date: Thu, 5 Oct 2017 01:40:12 +0530 Subject: [PATCH 17/73] Added Next Greater Element Element NGE 4 --> 5 5 --> 25 2 --> 25 25 --> -1 --- data_structures/Stacks/next.py | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) create mode 100644 data_structures/Stacks/next.py diff --git a/data_structures/Stacks/next.py b/data_structures/Stacks/next.py new file mode 100644 index 000000000..9765900c0 --- /dev/null +++ b/data_structures/Stacks/next.py @@ -0,0 +1,16 @@ +# Function to print element and NGE pair for all elements of list +def printNGE(arr): + + for i in range(0, len(arr), 1): + + next = -1 + for j in range(i+1, len(arr), 1): + if arr[i] < arr[j]: + next = arr[j] + break + + print(str(arr[i]) + " -- " + str(next)) + +# Driver program to test above function +arr = [11,13,21,3] +printNGE(arr) From 17e1a92f499bb3d4f8ccabe084934f76d048a92a Mon Sep 17 00:00:00 2001 From: Chris McLennon Date: Thu, 5 Oct 2017 22:24:02 -0500 Subject: [PATCH 18/73] Refactor Stack --- .../Stacks/Balanced_Parentheses.py | 27 -------- .../Stacks/Infix_To_Postfix_Conversion.py | 48 ------------- data_structures/Stacks/Stack.py | 50 -------------- .../Stacks/balanced_parentheses.py | 21 ++++++ .../Stacks/infix_to_postfix_conversion.py | 62 +++++++++++++++++ data_structures/Stacks/stack.py | 68 +++++++++++++++++++ 6 files changed, 151 insertions(+), 125 deletions(-) delete mode 100644 data_structures/Stacks/Balanced_Parentheses.py delete mode 100644 data_structures/Stacks/Infix_To_Postfix_Conversion.py delete mode 100644 data_structures/Stacks/Stack.py create mode 100644 data_structures/Stacks/balanced_parentheses.py create mode 100644 data_structures/Stacks/infix_to_postfix_conversion.py create mode 100644 data_structures/Stacks/stack.py diff --git a/data_structures/Stacks/Balanced_Parentheses.py b/data_structures/Stacks/Balanced_Parentheses.py deleted file mode 100644 index 6b7740380..000000000 --- a/data_structures/Stacks/Balanced_Parentheses.py +++ /dev/null @@ -1,27 +0,0 @@ -# Author: OMKAR PATHAK - -import Stack - -def parseParenthesis(string): - balanced = 1 - index = 0 - myStack = Stack.Stack(len(string)) - while (index < len(string)) and (balanced == 1): - check = string[index] - if check == '(': - myStack.push(check) - else: - if myStack.isEmpty(): - balanced = 0 - else: - myStack.pop() - index += 1 - - if balanced == 1 and myStack.isEmpty(): - return True - else: - return False - -if __name__ == '__main__': - print(parseParenthesis('((()))')) # True - print(parseParenthesis('((())')) # False diff --git a/data_structures/Stacks/Infix_To_Postfix_Conversion.py b/data_structures/Stacks/Infix_To_Postfix_Conversion.py deleted file mode 100644 index e33926a3d..000000000 --- a/data_structures/Stacks/Infix_To_Postfix_Conversion.py +++ /dev/null @@ -1,48 +0,0 @@ -# Author: OMKAR PATHAK - -import Stack - -def isOperand(char): - return (ord(char) >= ord('a') and ord(char) <= ord('z')) or (ord(char) >= ord('A') and ord(char) <= ord('Z')) - -def precedence(char): - if char == '+' or char == '-': - return 1 - elif char == '*' or char == '/': - return 2 - elif char == '^': - return 3 - else: - return -1 - -def infixToPostfix(myExp, myStack): - postFix = [] - for i in range(len(myExp)): - if (isOperand(myExp[i])): - postFix.append(myExp[i]) - elif(myExp[i] == '('): - myStack.push(myExp[i]) - elif(myExp[i] == ')'): - topOperator = myStack.pop() - while(not myStack.isEmpty() and topOperator != '('): - postFix.append(topOperator) - topOperator = myStack.pop() - else: - while (not myStack.isEmpty()) and (precedence(myExp[i]) <= precedence(myStack.peek())): - postFix.append(myStack.pop()) - myStack.push(myExp[i]) - - while(not myStack.isEmpty()): - postFix.append(myStack.pop()) - return ' '.join(postFix) - -if __name__ == '__main__': - myExp = 'a+b*(c^d-e)^(f+g*h)-i' - myExp = [i for i in myExp] - print('Infix:',' '.join(myExp)) - myStack = Stack.Stack(len(myExp)) - print('Postfix:',infixToPostfix(myExp, myStack)) - - # OUTPUT: - # Infix: a + b * ( c ^ d - e ) ^ ( f + g * h ) - i - # Postfix: a b c d ^ e - f g h * + ^ * + i - diff --git a/data_structures/Stacks/Stack.py b/data_structures/Stacks/Stack.py deleted file mode 100644 index 41bbdc9d2..000000000 --- a/data_structures/Stacks/Stack.py +++ /dev/null @@ -1,50 +0,0 @@ -# Author: OMKAR PATHAK - -class Stack(object): - def __init__(self, limit = 10): - self.stack = [] - self.limit = limit - - # for printing the stack contents - def __str__(self): - return ' '.join([str(i) for i in self.stack]) - - # for pushing an element on to the stack - def push(self, data): - if len(self.stack) >= self.limit: - print('Stack Overflow') - else: - self.stack.append(data) - - # for popping the uppermost element - def pop(self): - if len(self.stack) <= 0: - return -1 - else: - return self.stack.pop() - - # for peeking the top-most element of the stack - def peek(self): - if len(self.stack) <= 0: - return -1 - else: - return self.stack[len(self.stack) - 1] - - # to check if stack is empty - def isEmpty(self): - return self.stack == [] - - # for checking the size of stack - def size(self): - return len(self.stack) - -if __name__ == '__main__': - myStack = Stack() - for i in range(10): - myStack.push(i) - print(myStack) - myStack.pop() # popping the top element - print(myStack) - myStack.peek() # printing the top element - myStack.isEmpty() - myStack.size() diff --git a/data_structures/Stacks/balanced_parentheses.py b/data_structures/Stacks/balanced_parentheses.py new file mode 100644 index 000000000..1c9a84843 --- /dev/null +++ b/data_structures/Stacks/balanced_parentheses.py @@ -0,0 +1,21 @@ +from Stack import Stack + +__author__ = 'Omkar Pathak' + + +def balanced_parentheses(parentheses): + """ Use a stack to check if a string of parentheses are balanced.""" + stack = Stack(len(parentheses)) + for parenthesis in parentheses: + if parenthesis == '(': + stack.push(parenthesis) + elif parenthesis == ')': + stack.pop() + return not stack.is_empty() + + +if __name__ == '__main__': + examples = ['((()))', '((())'] + print('Balanced parentheses demonstration:\n') + for example in examples: + print(example + ': ' + str(balanced_parentheses(example))) diff --git a/data_structures/Stacks/infix_to_postfix_conversion.py b/data_structures/Stacks/infix_to_postfix_conversion.py new file mode 100644 index 000000000..f0a8fd072 --- /dev/null +++ b/data_structures/Stacks/infix_to_postfix_conversion.py @@ -0,0 +1,62 @@ +import string + +from Stack import Stack + +__author__ = 'Omkar Pathak' + + +def is_operand(char): + return char in string.ascii_letters or char in string.digits + + +def precedence(char): + """ Return integer value representing an operator's precedence, or + order of operation. + + https://en.wikipedia.org/wiki/Order_of_operations + """ + dictionary = {'+': 1, '-': 1, + '*': 2, '/': 2, + '^': 3} + return dictionary.get(char, -1) + + +def infix_to_postfix(expression): + """ Convert infix notation to postfix notation using the Shunting-yard + algorithm. + + https://en.wikipedia.org/wiki/Shunting-yard_algorithm + https://en.wikipedia.org/wiki/Infix_notation + https://en.wikipedia.org/wiki/Reverse_Polish_notation + """ + stack = Stack(len(expression)) + postfix = [] + for char in expression: + if is_operand(char): + postfix.append(char) + elif char not in {'(', ')'}: + while (not stack.is_empty() + and precedence(char) <= precedence(stack.peek())): + postfix.append(stack.pop()) + stack.push(char) + elif char == '(': + stack.push(char) + elif char == ')': + while not stack.is_empty() and stack.peek() != '(': + postfix.append(stack.pop()) + # Pop '(' from stack. If there is no '(', there is a mismatched + # parentheses. + if stack.peek() != '(': + raise ValueError('Mismatched parentheses') + stack.pop() + while not stack.is_empty(): + postfix.append(stack.pop()) + return ' '.join(postfix) + + +if __name__ == '__main__': + expression = 'a+b*(c^d-e)^(f+g*h)-i' + + print('Infix to Postfix Notation demonstration:\n') + print('Infix notation: ' + expression) + print('Postfix notation: ' + infix_to_postfix(expression)) diff --git a/data_structures/Stacks/stack.py b/data_structures/Stacks/stack.py new file mode 100644 index 000000000..0b100abf3 --- /dev/null +++ b/data_structures/Stacks/stack.py @@ -0,0 +1,68 @@ +__author__ = 'Omkar Pathak' + + +class Stack(object): + """ A stack is an abstract data type that serves as a collection of + elements with two principal operations: push() and pop(). push() adds an + element to the top of the stack, and pop() removes an element from the top + of a stack. The order in which elements come off of a stack are + Last In, First Out (LIFO). + + https://en.wikipedia.org/wiki/Stack_(abstract_data_type) + """ + + def __init__(self, limit=10): + self.stack = [] + self.limit = limit + + def __bool__(self): + return not bool(self.stack) + + def __str__(self): + return str(self.stack) + + def push(self, data): + """ Push an element to the top of the stack.""" + if len(self.stack) >= self.limit: + raise StackOverflowError + self.stack.append(data) + + def pop(self): + """ Pop an element off of the top of the stack.""" + if self.stack: + return self.stack.pop() + else: + raise IndexError('pop from an empty stack') + + def peek(self): + """ Peek at the top-most element of the stack.""" + if self.stack: + return self.stack[-1] + + def is_empty(self): + """ Check if a stack is empty.""" + return not bool(self.stack) + + def size(self): + """ Return the size of the stack.""" + return len(self.stack) + + +class StackOverflowError(BaseException): + pass + + +if __name__ == '__main__': + stack = Stack() + for i in range(10): + stack.push(i) + + print('Stack demonstration:\n') + print('Initial stack: ' + str(stack)) + print('pop(): ' + str(stack.pop())) + print('After pop(), the stack is now: ' + str(stack)) + print('peek(): ' + str(stack.peek())) + stack.push(100) + print('After push(100), the stack is now: ' + str(stack)) + print('is_empty(): ' + str(stack.is_empty())) + print('size(): ' + str(stack.size())) From e8d0c7e54a2ea80fd42f482a5a80ac0dd2bffa2b Mon Sep 17 00:00:00 2001 From: aravindiiitb Date: Fri, 6 Oct 2017 12:11:19 +0530 Subject: [PATCH 19/73] Added Code in Dynamic Programming section for Longest Strictly Increasing Subsequence in O(nlogn) time --- ...longest_increasing_subsequence_O(nlogn).py | 40 +++++++++++++++++++ 1 file changed, 40 insertions(+) create mode 100644 dynamic_programming/longest_increasing_subsequence_O(nlogn).py diff --git a/dynamic_programming/longest_increasing_subsequence_O(nlogn).py b/dynamic_programming/longest_increasing_subsequence_O(nlogn).py new file mode 100644 index 000000000..3ebb4a137 --- /dev/null +++ b/dynamic_programming/longest_increasing_subsequence_O(nlogn).py @@ -0,0 +1,40 @@ +############################# +# Author: Aravind Kashyap +# File: lis.py +# comments: This programme outputs the Longest Strictly Increasing Subsequence in O(NLogN) +# Where N is the Number of elements in the list +############################# +def CeilIndex(v,l,r,key): + while r-l > 1: + m = (l + r)/2 + if v[m] >= key: + r = m + else: + l = m + + return r + + +def LongestIncreasingSubsequenceLength(v): + if(len(v) == 0): + return 0 + + tail = [0]*len(v) + length = 1 + + tail[0] = v[0] + + for i in range(1,len(v)): + if v[i] < tail[0]: + tail[0] = v[i] + elif v[i] > tail[length-1]: + tail[length] = v[i] + length += 1 + else: + tail[CeilIndex(tail,-1,length-1,v[i])] = v[i] + + return length + + +v = [2, 5, 3, 7, 11, 8, 10, 13, 6] +print LongestIncreasingSubsequenceLength(v) From 014786e340622f28cbd10dd901f1ce723cb20a19 Mon Sep 17 00:00:00 2001 From: KyleScharnhorst Date: Sat, 7 Oct 2017 06:47:50 -0700 Subject: [PATCH 20/73] Fix: typo in multiple files. --- dynamic_programming/fibonacci.py | 2 +- searches/binary_search.py | 2 +- searches/linear_search.py | 2 +- sorts/bogosort.py | 2 +- sorts/bubble_sort.py | 2 +- sorts/cocktail_shaker_sort.py | 2 +- sorts/gnome_sort.py | 2 +- sorts/insertion_sort.py | 2 +- sorts/merge_sort.py | 2 +- sorts/quick_sort.py | 2 +- sorts/selection_sort.py | 2 +- sorts/shell_sort.py | 2 +- traverals/binary_tree_traversals.py | 2 +- 13 files changed, 13 insertions(+), 13 deletions(-) diff --git a/dynamic_programming/fibonacci.py b/dynamic_programming/fibonacci.py index 692cb756a..5eaa81b3e 100644 --- a/dynamic_programming/fibonacci.py +++ b/dynamic_programming/fibonacci.py @@ -30,7 +30,7 @@ if __name__ == '__main__': import sys print("\n********* Fibonacci Series Using Dynamic Programming ************\n") - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/searches/binary_search.py b/searches/binary_search.py index 13b54f498..ce9584aa8 100644 --- a/searches/binary_search.py +++ b/searches/binary_search.py @@ -137,7 +137,7 @@ def __assert_sorted(collection): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/searches/linear_search.py b/searches/linear_search.py index 24479e45b..ce8098b1a 100644 --- a/searches/linear_search.py +++ b/searches/linear_search.py @@ -41,7 +41,7 @@ def linear_search(sequence, target): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/bogosort.py b/sorts/bogosort.py index 2512dab51..ce1982c53 100644 --- a/sorts/bogosort.py +++ b/sorts/bogosort.py @@ -41,7 +41,7 @@ def bogosort(collection): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/bubble_sort.py b/sorts/bubble_sort.py index 54d69e5ba..d26adc89c 100644 --- a/sorts/bubble_sort.py +++ b/sorts/bubble_sort.py @@ -41,7 +41,7 @@ def bubble_sort(collection): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/cocktail_shaker_sort.py b/sorts/cocktail_shaker_sort.py index a21224632..c09d64408 100644 --- a/sorts/cocktail_shaker_sort.py +++ b/sorts/cocktail_shaker_sort.py @@ -23,7 +23,7 @@ def cocktail_shaker_sort(unsorted): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/gnome_sort.py b/sorts/gnome_sort.py index b353e31aa..4f04ff384 100644 --- a/sorts/gnome_sort.py +++ b/sorts/gnome_sort.py @@ -21,7 +21,7 @@ def gnome_sort(unsorted): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/insertion_sort.py b/sorts/insertion_sort.py index caaa9305c..33bd27c8f 100644 --- a/sorts/insertion_sort.py +++ b/sorts/insertion_sort.py @@ -41,7 +41,7 @@ def insertion_sort(collection): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/merge_sort.py b/sorts/merge_sort.py index 92a678016..ca8dbc33c 100644 --- a/sorts/merge_sort.py +++ b/sorts/merge_sort.py @@ -64,7 +64,7 @@ def merge_sort(collection): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/quick_sort.py b/sorts/quick_sort.py index 8974e1bd8..52e37b587 100644 --- a/sorts/quick_sort.py +++ b/sorts/quick_sort.py @@ -42,7 +42,7 @@ def quick_sort(ARRAY): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/selection_sort.py b/sorts/selection_sort.py index 14bc80463..752496e98 100644 --- a/sorts/selection_sort.py +++ b/sorts/selection_sort.py @@ -44,7 +44,7 @@ def selection_sort(collection): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/sorts/shell_sort.py b/sorts/shell_sort.py index fdb98a570..de3d84f72 100644 --- a/sorts/shell_sort.py +++ b/sorts/shell_sort.py @@ -45,7 +45,7 @@ def shell_sort(collection): if __name__ == '__main__': import sys - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input diff --git a/traverals/binary_tree_traversals.py b/traverals/binary_tree_traversals.py index 9cf118899..9d14a1e7e 100644 --- a/traverals/binary_tree_traversals.py +++ b/traverals/binary_tree_traversals.py @@ -84,7 +84,7 @@ if __name__ == '__main__': import sys print("\n********* Binary Tree Traversals ************\n") - # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin # otherwise 2.x's input builtin function is too "smart" if sys.version_info.major < 3: input_function = raw_input From b695175da3d6abac684a5385f5036046bb86abf8 Mon Sep 17 00:00:00 2001 From: Chinmoy Das Date: Sun, 8 Oct 2017 12:42:13 +0530 Subject: [PATCH 21/73] binary exponentiation --- other/binary_exponentiation.java | 77 ++++++++++++++++++++++++++++++++ 1 file changed, 77 insertions(+) create mode 100644 other/binary_exponentiation.java diff --git a/other/binary_exponentiation.java b/other/binary_exponentiation.java new file mode 100644 index 000000000..56461fc81 --- /dev/null +++ b/other/binary_exponentiation.java @@ -0,0 +1,77 @@ +/** +* Binary Exponentiation +* This is a method to find a^b in a time complexity of O(log b) +* This is one of the most commonly used methods of finding powers. +* Also useful in cases where solution to (a^b)%c is required, +* where a,b,c can be numbers over the computers calculation limits. +*/ + +/** + * @author chinmoy159 + * @version 1.0 dated 10/08/2017 + */ +public class bin_expo +{ + /** + * function :- b_expo (int a, int b) + * returns a^b + */ + public static int b_expo(int a, int b) + { + /* + * iterative solution + */ + int res; + for (res = 1; b > 0; a *=a, b >>= 1) { + if ((b&1) == 1) { + res *= a; + } + } + return res; + /* + * recursive solution + if (b == 0) { + return 1; + } + if (b == 1) { + return a; + } + if ((b & 1) == 1) { + return a * b_expo(a*a, b >> 1); + } else { + return b_expo (a*a, b >> 1); + } + */ + } + /** + * function :- b_expo (long a, long b, long c) + * return (a^b)%c + */ + public static long b_expo(long a, long b, long c) + { + /* + * iterative solution + */ + long res; + for (res = 1l; b > 0; a *=a, b >>= 1) { + if ((b&1) == 1) { + res = ((res%c) * (a%c)) % c; + } + } + return res; + /* + * recursive solution + if (b == 0) { + return 1; + } + if (b == 1) { + return a; + } + if ((b & 1) == 1) { + return ((a%c) * (b_expo(a*a, b >> 1)%c))%c; + } else { + return b_expo (a*a, b >> 1)%c; + } + */ + } +} From 677dfe93bb25d5a4faed94ac90388c1bcd82228f Mon Sep 17 00:00:00 2001 From: Chinmoy Das Date: Sun, 8 Oct 2017 12:58:59 +0530 Subject: [PATCH 22/73] Delete binary_exponentiation.java --- other/binary_exponentiation.java | 77 -------------------------------- 1 file changed, 77 deletions(-) delete mode 100644 other/binary_exponentiation.java diff --git a/other/binary_exponentiation.java b/other/binary_exponentiation.java deleted file mode 100644 index 56461fc81..000000000 --- a/other/binary_exponentiation.java +++ /dev/null @@ -1,77 +0,0 @@ -/** -* Binary Exponentiation -* This is a method to find a^b in a time complexity of O(log b) -* This is one of the most commonly used methods of finding powers. -* Also useful in cases where solution to (a^b)%c is required, -* where a,b,c can be numbers over the computers calculation limits. -*/ - -/** - * @author chinmoy159 - * @version 1.0 dated 10/08/2017 - */ -public class bin_expo -{ - /** - * function :- b_expo (int a, int b) - * returns a^b - */ - public static int b_expo(int a, int b) - { - /* - * iterative solution - */ - int res; - for (res = 1; b > 0; a *=a, b >>= 1) { - if ((b&1) == 1) { - res *= a; - } - } - return res; - /* - * recursive solution - if (b == 0) { - return 1; - } - if (b == 1) { - return a; - } - if ((b & 1) == 1) { - return a * b_expo(a*a, b >> 1); - } else { - return b_expo (a*a, b >> 1); - } - */ - } - /** - * function :- b_expo (long a, long b, long c) - * return (a^b)%c - */ - public static long b_expo(long a, long b, long c) - { - /* - * iterative solution - */ - long res; - for (res = 1l; b > 0; a *=a, b >>= 1) { - if ((b&1) == 1) { - res = ((res%c) * (a%c)) % c; - } - } - return res; - /* - * recursive solution - if (b == 0) { - return 1; - } - if (b == 1) { - return a; - } - if ((b & 1) == 1) { - return ((a%c) * (b_expo(a*a, b >> 1)%c))%c; - } else { - return b_expo (a*a, b >> 1)%c; - } - */ - } -} From a36ca7c42f800ff24db287e72ab58f0230b4482c Mon Sep 17 00:00:00 2001 From: Chinmoy Das Date: Sun, 8 Oct 2017 12:59:18 +0530 Subject: [PATCH 23/73] Create binary_exponentiation.py --- other/binary_exponentiation.py | 49 ++++++++++++++++++++++++++++++++++ 1 file changed, 49 insertions(+) create mode 100644 other/binary_exponentiation.py diff --git a/other/binary_exponentiation.py b/other/binary_exponentiation.py new file mode 100644 index 000000000..57b218b55 --- /dev/null +++ b/other/binary_exponentiation.py @@ -0,0 +1,49 @@ +""" +* Binary Exponentiation +* This is a method to find a^b in a time complexity of O(log b) +* This is one of the most commonly used methods of finding powers. +* Also useful in cases where solution to (a^b)%c is required, +* where a,b,c can be numbers over the computers calculation limits. +* Done using iteration, can also be done using recursion + +* @author chinmoy159 +* @version 1.0 dated 10/08/2017 +""" + + +def b_expo(a, b): + res = 1 + while b > 0: + if b&1: + res *= a + + a *= a + b >>= 1 + + return res + + +def b_expo(a, b, c): + res = 1 + while b > 0: + if b&1: + res = ((res%c) * (a%c)) % c + + a *= a + b >>= 1 + + return res + +""" +* Wondering how this method works ! +* It's pretty simple. +* Let's say you need to calculate a ^ b +* RULE 1 : a ^ b = (a*a) ^ (b/2) ---- example : 4 ^ 4 = (4*4) ^ (4/2) = 16 ^ 2 +* RULE 2 : IF b is ODD, then ---- a ^ b = a * (a ^ (b - 1)) :: where (b - 1) is even. +* Once b is even, repeat the process to get a ^ b +* Repeat the process till b = 1 OR b = 0, because a^1 = a AND a^0 = 1 +* +* As far as the modulo is concerned, +* the fact : (a*b) % c = ((a%c) * (b%c)) % c +* Now apply RULE 1 OR 2 whichever is required. +""" From f4c6578ece43ef1ebcdfcab448c326f72a40763c Mon Sep 17 00:00:00 2001 From: Chinmoy Das Date: Sun, 8 Oct 2017 13:00:13 +0530 Subject: [PATCH 24/73] Binary Exponentiation for a^b --- other/binary_exponentiation.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/other/binary_exponentiation.py b/other/binary_exponentiation.py index 57b218b55..964a646f8 100644 --- a/other/binary_exponentiation.py +++ b/other/binary_exponentiation.py @@ -1,5 +1,5 @@ """ -* Binary Exponentiation +* Binary Exponentiation for Powers * This is a method to find a^b in a time complexity of O(log b) * This is one of the most commonly used methods of finding powers. * Also useful in cases where solution to (a^b)%c is required, From f5917f589c6fe27a642cbf94ef6e230a40ab18f0 Mon Sep 17 00:00:00 2001 From: Chinmoy Das Date: Sun, 8 Oct 2017 13:10:05 +0530 Subject: [PATCH 25/73] Binary Exponentiation for Multiplication --- other/binary_exponentiation_2.py | 50 ++++++++++++++++++++++++++++++++ 1 file changed, 50 insertions(+) create mode 100644 other/binary_exponentiation_2.py diff --git a/other/binary_exponentiation_2.py b/other/binary_exponentiation_2.py new file mode 100644 index 000000000..217a616c9 --- /dev/null +++ b/other/binary_exponentiation_2.py @@ -0,0 +1,50 @@ +""" +* Binary Exponentiation with Multiplication +* This is a method to find a*b in a time complexity of O(log b) +* This is one of the most commonly used methods of finding result of multiplication. +* Also useful in cases where solution to (a*b)%c is required, +* where a,b,c can be numbers over the computers calculation limits. +* Done using iteration, can also be done using recursion + +* @author chinmoy159 +* @version 1.0 dated 10/08/2017 +""" + + +def b_expo(a, b): + res = 0 + while b > 0: + if b&1: + res += a + + a += a + b >>= 1 + + return res + + +def b_expo_mod(a, b, c): + res = 0 + while b > 0: + if b&1: + res = ((res%c) + (a%c)) % c + + a += a + b >>= 1 + + return res + + +""" +* Wondering how this method works ! +* It's pretty simple. +* Let's say you need to calculate a ^ b +* RULE 1 : a * b = (a+a) * (b/2) ---- example : 4 * 4 = (4+4) * (4/2) = 8 * 2 +* RULE 2 : IF b is ODD, then ---- a * b = a + (a * (b - 1)) :: where (b - 1) is even. +* Once b is even, repeat the process to get a * b +* Repeat the process till b = 1 OR b = 0, because a*1 = a AND a*0 = 0 +* +* As far as the modulo is concerned, +* the fact : (a+b) % c = ((a%c) + (b%c)) % c +* Now apply RULE 1 OR 2, whichever is required. +""" From 0393c5ad38d66d19cc7366b4bafd62cd984b049d Mon Sep 17 00:00:00 2001 From: Chinmoy Das Date: Sun, 8 Oct 2017 13:12:33 +0530 Subject: [PATCH 26/73] Update binary_exponentiation.py --- other/binary_exponentiation.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/other/binary_exponentiation.py b/other/binary_exponentiation.py index 964a646f8..1a30fb8fd 100644 --- a/other/binary_exponentiation.py +++ b/other/binary_exponentiation.py @@ -23,7 +23,7 @@ def b_expo(a, b): return res -def b_expo(a, b, c): +def b_expo_mod(a, b, c): res = 1 while b > 0: if b&1: From 7447a9f9c7bdef4ceef3a93cee110525f683927d Mon Sep 17 00:00:00 2001 From: Uday Patel Date: Mon, 9 Oct 2017 03:19:39 +0100 Subject: [PATCH 27/73] Added Ternary Search Algorithm --- searches/ternary_search.py | 112 +++++++++++++++++++++++++++++++++++++ 1 file changed, 112 insertions(+) create mode 100644 searches/ternary_search.py diff --git a/searches/ternary_search.py b/searches/ternary_search.py new file mode 100644 index 000000000..3b1c75314 --- /dev/null +++ b/searches/ternary_search.py @@ -0,0 +1,112 @@ +''' +This is a type of divide and conquer algorithm which divides the search space into +3 parts and finds the target value based on the property of the array or list +(usually monotonic property). + +Time Complexity : O(log3 N) +Space Complexity : O(1) +''' + +import sys + +# This is the precision for this function which can be altered. +# It is recommended for users to keep this number greater than or equal to 10. +precision = 10 + +# This is the linear search that will occur after the search space has become smaller. +def lin_search(left, right, A, target): + for i in range(left, right+1): + if(A[i] == target): + return i + +# This is the iterative method of the ternary search algorithm. +def ite_ternary_search(A, target): + left = 0 + right = len(A) - 1; + while(True): + if(left Date: Tue, 10 Oct 2017 21:41:01 +0530 Subject: [PATCH 28/73] Added counting sort in python --- sorts/countingsort.py | 41 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 41 insertions(+) create mode 100644 sorts/countingsort.py diff --git a/sorts/countingsort.py b/sorts/countingsort.py new file mode 100644 index 000000000..c7b502d8f --- /dev/null +++ b/sorts/countingsort.py @@ -0,0 +1,41 @@ +# Python program for counting sort + +# This is the main function that sort the given string arr[] in +# in the alphabetical order +def countSort(arr): + + # The output character array that will have sorted arr + output = [0 for i in range(256)] + + # Create a count array to store count of inidividul + # characters and initialize count array as 0 + count = [0 for i in range(256)] + + # For storing the resulting answer since the + # string is immutable + ans = ["" for _ in arr] + + # Store count of each character + for i in arr: + count[ord(i)] += 1 + + # Change count[i] so that count[i] now contains actual + # position of this character in output array + for i in range(256): + count[i] += count[i-1] + + # Build the output character array + for i in range(len(arr)): + output[count[ord(arr[i])]-1] = arr[i] + count[ord(arr[i])] -= 1 + + # Copy the output array to arr, so that arr now + # contains sorted characters + for i in range(len(arr)): + ans[i] = output[i] + return ans + +# Driver program to test above function +arr = "thisisthestring" +ans = countSort(arr) +print ("Sorted string array is %s" %("".join(ans))) From 875c6cde16e21684b96ad5545c68ac1667b157bc Mon Sep 17 00:00:00 2001 From: Tobias Date: Tue, 10 Oct 2017 21:46:07 -0700 Subject: [PATCH 29/73] Add Linear Congruential Generator --- other/LinearCongruentialGenerator.py | 34 ++++++++++++++++++++++++++++ 1 file changed, 34 insertions(+) create mode 100644 other/LinearCongruentialGenerator.py diff --git a/other/LinearCongruentialGenerator.py b/other/LinearCongruentialGenerator.py new file mode 100644 index 000000000..b1eaa6119 --- /dev/null +++ b/other/LinearCongruentialGenerator.py @@ -0,0 +1,34 @@ +__author__ = "Tobias Carryer" + +from time import time + +class LinearCongruentialGenerator(object): + """ + A pseudorandom number generator. + """ + + def __init__( self, multiplier, increment, modulo, seed=int(time()) ): + """ + These parameters are saved and used when nextNumber() is called. + + modulo is the largest number that can be generated (exclusive). The most + efficent values are powers of 2. 2^32 is a common value. + """ + self.multiplier = multiplier + self.increment = increment + self.modulo = modulo + self.seed = seed + + def next_number( self ): + """ + The smallest number that can be generated is zero. + The largest number that can be generated is modulo-1. modulo is set in the constructor. + """ + self.seed = (self.multiplier * self.seed + self.increment) % self.modulo + return self.seed + +if __name__ == "__main__": + # Show the LCG in action. + lcg = LinearCongruentialGenerator(1664525, 1013904223, 2<<31) + while True : + print lcg.next_number() \ No newline at end of file From aac224dc1b0c968ed52ab1d14332c4d9742f5d71 Mon Sep 17 00:00:00 2001 From: Sayan Bandyopadhyay Date: Thu, 12 Oct 2017 01:28:12 +0530 Subject: [PATCH 30/73] Update radix_sort.py This will fix the error in the list index showing as float --- sorts/radix_sort.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/sorts/radix_sort.py b/sorts/radix_sort.py index 82f8a38b4..29b51ad42 100644 --- a/sorts/radix_sort.py +++ b/sorts/radix_sort.py @@ -9,9 +9,9 @@ def radixsort(lst): buckets = [list() for _ in range( RADIX )] # split lst between lists - for i in lst: - tmp = i / placement - buckets[tmp % RADIX].append( i ) + for i in lst: + tmp = int((i / placement) % RADIX) + buckets[tmp].append(i) if maxLength and tmp > 0: maxLength = False From a07baadf04d3b1db9051f2ed2353abc83b35a732 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Kilian=20Rue=C3=9F?= Date: Thu, 12 Oct 2017 21:35:23 +0200 Subject: [PATCH 31/73] Added fastfibonacci.py --- dynamic_programming/fastfibonacci.py | 42 ++++++++++++++++++++++++++++ 1 file changed, 42 insertions(+) create mode 100644 dynamic_programming/fastfibonacci.py diff --git a/dynamic_programming/fastfibonacci.py b/dynamic_programming/fastfibonacci.py new file mode 100644 index 000000000..5957fbe0d --- /dev/null +++ b/dynamic_programming/fastfibonacci.py @@ -0,0 +1,42 @@ +""" +This program calculates the nth Fibonacci number in O(log(n)). +It's possible to calculate F(1000000) in less than a second. +""" +import sys + + +# returns F(n) +def fibonacci(n: int): + if n < 0: + raise ValueError("Negative arguments are not supported") + return _fib(n)[0] + + +# returns (F(n), F(n-1)) +def _fib(n: int): + if n == 0: + # (F(0), F(1)) + return (0, 1) + else: + # F(2n) = F(n)[2F(n+1) − F(n)] + # F(2n+1) = F(n+1)^2+F(n)^2 + a, b = _fib(n // 2) + c = a * (b * 2 - a) + d = a * a + b * b + if n % 2 == 0: + return (c, d) + else: + return (d, c + d) + + +if __name__ == "__main__": + args = sys.argv[1:] + if len(args) != 1: + print("Too few or too much parameters given.") + exit(1) + try: + n = int(args[0]) + except ValueError: + print("Could not convert data to an integer.") + exit(1) + print("F(%d) = %d" % (n, fibonacci(n))) From 86a5b0345fdbdf9931f00a26d80c61f6cf23c957 Mon Sep 17 00:00:00 2001 From: Corey Hu Date: Thu, 12 Oct 2017 23:56:14 -0700 Subject: [PATCH 32/73] Recursive solution to insert_tail in singly_LinkedList --- .../LinkedList/singly_LinkedList.py | 37 +++++++------------ 1 file changed, 13 insertions(+), 24 deletions(-) diff --git a/data_structures/LinkedList/singly_LinkedList.py b/data_structures/LinkedList/singly_LinkedList.py index 941e8a0fa..c9a3cec27 100644 --- a/data_structures/LinkedList/singly_LinkedList.py +++ b/data_structures/LinkedList/singly_LinkedList.py @@ -3,22 +3,15 @@ class Node:#create a Node self.data=data#given data self.next=None#given next to None class Linked_List: + pass - def insert_tail(Head,data):#insert the data at tail - tamp=Head#create a tamp as a head - if(tamp==None):#if linkedlist is empty - newNod=Node()#create newNode Node type and given data and next - newNod.data=data - newNod.next=None - Head=newNod + + def insert_tail(Head,data): + if(Head.next is None): + Head.next = Node(data) else: - while tamp.next!=None:#find the last Node - tamp=tamp.next - newNod = Node()#create a new node - newNod.data = data - newNod.next = None - tamp.next=newNod#put the newnode into last node - return Head#return first node of linked list + insert_tail(Head.next, data) + def insert_head(Head,data): tamp = Head if (tamp == None): @@ -32,16 +25,18 @@ class Linked_List: newNod.next = Head#put the Head at NewNode Next Head=newNod#make a NewNode to Head return Head - def Print(Head):#print every node data - tamp=Node() + + def printList(Head):#print every node data tamp=Head while tamp!=None: print(tamp.data) tamp=tamp.next + def delete_head(Head):#delete from head if Head!=None: Head=Head.next return Head#return new Head + def delete_tail(Head):#delete from tail if Head!=None: tamp = Node() @@ -50,12 +45,6 @@ class Linked_List: tamp = tamp.next tamp.next=None#delete the last element by give next None to 2nd last Element return Head + def isEmpty(Head): - if(Head==None):#check Head is None or Not - return True#return Ture if list is empty - else: - return False#check False if it's not empty - - - - + return Head is None #Return if Head is none \ No newline at end of file From e0211794da527caaa0e3621fa4a8ae60eed3c547 Mon Sep 17 00:00:00 2001 From: nandujkishor Date: Fri, 13 Oct 2017 20:33:40 +0530 Subject: [PATCH 33/73] Changed the typographical error (#132) Changed the typo in line 113 and 115 regarding recursive binary search algorithm, found by a user who commented in comments. --- searches/binary_search.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/searches/binary_search.py b/searches/binary_search.py index 8dc3008da..5ef0a0321 100644 --- a/searches/binary_search.py +++ b/searches/binary_search.py @@ -113,7 +113,7 @@ def binary_search_by_recursion(sorted_collection, item, left, right): return binary_search_by_recursion(sorted_collection, item, left, midpoint-1) else: return binary_search_by_recursion(sorted_collection, item, midpoint+1, right) - + def __assert_sorted(collection): """Check if collection is sorted, if not - raises :py:class:`ValueError` From 81ab3249d418396a3f7e8d35514e9fe8c9bb412b Mon Sep 17 00:00:00 2001 From: Sachin Arora Date: Fri, 13 Oct 2017 20:45:39 +0530 Subject: [PATCH 34/73] Revert "There were 2 codes for BFS and DFS in data-structure/Graph." (#163) --- .../Graph/P01_BreadthFirstSearch.py | 61 +++++++++++++++++++ data_structures/Graph/P02_DepthFirstSearch.py | 61 +++++++++++++++++++ 2 files changed, 122 insertions(+) create mode 100644 data_structures/Graph/P01_BreadthFirstSearch.py create mode 100644 data_structures/Graph/P02_DepthFirstSearch.py diff --git a/data_structures/Graph/P01_BreadthFirstSearch.py b/data_structures/Graph/P01_BreadthFirstSearch.py new file mode 100644 index 000000000..16b1b2007 --- /dev/null +++ b/data_structures/Graph/P01_BreadthFirstSearch.py @@ -0,0 +1,61 @@ +# Author: OMKAR PATHAK + +class Graph(): + def __init__(self): + self.vertex = {} + + # for printing the Graph vertexes + def printGraph(self): + for i in self.vertex.keys(): + print(i,' -> ', ' -> '.join([str(j) for j in self.vertex[i]])) + + # for adding the edge beween two vertexes + def addEdge(self, fromVertex, toVertex): + # check if vertex is already present, + if fromVertex in self.vertex.keys(): + self.vertex[fromVertex].append(toVertex) + else: + # else make a new vertex + self.vertex[fromVertex] = [toVertex] + + def BFS(self, startVertex): + # Take a list for stoting already visited vertexes + visited = [False] * len(self.vertex) + + # create a list to store all the vertexes for BFS + queue = [] + + # mark the source node as visited and enqueue it + visited[startVertex] = True + queue.append(startVertex) + + while queue: + startVertex = queue.pop(0) + print(startVertex, end = ' ') + + # mark all adjacent nodes as visited and print them + for i in self.vertex[startVertex]: + if visited[i] == False: + queue.append(i) + visited[i] = True + +if __name__ == '__main__': + g = Graph() + g.addEdge(0, 1) + g.addEdge(0, 2) + g.addEdge(1, 2) + g.addEdge(2, 0) + g.addEdge(2, 3) + g.addEdge(3, 3) + + g.printGraph() + print('BFS:') + g.BFS(2) + + # OUTPUT: + # 0  ->  1 -> 2 + # 1  ->  2 + # 2  ->  0 -> 3 + # 3  ->  3 + # BFS: + # 2 0 3 1 diff --git a/data_structures/Graph/P02_DepthFirstSearch.py b/data_structures/Graph/P02_DepthFirstSearch.py new file mode 100644 index 000000000..94ef3cb86 --- /dev/null +++ b/data_structures/Graph/P02_DepthFirstSearch.py @@ -0,0 +1,61 @@ +# Author: OMKAR PATHAK + +class Graph(): + def __init__(self): + self.vertex = {} + + # for printing the Graph vertexes + def printGraph(self): + print(self.vertex) + for i in self.vertex.keys(): + print(i,' -> ', ' -> '.join([str(j) for j in self.vertex[i]])) + + # for adding the edge beween two vertexes + def addEdge(self, fromVertex, toVertex): + # check if vertex is already present, + if fromVertex in self.vertex.keys(): + self.vertex[fromVertex].append(toVertex) + else: + # else make a new vertex + self.vertex[fromVertex] = [toVertex] + + def DFS(self): + # visited array for storing already visited nodes + visited = [False] * len(self.vertex) + + # call the recursive helper function + for i in range(len(self.vertex)): + if visited[i] == False: + self.DFSRec(i, visited) + + def DFSRec(self, startVertex, visited): + # mark start vertex as visited + visited[startVertex] = True + + print(startVertex, end = ' ') + + # Recur for all the vertexes that are adjacent to this node + for i in self.vertex.keys(): + if visited[i] == False: + self.DFSRec(i, visited) + +if __name__ == '__main__': + g = Graph() + g.addEdge(0, 1) + g.addEdge(0, 2) + g.addEdge(1, 2) + g.addEdge(2, 0) + g.addEdge(2, 3) + g.addEdge(3, 3) + + g.printGraph() + print('DFS:') + g.DFS() + + # OUTPUT: + # 0  ->  1 -> 2 + # 1  ->  2 + # 2  ->  0 -> 3 + # 3  ->  3 + # DFS: + # 0 1 2 3 From 974acef310bc70dc634b651d9e8ea502ae09ad04 Mon Sep 17 00:00:00 2001 From: Sachin Arora Date: Fri, 13 Oct 2017 21:03:16 +0530 Subject: [PATCH 35/73] Deleting duplicate BFS and DFS files. (#164) * Deleting duplicate file BFS. * deleting duplicate file DFS. * Rename P01_BreadthFirstSearch.py to BreadthFirstSearch.py * Rename P02_DepthFirstSearch.py to DepthFirstSearch.py --- ...thFirstSearch.py => BreadthFirstSearch.py} | 0 data_structures/Graph/Breadth_First_Search.py | 72 ------------------- data_structures/Graph/Deep_First_Search.py | 32 --------- ...epthFirstSearch.py => DepthFirstSearch.py} | 0 4 files changed, 104 deletions(-) rename data_structures/Graph/{P01_BreadthFirstSearch.py => BreadthFirstSearch.py} (100%) delete mode 100644 data_structures/Graph/Breadth_First_Search.py delete mode 100644 data_structures/Graph/Deep_First_Search.py rename data_structures/Graph/{P02_DepthFirstSearch.py => DepthFirstSearch.py} (100%) diff --git a/data_structures/Graph/P01_BreadthFirstSearch.py b/data_structures/Graph/BreadthFirstSearch.py similarity index 100% rename from data_structures/Graph/P01_BreadthFirstSearch.py rename to data_structures/Graph/BreadthFirstSearch.py diff --git a/data_structures/Graph/Breadth_First_Search.py b/data_structures/Graph/Breadth_First_Search.py deleted file mode 100644 index 92a6e819b..000000000 --- a/data_structures/Graph/Breadth_First_Search.py +++ /dev/null @@ -1,72 +0,0 @@ -class GRAPH: - """docstring for GRAPH""" - def __init__(self, nodes): - self.nodes = nodes - self.graph = [[0]*nodes for i in range (nodes)] - self.visited = [0]*nodes - - - def show(self): - - for i in self.graph: - for j in i: - print(j, end=' ') - print(' ') - def bfs(self,v): - - visited = [False]*self.vertex - visited[v - 1] = True - print('%d visited' % (v)) - - queue = [v - 1] - while len(queue) > 0: - v = queue[0] - for u in range(self.vertex): - if self.graph[v][u] == 1: - if visited[u] is False: - visited[u] = True - queue.append(u) - print('%d visited' % (u +1)) - queue.pop(0) - -g = Graph(10) - -g.add_edge(1,2) -g.add_edge(1,3) -g.add_edge(1,4) -g.add_edge(2,5) -g.add_edge(3,6) -g.add_edge(3,7) -g.add_edge(4,8) -g.add_edge(5,9) -g.add_edge(6,10) -g.bfs(4) - -print(self.graph) - - def add_edge(self, i, j): - self.graph[i][j]=1 - self.graph[j][i]=1 - - def bfs(self, s): - queue = [s] - self.visited[s] = 1 - while len(queue)!= 0: - x = queue.pop(0) - print(x) - for i in range(0, self.nodes): - if self.graph[x][i] == 1 and self.visited[i] == 0: - queue.append(i) - self.visited[i] = 1 - -n = int(input("Enter the number of Nodes : ")) -g = GRAPH(n) -e = int(input("Enter the no of edges : ")) -print("Enter the edges (u v)") - -for i in range(0, e): - u ,v = map(int, raw_input().split()) - g.add_edge(u, v) - -s = int(input("Enter the source node :")) -g.bfs(s) diff --git a/data_structures/Graph/Deep_First_Search.py b/data_structures/Graph/Deep_First_Search.py deleted file mode 100644 index 656ddfbaf..000000000 --- a/data_structures/Graph/Deep_First_Search.py +++ /dev/null @@ -1,32 +0,0 @@ -class GRAPH: - """docstring for GRAPH""" - def __init__(self, nodes): - self.nodes=nodes - self.graph=[[0]*nodes for i in range (nodes)] - self.visited=[0]*nodes - - - def show(self): - print self.graph - - def add_edge(self, i, j): - self.graph[i][j]=1 - self.graph[j][i]=1 - - def dfs(self,s): - self.visited[s]=1 - print(s) - for i in range(0,self.nodes): - if self.visited[i]==0 and self.graph[s][i]==1: - self.dfs(i) - - -n=int(input("Enter the number of Nodes : ")) -g=GRAPH(n) -e=int(input("Enter the no of edges : ")) -print("Enter the edges (u v)") -for i in range(0,e): - u,v=map(int, raw_input().split()) - g.add_edge(u,v) -s=int(input("Enter the source node :")) -g.dfs(s) diff --git a/data_structures/Graph/P02_DepthFirstSearch.py b/data_structures/Graph/DepthFirstSearch.py similarity index 100% rename from data_structures/Graph/P02_DepthFirstSearch.py rename to data_structures/Graph/DepthFirstSearch.py From 35d38737168ebfe4eb54e829f98dc31296aa52dd Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andr=C3=A9=20Almeida?= Date: Sat, 14 Oct 2017 03:07:02 +0000 Subject: [PATCH 36/73] Add counting sort --- sorts/counting_sort.py | 72 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 72 insertions(+) create mode 100644 sorts/counting_sort.py diff --git a/sorts/counting_sort.py b/sorts/counting_sort.py new file mode 100644 index 000000000..13e4554ae --- /dev/null +++ b/sorts/counting_sort.py @@ -0,0 +1,72 @@ +""" +This is pure python implementation of counting sort algorithm +For doctests run following command: +python -m doctest -v counting_sort.py +or +python3 -m doctest -v counting_sort.py +For manual testing run: +python counting_sort.py +""" + +from __future__ import print_function + + +def counting_sort(collection): + """Pure implementation of counting sort algorithm in Python + :param collection: some mutable ordered collection with heterogeneous + comparable items inside + :return: the same collection ordered by ascending + Examples: + >>> counting_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + >>> counting_sort([]) + [] + >>> counting_sort([-2, -5, -45]) + [-45, -5, -2] + """ + # if the collection is empty, returns empty + if collection == []: + return [] + + # get some information about the collection + coll_len = len(collection) + coll_max = max(collection) + coll_min = min(collection) + + # create the counting array + counting_arr_length = coll_max + 1 - coll_min + counting_arr = [0] * counting_arr_length + + # count how much a number appears in the collection + for number in collection: + counting_arr[number - coll_min] += 1 + + # sum each position with it's predecessors. now, counting_arr[i] tells + # us how many elements <= i has in the collection + for i in range(1, counting_arr_length): + counting_arr[i] = counting_arr[i] + counting_arr[i-1] + + # create the output collection + ordered = [0] * coll_len + + # place the elements in the output, respecting the original order (stable + # sort) from end to begin, updating counting_arr + for i in reversed(range(0, coll_len)): + ordered[counting_arr[collection[i] - coll_min]-1] = collection[i] + counting_arr[collection[i] - coll_min] -= 1 + + return ordered + + +if __name__ == '__main__': + import sys + # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + print(counting_sort(unsorted)) From eb8375d13801eb812a76aa689b062a4d66d410ea Mon Sep 17 00:00:00 2001 From: Harshil Date: Sat, 14 Oct 2017 09:54:52 +0530 Subject: [PATCH 37/73] Commented travis tag Commented travis tag untill we find suitable travis.yml --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 9589bccd9..d77e17e75 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,4 @@ -# The Algorithms - Python [![Build Status](https://travis-ci.org/TheAlgorithms/Python.svg)](https://travis-ci.org/TheAlgorithms/Python) +# The Algorithms - Python ### All algorithms implemented in Python (for education) From d7fccf50690f84e0e3072b3c0fc7e159031078e8 Mon Sep 17 00:00:00 2001 From: yeggasd Date: Sun, 15 Oct 2017 00:44:53 +0800 Subject: [PATCH 38/73] Updated README.md Added Vigenere Cipher description --- README.md | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/README.md b/README.md index d77e17e75..70077e98f 100644 --- a/README.md +++ b/README.md @@ -128,6 +128,13 @@ The method is named after **Julius Caesar**, who used it in his private correspo The encryption step performed by a Caesar cipher is often incorporated as part of more complex schemes, such as the Vigenère cipher, and still has modern application in the ROT13 system. As with all single-alphabet substitution ciphers, the Caesar cipher is easily broken and in modern practice offers essentially no communication security. ###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Caesar_cipher) +### Vigenère +The **Vigenère cipher** is a method of encrypting alphabetic text by using a series of **interwoven Caesar ciphers** based on the letters of a keyword. It is **a form of polyalphabetic substitution**.
+The Vigenère cipher has been reinvented many times. The method was originally described by Giovan Battista Bellaso in his 1553 book La cifra del. Sig. Giovan Battista Bellaso; however, the scheme was later misattributed to Blaise de Vigenère in the 19th century, and is now widely known as the "Vigenère cipher".
+Though the cipher is easy to understand and implement, for three centuries it resisted all attempts to break it; this earned it the description **le chiffre indéchiffrable**(French for 'the indecipherable cipher'). +Many people have tried to implement encryption schemes that are essentially Vigenère ciphers. Friedrich Kasiski was the first to publish a general method of deciphering a Vigenère cipher in 1863. +###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher) + ### Transposition In cryptography, a **transposition cipher** is a method of encryption by which the positions held by units of plaintext (which are commonly characters or groups of characters) are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext. That is, the order of the units is changed (the plaintext is reordered).
Mathematically a bijective function is used on the characters' positions to encrypt and an inverse function to decrypt. From d70b9268fe2d05f5ff6197b957b98f935fb13e91 Mon Sep 17 00:00:00 2001 From: Sarbajit Saha Date: Sun, 15 Oct 2017 21:25:54 +0530 Subject: [PATCH 39/73] fixed spelling of coma to comma --- searches/binary_search.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/searches/binary_search.py b/searches/binary_search.py index 340649e4f..c54aa96a1 100644 --- a/searches/binary_search.py +++ b/searches/binary_search.py @@ -144,7 +144,7 @@ if __name__ == '__main__': else: input_function = input - user_input = input_function('Enter numbers separated by coma:\n') + user_input = input_function('Enter numbers separated by comma:\n') collection = [int(item) for item in user_input.split(',')] try: __assert_sorted(collection) From 6d192700c686a9d432c7ec0369fcc0cacb5875bd Mon Sep 17 00:00:00 2001 From: Sarbajit Saha Date: Sun, 15 Oct 2017 21:41:10 +0530 Subject: [PATCH 40/73] added interpolation search --- searches/interpolation_search.py | 102 +++++++++++++++++++++++++++++++ 1 file changed, 102 insertions(+) create mode 100644 searches/interpolation_search.py diff --git a/searches/interpolation_search.py b/searches/interpolation_search.py new file mode 100644 index 000000000..068d9c554 --- /dev/null +++ b/searches/interpolation_search.py @@ -0,0 +1,102 @@ +""" +This is pure python implementation of interpolation search algorithm +""" +from __future__ import print_function +import bisect + + +def interpolation_search(sorted_collection, item): + """Pure implementation of interpolation search algorithm in Python + Be careful collection must be sorted, otherwise result will be + unpredictable + :param sorted_collection: some sorted collection with comparable items + :param item: item value to search + :return: index of found item or None if item is not found + """ + left = 0 + right = len(sorted_collection) - 1 + + while left <= right: + point = left + ((item - sorted_collection[left]) * (right - left)) // (sorted_collection[right] - sorted_collection[left]) + + #out of range check + if point<0 or point>=len(sorted_collection): + return None + + current_item = sorted_collection[point] + if current_item == item: + return point + else: + if item < current_item: + right = point - 1 + else: + left = point + 1 + return None + + +def interpolation_search_by_recursion(sorted_collection, item, left, right): + + """Pure implementation of interpolation search algorithm in Python by recursion + Be careful collection must be sorted, otherwise result will be + unpredictable + First recursion should be started with left=0 and right=(len(sorted_collection)-1) + :param sorted_collection: some sorted collection with comparable items + :param item: item value to search + :return: index of found item or None if item is not found + """ + point = left + ((item - sorted_collection[left]) * (right - left)) // (sorted_collection[right] - sorted_collection[left]) + + #out of range check + if point<0 or point>=len(sorted_collection): + return None + + if sorted_collection[point] == item: + return point + elif sorted_collection[point] > item: + return interpolation_search_by_recursion(sorted_collection, item, left, point-1) + else: + return interpolation_search_by_recursion(sorted_collection, item, point+1, right) + +def __assert_sorted(collection): + """Check if collection is sorted, if not - raises :py:class:`ValueError` + :param collection: collection + :return: True if collection is sorted + :raise: :py:class:`ValueError` if collection is not sorted + Examples: + >>> __assert_sorted([0, 1, 2, 4]) + True + >>> __assert_sorted([10, -1, 5]) + Traceback (most recent call last): + ... + ValueError: Collection must be sorted + """ + if collection != sorted(collection): + raise ValueError('Collection must be sorted') + return True + + +if __name__ == '__main__': + import sys + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by comma:\n') + collection = [int(item) for item in user_input.split(',')] + try: + __assert_sorted(collection) + except ValueError: + sys.exit('Sequence must be sorted to apply interpolation search') + + target_input = input_function( + 'Enter a single number to be found in the list:\n' + ) + target = int(target_input) + result = interpolation_search(collection, target) + if result is not None: + print('{} found at positions: {}'.format(target, result)) + else: + print('Not found') \ No newline at end of file From cf7d2cbec6cf29d1bbb455ac2366746a0605441a Mon Sep 17 00:00:00 2001 From: agdenadel Date: Mon, 16 Oct 2017 20:20:00 -0400 Subject: [PATCH 41/73] Fix typo in traversals --- {traverals => traversals}/binary_tree_traversals.py | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename {traverals => traversals}/binary_tree_traversals.py (100%) diff --git a/traverals/binary_tree_traversals.py b/traversals/binary_tree_traversals.py similarity index 100% rename from traverals/binary_tree_traversals.py rename to traversals/binary_tree_traversals.py From 0dcf27f3f2558e144b1076b09f5c1bfcfb2f8d9d Mon Sep 17 00:00:00 2001 From: Vishal Gupta Date: Fri, 20 Oct 2017 13:47:09 +0530 Subject: [PATCH 42/73] Added basic-graphs.py with common graph algorithms --- Graphs/basic-graphs.py | 267 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 267 insertions(+) create mode 100644 Graphs/basic-graphs.py diff --git a/Graphs/basic-graphs.py b/Graphs/basic-graphs.py new file mode 100644 index 000000000..fc78e5652 --- /dev/null +++ b/Graphs/basic-graphs.py @@ -0,0 +1,267 @@ +# Accept No. of Nodes and edges +n, m = map(int, raw_input().split(" ")) + +# Initialising Dictionary of edges +g = {} +for i in xrange(n): + g[i + 1] = [] + +""" +-------------------------------------------------------------------------------- + Accepting edges of Unweighted Directed Graphs +-------------------------------------------------------------------------------- +""" +for _ in xrange(m): + x, y = map(int, raw_input().split(" ")) + g[x].append(y) + +""" +-------------------------------------------------------------------------------- + Accepting edges of Unweighted Undirected Graphs +-------------------------------------------------------------------------------- +""" +for _ in xrange(m): + x, y = map(int, raw_input().split(" ")) + g[x].append(y) + g[y].append(x) + +""" +-------------------------------------------------------------------------------- + Accepting edges of Weighted Undirected Graphs +-------------------------------------------------------------------------------- +""" +for _ in xrange(m): + x, y, r = map(int, raw_input().split(" ")) + g[x].append([y, r]) + g[y].append([x, r]) + +""" +-------------------------------------------------------------------------------- + Depth First Search. + Args : G - Dictionary of edges + s - Starting Node + Vars : vis - Set of visited nodes + S - Traversal Stack +-------------------------------------------------------------------------------- +""" + + +def dfs(G, s): + vis, S = set([s]), [s] + print s + while S: + flag = 0 + for i in G[S[-1]]: + if i not in vis: + S.append(i) + vis.add(i) + flag = 1 + print i + break + if not flag: + S.pop() + + +""" +-------------------------------------------------------------------------------- + Breadth First Search. + Args : G - Dictionary of edges + s - Starting Node + Vars : vis - Set of visited nodes + Q - Traveral Stack +-------------------------------------------------------------------------------- +""" +from collections import deque + + +def bfs(G, s): + vis, Q = set([s]), deque([s]) + print s + while Q: + u = Q.popleft() + for v in G[u]: + if v not in vis: + vis.add(v) + Q.append(v) + print v + + +""" +-------------------------------------------------------------------------------- + Dijkstra's shortest path Algorithm + Args : G - Dictionary of edges + s - Starting Node + Vars : dist - Dictionary storing shortest distance from s to every other node + known - Set of knows nodes + path - Preceding node in path +-------------------------------------------------------------------------------- +""" + + +def dijk(G, s): + dist, known, path = {s: 0}, set(), {s: 0} + while True: + if len(known) == len(G) - 1: + break + mini = 100000 + for i in dist: + if i not in known and dist[i] < mini: + mini = dist[i] + u = i + known.add(u) + for v in G[u]: + if v[0] not in known: + if dist[u] + v[1] < dist.get(v[0], 100000): + dist[v[0]] = dist[u] + v[1] + path[v[0]] = u + for i in dist: + if i != s: + print dist[i] + + +""" +-------------------------------------------------------------------------------- + Topological Sort +-------------------------------------------------------------------------------- +""" +from collections import deque + + +def topo(G, ind=None, Q=[1]): + if ind == None: + ind = [0] * (len(G) + 1) # SInce oth Index is ignored + for u in G: + for v in G[u]: + ind[v] += 1 + Q = deque() + for i in G: + if ind[i] == 0: + Q.append(i) + if len(Q) == 0: + return + v = Q.popleft() + print v + for w in G[v]: + ind[w] -= 1 + if ind[w] == 0: + Q.append(w) + topo(G, ind, Q) + + +""" +-------------------------------------------------------------------------------- + Reading an Adjacency matrix +-------------------------------------------------------------------------------- +""" + + +def adjm(): + n, a = input(), [] + for i in xrange(n): + a.append(map(int, raw_input().split())) + return a, n + + +""" +-------------------------------------------------------------------------------- + Floyd Warshall's algorithm + Args : G - Dictionary of edges + s - Starting Node + Vars : dist - Dictionary storing shortest distance from s to every other node + known - Set of knows nodes + path - Preceding node in path + +-------------------------------------------------------------------------------- +""" + + +def floy((A, n)): + dist = list(A) + path = [[0] * n for i in xrange(n)] + for k in xrange(n): + for i in xrange(n): + for j in xrange(n): + if dist[i][j] > dist[i][k] + dist[k][j]: + dist[i][j] = dist[i][k] + dist[k][j] + path[i][k] = k + print dist + + +""" +-------------------------------------------------------------------------------- + Prim's MST Algorithm + Args : G - Dictionary of edges + s - Starting Node + Vars : dist - Dictionary storing shortest distance from s to nearest node + known - Set of knows nodes + path - Preceding node in path +-------------------------------------------------------------------------------- +""" + + +def prim(G, s): + dist, known, path = {s: 0}, set(), {s: 0} + while True: + if len(known) == len(G) - 1: + break + mini = 100000 + for i in dist: + if i not in known and dist[i] < mini: + mini = dist[i] + u = i + known.add(u) + for v in G[u]: + if v[0] not in known: + if v[1] < dist.get(v[0], 100000): + dist[v[0]] = v[1] + path[v[0]] = u + + +""" +-------------------------------------------------------------------------------- + Accepting Edge list + Vars : n - Number of nodes + m - Number of edges + Returns : l - Edge list + n - Number of Nodes +-------------------------------------------------------------------------------- +""" + + +def edglist(): + n, m = map(int, raw_input().split(" ")) + l = [] + for i in xrange(m): + l.append(map(int, raw_input().split(' '))) + return l, n + + +""" +-------------------------------------------------------------------------------- + Kruskal's MST Algorithm + Args : E - Edge list + n - Number of Nodes + Vars : s - Set of all nodes as unique disjoint sets (initially) +-------------------------------------------------------------------------------- +""" + + +def krusk((E, n)): + # Sort edges on the basis of distance + E.sort(reverse=True, key=lambda x: x[2]) + s = [set([i]) for i in range(1, n + 1)] + while True: + if len(s) == 1: + break + print s + x = E.pop() + for i in xrange(len(s)): + if x[0] in s[i]: + break + for j in xrange(len(s)): + if x[1] in s[j]: + if i == j: + break + s[j].update(s[i]) + s.pop(i) + break From edaa2c15889b250c777f583fda5725cf073b18f2 Mon Sep 17 00:00:00 2001 From: Sarot Busala Date: Fri, 20 Oct 2017 16:26:07 +0700 Subject: [PATCH 43/73] Floyd Warshall Algorithm upload simple Floyd-Warshall Algorithm (No path stored) --- dynamic_programming/FloydWarshall.py | 37 ++++++++++++++++++++++++++++ 1 file changed, 37 insertions(+) create mode 100644 dynamic_programming/FloydWarshall.py diff --git a/dynamic_programming/FloydWarshall.py b/dynamic_programming/FloydWarshall.py new file mode 100644 index 000000000..bf7714124 --- /dev/null +++ b/dynamic_programming/FloydWarshall.py @@ -0,0 +1,37 @@ +import math + +class Graph: + + def __init__(self, N = 0): # a graph with Node 0,1,...,N-1 + self.N = N + self.W = [[math.inf for j in range(0,N)] for i in range(0,N)] # adjacency matrix for weight + self.dp = [[math.inf for j in range(0,N)] for i in range(0,N)] # dp[i][j] stores minimum distance from i to j + + def addEdge(self, u, v, w): + self.dp[u][v] = w; + + def floyd_warshall(self): + for k in range(0,self.N): + for i in range(0,self.N): + for j in range(0,self.N): + self.dp[i][j] = min(self.dp[i][j], self.dp[i][k] + self.dp[k][j]) + + def showMin(self, u, v): + return self.dp[u][v] + +if __name__ == '__main__': + graph = Graph(5) + graph.addEdge(0,2,9) + graph.addEdge(0,4,10) + graph.addEdge(1,3,5) + graph.addEdge(2,3,7) + graph.addEdge(3,0,10) + graph.addEdge(3,1,2) + graph.addEdge(3,2,1) + graph.addEdge(3,4,6) + graph.addEdge(4,1,3) + graph.addEdge(4,2,4) + graph.addEdge(4,3,9) + graph.floyd_warshall() + graph.showMin(1,4) + graph.showMin(0,3) From d68d0ef05c024cb90f96b379c1206b3487847cbc Mon Sep 17 00:00:00 2001 From: Sarot Busala Date: Fri, 20 Oct 2017 16:45:17 +0700 Subject: [PATCH 44/73] Add Fenwick Tree Add Fenwick Tree (Binary Index Tree) --- data_structures/Binary Tree/FenwickTree.py | 28 ++++++++++++++++++++++ 1 file changed, 28 insertions(+) create mode 100644 data_structures/Binary Tree/FenwickTree.py diff --git a/data_structures/Binary Tree/FenwickTree.py b/data_structures/Binary Tree/FenwickTree.py new file mode 100644 index 000000000..02e2d6151 --- /dev/null +++ b/data_structures/Binary Tree/FenwickTree.py @@ -0,0 +1,28 @@ +class FenwickTree: + + def __init__(self, SIZE): # create fenwick tree with size SIZE + self.Size = SIZE + self.ft = [0 for i in range (0,SIZE)] + + def update(self, i, val): # update data (adding) in index i in O(lg N) + while (i < self.Size): + self.ft[i] += val + i += i & (-i) + + def query(self, i): # query cumulative data from index 0 to i in O(lg N) + ret = 0 + while (i > 0): + ret += self.ft[i] + i -= i & (-i) + return ret + +if __name__ == '__main__': + f = FenwickTree(100) + f.update(1,20) + f.update(4,4) + print (f.query(1)) + print (f.query(3)) + print (f.query(4)) + f.update(2,-5) + print (f.query(1)) + print (f.query(3)) From 29f8e5edd87bfbcb1e2af1fd6c6a2610fbd28e49 Mon Sep 17 00:00:00 2001 From: Vishal Kumar Date: Fri, 20 Oct 2017 16:10:33 +0530 Subject: [PATCH 45/73] Create Arrays "Arrays implementation" using python programming. --- data_structures/Arrays | 1 + 1 file changed, 1 insertion(+) create mode 100644 data_structures/Arrays diff --git a/data_structures/Arrays b/data_structures/Arrays new file mode 100644 index 000000000..03eaefac1 --- /dev/null +++ b/data_structures/Arrays @@ -0,0 +1 @@ +Arrays implimentation using python programming. From e7e8558b639ba235585303a74b32273a48d8f8a8 Mon Sep 17 00:00:00 2001 From: Sarot Busala Date: Fri, 20 Oct 2017 18:24:11 +0700 Subject: [PATCH 46/73] Add Segment Tree Add simple Segment Tree (No optimization) --- data_structures/Binary Tree/SegmentTree.py | 64 ++++++++++++++++++++++ 1 file changed, 64 insertions(+) create mode 100644 data_structures/Binary Tree/SegmentTree.py diff --git a/data_structures/Binary Tree/SegmentTree.py b/data_structures/Binary Tree/SegmentTree.py new file mode 100644 index 000000000..cf47ca7d7 --- /dev/null +++ b/data_structures/Binary Tree/SegmentTree.py @@ -0,0 +1,64 @@ +import math + +class SegmentTree: + + def __init__(self, N): + self.N = N + self.st = [0 for i in range(0,4*N)] # approximate the overall size of segment tree with array N + + def left(self, idx): + return idx*2 + + def right(self, idx): + return idx*2 + 1 + + def build(self, idx, l, r, A): + if l==r: + self.st[idx] = A[l-1] + else : + mid = (l+r)//2 + self.build(self.left(idx),l,mid, A) + self.build(self.right(idx),mid+1,r, A) + self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)]) + + def update(self, idx, l, r, a, b, val): # update(1, 1, N, a, b, v) for update val v to [a,b] + if r < a or l > b: + return True + if l == r : + self.st[idx] = val + return True + mid = (l+r)//2 + self.update(self.left(idx),l,mid,a,b,val) + self.update(self.right(idx),mid+1,r,a,b,val) + self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)]) + return True + + def query(self, idx, l, r, a, b): #query(1, 1, N, a, b) for query max of [a,b] + if r < a or l > b: + return -math.inf + if l >= a and r <= b: + return self.st[idx] + mid = (l+r)//2 + q1 = self.query(self.left(idx),l,mid,a,b) + q2 = self.query(self.right(idx),mid+1,r,a,b) + return max(q1,q2) + + def showData(self): + showList = [] + for i in range(1,N+1): + showList += [self.query(1, 1, self.N, i, i)] + print (showList) + + +if __name__ == '__main__': + A = [1,2,-4,7,3,-5,6,11,-20,9,14,15,5,2,-8] + N = 15 + segt = SegmentTree(N) + segt.build(1,1,N,A) + print (segt.query(1,1,N,4,6)) + print (segt.query(1,1,N,7,11)) + print (segt.query(1,1,N,7,12)) + segt.update(1,1,N,1,3,111) + print (segt.query(1,1,N,1,15)) + segt.update(1,1,N,7,8,235) + segt.showData() From 2617de848ea6f8e209c871dd1ac488401f1aace7 Mon Sep 17 00:00:00 2001 From: Sarot Busala Date: Fri, 20 Oct 2017 18:47:06 +0700 Subject: [PATCH 47/73] Add Lazy Segment Tree Add Lazy Segment Tree with Lazy Approach --- .../Binary Tree/LazySegmentTree.py | 90 +++++++++++++++++++ 1 file changed, 90 insertions(+) create mode 100644 data_structures/Binary Tree/LazySegmentTree.py diff --git a/data_structures/Binary Tree/LazySegmentTree.py b/data_structures/Binary Tree/LazySegmentTree.py new file mode 100644 index 000000000..bbd880a06 --- /dev/null +++ b/data_structures/Binary Tree/LazySegmentTree.py @@ -0,0 +1,90 @@ +import math + +class SegmentTree: + + def __init__(self, N): + self.N = N + self.st = [0 for i in range(0,4*N)] # approximate the overall size of segment tree with array N + self.lazy = [0 for i in range(0,4*N)] # create array to store lazy update + self.flag = [0 for i in range(0,4*N)] # flag for lazy update + + def left(self, idx): + return idx*2 + + def right(self, idx): + return idx*2 + 1 + + def build(self, idx, l, r, A): + if l==r: + self.st[idx] = A[l-1] + else : + mid = (l+r)//2 + self.build(self.left(idx),l,mid, A) + self.build(self.right(idx),mid+1,r, A) + self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)]) + + # update with O(lg N) (Normal segment tree without lazy update will take O(Nlg N) for each update) + def update(self, idx, l, r, a, b, val): # update(1, 1, N, a, b, v) for update val v to [a,b] + if self.flag[idx] == True: + self.st[idx] = self.lazy[idx] + self.flag[idx] = False + if l!=r: + self.lazy[self.left(idx)] = self.lazy[idx] + self.lazy[self.right(idx)] = self.lazy[idx] + self.flag[self.left(idx)] = True + self.flag[self.right(idx)] = True + + if r < a or l > b: + return True + if l >= a and r <= b : + self.st[idx] = val + if l!=r: + self.lazy[self.left(idx)] = val + self.lazy[self.right(idx)] = val + self.flag[self.left(idx)] = True + self.flag[self.right(idx)] = True + return True + mid = (l+r)//2 + self.update(self.left(idx),l,mid,a,b,val) + self.update(self.right(idx),mid+1,r,a,b,val) + self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)]) + return True + + # query with O(lg N) + def query(self, idx, l, r, a, b): #query(1, 1, N, a, b) for query max of [a,b] + if self.flag[idx] == True: + self.st[idx] = self.lazy[idx] + self.flag[idx] = False + if l != r: + self.lazy[self.left(idx)] = self.lazy[idx] + self.lazy[self.right(idx)] = self.lazy[idx] + self.flag[self.left(idx)] = True + self.flag[self.right(idx)] = True + if r < a or l > b: + return -math.inf + if l >= a and r <= b: + return self.st[idx] + mid = (l+r)//2 + q1 = self.query(self.left(idx),l,mid,a,b) + q2 = self.query(self.right(idx),mid+1,r,a,b) + return max(q1,q2) + + def showData(self): + showList = [] + for i in range(1,N+1): + showList += [self.query(1, 1, self.N, i, i)] + print (showList) + + +if __name__ == '__main__': + A = [1,2,-4,7,3,-5,6,11,-20,9,14,15,5,2,-8] + N = 15 + segt = SegmentTree(N) + segt.build(1,1,N,A) + print (segt.query(1,1,N,4,6)) + print (segt.query(1,1,N,7,11)) + print (segt.query(1,1,N,7,12)) + segt.update(1,1,N,1,3,111) + print (segt.query(1,1,N,1,15)) + segt.update(1,1,N,7,8,235) + segt.showData() From fe7b86c9ffed033d3ee47445e288819828c05537 Mon Sep 17 00:00:00 2001 From: Shivam sharma Date: Fri, 20 Oct 2017 18:03:43 +0530 Subject: [PATCH 48/73] Add files via upload --- sorts/external-sort.py | 161 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 161 insertions(+) create mode 100644 sorts/external-sort.py diff --git a/sorts/external-sort.py b/sorts/external-sort.py new file mode 100644 index 000000000..eca26012d --- /dev/null +++ b/sorts/external-sort.py @@ -0,0 +1,161 @@ +#!/usr/bin/env python + +# +# Sort large text files in a minimum amount of memory +# +import os +import sys +import argparse + +class FileSplitter(object): + BLOCK_FILENAME_FORMAT = 'block_{0}.dat' + + def __init__(self, filename): + self.filename = filename + self.block_filenames = [] + + def write_block(self, data, block_number): + filename = self.BLOCK_FILENAME_FORMAT.format(block_number) + file = open(filename, 'w') + file.write(data) + file.close() + self.block_filenames.append(filename) + + def get_block_filenames(self): + return self.block_filenames + + def split(self, block_size, sort_key=None): + file = open(self.filename, 'r') + i = 0 + + while True: + lines = file.readlines(block_size) + + if lines == []: + break + + if sort_key is None: + lines.sort() + else: + lines.sort(key=sort_key) + + self.write_block(''.join(lines), i) + i += 1 + + def cleanup(self): + map(lambda f: os.remove(f), self.block_filenames) + + +class NWayMerge(object): + def select(self, choices): + min_index = -1 + min_str = None + + for i in range(len(choices)): + if min_str is None or choices[i] < min_str: + min_index = i + + return min_index + + +class FilesArray(object): + def __init__(self, files): + self.files = files + self.empty = set() + self.num_buffers = len(files) + self.buffers = {i: None for i in range(self.num_buffers)} + + def get_dict(self): + return {i: self.buffers[i] for i in range(self.num_buffers) if i not in self.empty} + + def refresh(self): + for i in range(self.num_buffers): + if self.buffers[i] is None and i not in self.empty: + self.buffers[i] = self.files[i].readline() + + if self.buffers[i] == '': + self.empty.add(i) + + if len(self.empty) == self.num_buffers: + return False + + return True + + def unshift(self, index): + value = self.buffers[index] + self.buffers[index] = None + + return value + + +class FileMerger(object): + def __init__(self, merge_strategy): + self.merge_strategy = merge_strategy + + def merge(self, filenames, outfilename, buffer_size): + outfile = open(outfilename, 'w', buffer_size) + buffers = FilesArray(self.get_file_handles(filenames, buffer_size)) + + while buffers.refresh(): + min_index = self.merge_strategy.select(buffers.get_dict()) + outfile.write(buffers.unshift(min_index)) + + def get_file_handles(self, filenames, buffer_size): + files = {} + + for i in range(len(filenames)): + files[i] = open(filenames[i], 'r', buffer_size) + + return files + + + +class ExternalSort(object): + def __init__(self, block_size): + self.block_size = block_size + + def sort(self, filename, sort_key=None): + num_blocks = self.get_number_blocks(filename, self.block_size) + splitter = FileSplitter(filename) + splitter.split(self.block_size, sort_key) + + merger = FileMerger(NWayMerge()) + buffer_size = self.block_size / (num_blocks + 1) + merger.merge(splitter.get_block_filenames(), filename + '.out', buffer_size) + + splitter.cleanup() + + def get_number_blocks(self, filename, block_size): + return (os.stat(filename).st_size / block_size) + 1 + + +def parse_memory(string): + if string[-1].lower() == 'k': + return int(string[:-1]) * 1024 + elif string[-1].lower() == 'm': + return int(string[:-1]) * 1024 * 1024 + elif string[-1].lower() == 'g': + return int(string[:-1]) * 1024 * 1024 * 1024 + else: + return int(string) + + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('-m', + '--mem', + help='amount of memory to use for sorting', + default='100M') + parser.add_argument('filename', + metavar='', + nargs=1, + help='name of file to sort') + args = parser.parse_args() + + sorter = ExternalSort(parse_memory(args.mem)) + sorter.sort(args.filename[0]) + + +if __name__ == '__main__': +main() \ No newline at end of file From b0d53015fe130b7d0b4cb208c90dee4c965a397a Mon Sep 17 00:00:00 2001 From: Danni Date: Fri, 20 Oct 2017 12:35:53 -0400 Subject: [PATCH 49/73] fixed issue#171 --- other/nested_brackets.py | 32 ++++++++++++-------------------- 1 file changed, 12 insertions(+), 20 deletions(-) diff --git a/other/nested_brackets.py b/other/nested_brackets.py index ea681ded5..f486190f4 100644 --- a/other/nested_brackets.py +++ b/other/nested_brackets.py @@ -18,28 +18,20 @@ returns true if S is nested and false otherwise. def is_balanced(S): stack = [] - + open_brackets = set({'(', '[', '{'}) + closed_brackets = set({')', ']', '}'}) + open_to_closed = dict({'{':'}', '[':']', '(':')'}) + for i in range(len(S)): - - if S[i] == '(' or S[i] == '{' or S[i] == '[': + + if S[i] in open_brackets: stack.append(S[i]) - - else: - - if len(stack) > 0: - - pair = stack.pop() + S[i] - - if pair != '[]' and pair != '()' and pair != '{}': - return False - - else: + + elif S[i] in closed_brackets: + if len(stack) == 0 or (len(stack) > 0 and open_to_closed[stack.pop()] != S[i]): return False - - if len(stack) == 0: - return True - - return False + + return len(stack) == 0 def main(): @@ -48,7 +40,7 @@ def main(): if is_balanced(S): print(S, "is balanced") - + else: print(S, "is not balanced") From 226a0a4ad8d382a5f6db102ded889b7455731df4 Mon Sep 17 00:00:00 2001 From: Tony De La Nuez Date: Sun, 22 Oct 2017 18:04:10 -0500 Subject: [PATCH 50/73] Adding reverse() to singly-linked list Updating singly-linked list to include a reverse method using the three-way shuffle method. --- .../LinkedList/singly_LinkedList.py | 18 +++++++++++++++++- 1 file changed, 17 insertions(+), 1 deletion(-) diff --git a/data_structures/LinkedList/singly_LinkedList.py b/data_structures/LinkedList/singly_LinkedList.py index c9a3cec27..8828ce6cc 100644 --- a/data_structures/LinkedList/singly_LinkedList.py +++ b/data_structures/LinkedList/singly_LinkedList.py @@ -47,4 +47,20 @@ class Linked_List: return Head def isEmpty(Head): - return Head is None #Return if Head is none \ No newline at end of file + return Head is None #Return if Head is none + + def reverse(Head): + prev = None + current = Head + + while(current): + # Store the current node's next node. + next_node = current.next + # Make the current node's next point backwards + current.next = prev + # Make the previous node be the current node + prev = current + # Make the current node the next node (to progress iteration) + current = next_node + # Return prev in order to put the head at the end + Head = prev From 850953c2aad57b510d0c6f1bc7a3fbb7f662a4c7 Mon Sep 17 00:00:00 2001 From: Tony De La Nuez Date: Sun, 22 Oct 2017 18:06:45 -0500 Subject: [PATCH 51/73] Two-sum, common interview problem. --- other/two-sum.py | 28 ++++++++++++++++++++++++++++ 1 file changed, 28 insertions(+) create mode 100644 other/two-sum.py diff --git a/other/two-sum.py b/other/two-sum.py new file mode 100644 index 000000000..4a522b6d4 --- /dev/null +++ b/other/two-sum.py @@ -0,0 +1,28 @@ +""" +Given an array of integers, return indices of the two numbers such that they add up to a specific target. + +You may assume that each input would have exactly one solution, and you may not use the same element twice. + +Example: +Given nums = [2, 7, 11, 15], target = 9, + +Because nums[0] + nums[1] = 2 + 7 = 9, +return [0, 1]. +""" + +def twoSum(nums, target): + """ + :type nums: List[int] + :type target: int + :rtype: List[int] + """ + chk_map = {} + for index, val in enumerate(nums): + compl = target - val + if compl in chk_map: + indices = [chk_map[compl], index] + print(indices) + return [indices] + else: + chk_map[val] = index + return False From 0ad029cb11eefdf2e44fa7fcf8a71eaa2b98b5a4 Mon Sep 17 00:00:00 2001 From: Pablo Date: Sun, 22 Oct 2017 20:13:06 -0300 Subject: [PATCH 52/73] Added getNode function and made changes to insert function --- .../Binary Tree/binary_seach_tree.py | 99 ++++++++----- .../Binary Tree/binary_search_tree.py | 130 ++++++++++++++++++ 2 files changed, 193 insertions(+), 36 deletions(-) create mode 100644 data_structures/Binary Tree/binary_search_tree.py diff --git a/data_structures/Binary Tree/binary_seach_tree.py b/data_structures/Binary Tree/binary_seach_tree.py index 9e468f775..2993c3cdc 100644 --- a/data_structures/Binary Tree/binary_seach_tree.py +++ b/data_structures/Binary Tree/binary_seach_tree.py @@ -2,7 +2,6 @@ A binary search Tree ''' - class Node: def __init__(self, label): @@ -35,32 +34,49 @@ class BinarySearchTree: self.root = None def insert(self, label): - # Create a new Node - - node = Node(label) - + new_node = Node(label) + # If Tree is empty if self.empty(): - self.root = node + self.root = new_node else: - dad_node = None + #If Tree is not empty + parent_node = None curr_node = self.root - - while True: - if curr_node is not None: - - dad_node = curr_node - - if node.getLabel() < curr_node.getLabel(): - curr_node = curr_node.getLeft() - else: - curr_node = curr_node.getRight() + #While we don't get to a leaf + while curr_node is not None: + #We keep reference of the parent node + parent_node = curr_node + #If node label is less than current node + if new_node.getLabel() < curr_node.getLabel(): + #We go left + curr_node = curr_node.getLeft() else: - if node.getLabel() < dad_node.getLabel(): - dad_node.setLeft(node) - else: - dad_node.setRight(node) - break + #Else we go right + curr_node = curr_node.getRight() + #We insert the new node in a leaf + if new_node.getLabel() < parent_node.getLabel(): + parent_node.setLeft(new_node) + else: + parent_node.setRight(new_node) + + def getNode(self, label): + curr_node = None + #If the tree is not empty + if(not self.empty()): + #Get tree root + curr_node = self.getRoot() + #While we don't find the node we look for + #I am using lazy evaluation here to avoid NoneType Attribute error + while curr_node is not None and curr_node.getLabel() is not label: + #If node label is less than current node + if label < curr_node.getLabel(): + #We go left + curr_node = curr_node.getLeft() + else: + #Else we go right + curr_node = curr_node.getRight() + return curr_node def empty(self): if self.root is None: @@ -69,15 +85,13 @@ class BinarySearchTree: def preShow(self, curr_node): if curr_node is not None: - print(curr_node.getLabel(), end=" ") - + print(curr_node.getLabel()) self.preShow(curr_node.getLeft()) self.preShow(curr_node.getRight()) def getRoot(self): return self.root - ''' Example 8 @@ -89,15 +103,28 @@ Example 4 7 13 ''' -t = BinarySearchTree() -t.insert(8) -t.insert(3) -t.insert(1) -t.insert(6) -t.insert(4) -t.insert(7) -t.insert(10) -t.insert(14) -t.insert(13) -t.preShow(t.getRoot()) +if __name__ == "__main__": + t = BinarySearchTree() + t.insert(8) + t.insert(3) + t.insert(1) + t.insert(6) + t.insert(4) + t.insert(7) + t.insert(10) + t.insert(14) + t.insert(13) + + t.preShow(t.getRoot()) + + if(t.getNode(6) is not None): + print("The label 6 exists") + else: + print("The label 6 doesn't exist") + + if(t.getNode(-1) is not None): + print("The label -1 exists") + else: + print("The label -1 doesn't exist") + diff --git a/data_structures/Binary Tree/binary_search_tree.py b/data_structures/Binary Tree/binary_search_tree.py new file mode 100644 index 000000000..2993c3cdc --- /dev/null +++ b/data_structures/Binary Tree/binary_search_tree.py @@ -0,0 +1,130 @@ +''' +A binary search Tree +''' + +class Node: + + def __init__(self, label): + self.label = label + self.left = None + self.right = None + + def getLabel(self): + return self.label + + def setLabel(self, label): + self.label = label + + def getLeft(self): + return self.left + + def setLeft(self, left): + self.left = left + + def getRight(self): + return self.right + + def setRight(self, right): + self.right = right + + +class BinarySearchTree: + + def __init__(self): + self.root = None + + def insert(self, label): + # Create a new Node + new_node = Node(label) + # If Tree is empty + if self.empty(): + self.root = new_node + else: + #If Tree is not empty + parent_node = None + curr_node = self.root + #While we don't get to a leaf + while curr_node is not None: + #We keep reference of the parent node + parent_node = curr_node + #If node label is less than current node + if new_node.getLabel() < curr_node.getLabel(): + #We go left + curr_node = curr_node.getLeft() + else: + #Else we go right + curr_node = curr_node.getRight() + #We insert the new node in a leaf + if new_node.getLabel() < parent_node.getLabel(): + parent_node.setLeft(new_node) + else: + parent_node.setRight(new_node) + + def getNode(self, label): + curr_node = None + #If the tree is not empty + if(not self.empty()): + #Get tree root + curr_node = self.getRoot() + #While we don't find the node we look for + #I am using lazy evaluation here to avoid NoneType Attribute error + while curr_node is not None and curr_node.getLabel() is not label: + #If node label is less than current node + if label < curr_node.getLabel(): + #We go left + curr_node = curr_node.getLeft() + else: + #Else we go right + curr_node = curr_node.getRight() + return curr_node + + def empty(self): + if self.root is None: + return True + return False + + def preShow(self, curr_node): + if curr_node is not None: + print(curr_node.getLabel()) + self.preShow(curr_node.getLeft()) + self.preShow(curr_node.getRight()) + + def getRoot(self): + return self.root + +''' +Example + 8 + / \ + 3 10 + / \ \ + 1 6 14 + / \ / + 4 7 13 +''' + + +if __name__ == "__main__": + t = BinarySearchTree() + t.insert(8) + t.insert(3) + t.insert(1) + t.insert(6) + t.insert(4) + t.insert(7) + t.insert(10) + t.insert(14) + t.insert(13) + + t.preShow(t.getRoot()) + + if(t.getNode(6) is not None): + print("The label 6 exists") + else: + print("The label 6 doesn't exist") + + if(t.getNode(-1) is not None): + print("The label -1 exists") + else: + print("The label -1 doesn't exist") + From 3786c0d0eae4c242883092ae47603667a7fbfac7 Mon Sep 17 00:00:00 2001 From: Pablo Date: Sun, 22 Oct 2017 20:30:53 -0300 Subject: [PATCH 53/73] Deleted binary_seach_tree --- .../Binary Tree/binary_seach_tree.py | 130 ------------------ 1 file changed, 130 deletions(-) delete mode 100644 data_structures/Binary Tree/binary_seach_tree.py diff --git a/data_structures/Binary Tree/binary_seach_tree.py b/data_structures/Binary Tree/binary_seach_tree.py deleted file mode 100644 index 2993c3cdc..000000000 --- a/data_structures/Binary Tree/binary_seach_tree.py +++ /dev/null @@ -1,130 +0,0 @@ -''' -A binary search Tree -''' - -class Node: - - def __init__(self, label): - self.label = label - self.left = None - self.right = None - - def getLabel(self): - return self.label - - def setLabel(self, label): - self.label = label - - def getLeft(self): - return self.left - - def setLeft(self, left): - self.left = left - - def getRight(self): - return self.right - - def setRight(self, right): - self.right = right - - -class BinarySearchTree: - - def __init__(self): - self.root = None - - def insert(self, label): - # Create a new Node - new_node = Node(label) - # If Tree is empty - if self.empty(): - self.root = new_node - else: - #If Tree is not empty - parent_node = None - curr_node = self.root - #While we don't get to a leaf - while curr_node is not None: - #We keep reference of the parent node - parent_node = curr_node - #If node label is less than current node - if new_node.getLabel() < curr_node.getLabel(): - #We go left - curr_node = curr_node.getLeft() - else: - #Else we go right - curr_node = curr_node.getRight() - #We insert the new node in a leaf - if new_node.getLabel() < parent_node.getLabel(): - parent_node.setLeft(new_node) - else: - parent_node.setRight(new_node) - - def getNode(self, label): - curr_node = None - #If the tree is not empty - if(not self.empty()): - #Get tree root - curr_node = self.getRoot() - #While we don't find the node we look for - #I am using lazy evaluation here to avoid NoneType Attribute error - while curr_node is not None and curr_node.getLabel() is not label: - #If node label is less than current node - if label < curr_node.getLabel(): - #We go left - curr_node = curr_node.getLeft() - else: - #Else we go right - curr_node = curr_node.getRight() - return curr_node - - def empty(self): - if self.root is None: - return True - return False - - def preShow(self, curr_node): - if curr_node is not None: - print(curr_node.getLabel()) - self.preShow(curr_node.getLeft()) - self.preShow(curr_node.getRight()) - - def getRoot(self): - return self.root - -''' -Example - 8 - / \ - 3 10 - / \ \ - 1 6 14 - / \ / - 4 7 13 -''' - - -if __name__ == "__main__": - t = BinarySearchTree() - t.insert(8) - t.insert(3) - t.insert(1) - t.insert(6) - t.insert(4) - t.insert(7) - t.insert(10) - t.insert(14) - t.insert(13) - - t.preShow(t.getRoot()) - - if(t.getNode(6) is not None): - print("The label 6 exists") - else: - print("The label 6 doesn't exist") - - if(t.getNode(-1) is not None): - print("The label -1 exists") - else: - print("The label -1 doesn't exist") - From da58cd92f3f5aec99794d1cf901df67f12ea95c1 Mon Sep 17 00:00:00 2001 From: Anurag Kumar Date: Mon, 23 Oct 2017 15:32:51 +0530 Subject: [PATCH 54/73] added Sierpinski Triangle generation module(fractal structures). --- other/sierpinski_triangle.py | 64 ++++++++++++++++++++++++++++++++++++ 1 file changed, 64 insertions(+) create mode 100644 other/sierpinski_triangle.py diff --git a/other/sierpinski_triangle.py b/other/sierpinski_triangle.py new file mode 100644 index 000000000..e566f693f --- /dev/null +++ b/other/sierpinski_triangle.py @@ -0,0 +1,64 @@ +'''Author Anurag Kumar | anuragkumarak95@gmail.com | git/anuragkumarak95 + +Simple example of Fractal generation using recursive function. + +What is Sierpinski Triangle? +>>The Sierpinski triangle (also with the original orthography Sierpinski), also called the Sierpinski gasket or the Sierpinski Sieve, +is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller +equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e., +it is a mathematically generated pattern that can be reproducible at any magnification or reduction. It is named after +the Polish mathematician Wacław Sierpinski, but appeared as a decorative pattern many centuries prior to the work of Sierpinski. + +Requirements(pip): + - turtle + +Python: + - 2.6 + +Usage: + - $python sierpinski_triangle.py + +Credits: This code was written by editing the code from http://www.lpb-riannetrujillo.com/blog/python-fractal/ + +''' +import turtle +import sys +PROGNAME = 'Sierpinski Triangle' +if len(sys.argv) !=2: + raise Exception('right format for using this script: $python fractals.py ') + +myPen = turtle.Turtle() +myPen.ht() +myPen.speed(5) +myPen.pencolor('red') + +points = [[-175,-125],[0,175],[175,-125]] #size of triangle + +def getMid(p1,p2): + return ( (p1[0]+p2[0]) / 2, (p1[1] + p2[1]) / 2) #find midpoint + +def triangle(points,depth): + + myPen.up() + myPen.goto(points[0][0],points[0][1]) + myPen.down() + myPen.goto(points[1][0],points[1][1]) + myPen.goto(points[2][0],points[2][1]) + myPen.goto(points[0][0],points[0][1]) + + if depth>0: + triangle([points[0], + getMid(points[0], points[1]), + getMid(points[0], points[2])], + depth-1) + triangle([points[1], + getMid(points[0], points[1]), + getMid(points[1], points[2])], + depth-1) + triangle([points[2], + getMid(points[2], points[1]), + getMid(points[0], points[2])], + depth-1) + + +triangle(points,int(sys.argv[1])) \ No newline at end of file From 7180f08204e252b647587aa6686bee1523d83873 Mon Sep 17 00:00:00 2001 From: Gilberto Alexandre dos Santos Date: Mon, 23 Oct 2017 22:36:38 -0300 Subject: [PATCH 55/73] Created Union-Find algorithm --- data_structures/UnionFind/__init__.py | 0 data_structures/UnionFind/tests_union_find.py | 77 ++++++++++++++++ data_structures/UnionFind/union_find.py | 87 +++++++++++++++++++ 3 files changed, 164 insertions(+) create mode 100644 data_structures/UnionFind/__init__.py create mode 100644 data_structures/UnionFind/tests_union_find.py create mode 100644 data_structures/UnionFind/union_find.py diff --git a/data_structures/UnionFind/__init__.py b/data_structures/UnionFind/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/data_structures/UnionFind/tests_union_find.py b/data_structures/UnionFind/tests_union_find.py new file mode 100644 index 000000000..bdcc01033 --- /dev/null +++ b/data_structures/UnionFind/tests_union_find.py @@ -0,0 +1,77 @@ +from union_find import UnionFind +import unittest + + +class TestUnionFind(unittest.TestCase): + def test_init_with_valid_size(self): + uf = UnionFind(5) + self.assertEqual(uf.size, 5) + + def test_init_with_invalid_size(self): + with self.assertRaises(ValueError): + uf = UnionFind(0) + + with self.assertRaises(ValueError): + uf = UnionFind(-5) + + def test_union_with_valid_values(self): + uf = UnionFind(10) + + for i in range(11): + for j in range(11): + uf.union(i, j) + + def test_union_with_invalid_values(self): + uf = UnionFind(10) + + with self.assertRaises(ValueError): + uf.union(-1, 1) + + with self.assertRaises(ValueError): + uf.union(11, 1) + + def test_same_set_with_valid_values(self): + uf = UnionFind(10) + + for i in range(11): + for j in range(11): + if i == j: + self.assertTrue(uf.same_set(i, j)) + else: + self.assertFalse(uf.same_set(i, j)) + + uf.union(1, 2) + self.assertTrue(uf.same_set(1, 2)) + + uf.union(3, 4) + self.assertTrue(uf.same_set(3, 4)) + + self.assertFalse(uf.same_set(1, 3)) + self.assertFalse(uf.same_set(1, 4)) + self.assertFalse(uf.same_set(2, 3)) + self.assertFalse(uf.same_set(2, 4)) + + uf.union(1, 3) + self.assertTrue(uf.same_set(1, 3)) + self.assertTrue(uf.same_set(1, 4)) + self.assertTrue(uf.same_set(2, 3)) + self.assertTrue(uf.same_set(2, 4)) + + uf.union(4, 10) + self.assertTrue(uf.same_set(1, 10)) + self.assertTrue(uf.same_set(2, 10)) + self.assertTrue(uf.same_set(3, 10)) + self.assertTrue(uf.same_set(4, 10)) + + def test_same_set_with_invalid_values(self): + uf = UnionFind(10) + + with self.assertRaises(ValueError): + uf.same_set(-1, 1) + + with self.assertRaises(ValueError): + uf.same_set(11, 0) + + +if __name__ == '__main__': + unittest.main() diff --git a/data_structures/UnionFind/union_find.py b/data_structures/UnionFind/union_find.py new file mode 100644 index 000000000..40eea67ac --- /dev/null +++ b/data_structures/UnionFind/union_find.py @@ -0,0 +1,87 @@ +class UnionFind(): + """ + https://en.wikipedia.org/wiki/Disjoint-set_data_structure + + The union-find is a disjoint-set data structure + + You can merge two sets and tell if one set belongs to + another one. + + It's used on the Kruskal Algorithm + (https://en.wikipedia.org/wiki/Kruskal%27s_algorithm) + + The elements are in range [0, size] + """ + def __init__(self, size): + if size <= 0: + raise ValueError("size should be greater than 0") + + self.size = size + + # The below plus 1 is because we are using elements + # in range [0, size]. It makes more sense. + + # Every set begins with only itself + self.root = [i for i in range(size+1)] + + # This is used for heuristic union by rank + self.weight = [0 for i in range(size+1)] + + def union(self, u, v): + """ + Union of the sets u and v. + Complexity: log(n). + Amortized complexity: < 5 (it's very fast). + """ + + self._validate_element_range(u, "u") + self._validate_element_range(v, "v") + + if u == v: + return + + # Using union by rank will guarantee the + # log(n) complexity + rootu = self._root(u) + rootv = self._root(v) + weight_u = self.weight[rootu] + weight_v = self.weight[rootv] + if weight_u >= weight_v: + self.root[rootv] = rootu + if weight_u == weight_v: + self.weight[rootu] += 1 + else: + self.root[rootu] = rootv + + def same_set(self, u, v): + """ + Return true if the elements u and v belongs to + the same set + """ + + self._validate_element_range(u, "u") + self._validate_element_range(v, "v") + + return self._root(u) == self._root(v) + + def _root(self, u): + """ + Get the element set root. + This uses the heuristic path compression + See wikipedia article for more details. + """ + + if u != self.root[u]: + self.root[u] = self._root(self.root[u]) + + return self.root[u] + + def _validate_element_range(self, u, element_name): + """ + Raises ValueError if element is not in range + """ + if u < 0 or u > self.size: + msg = ("element {0} with value {1} " + "should be in range [0~{2}]")\ + .format(element_name, u, self.size) + raise ValueError(msg) From 88c881d5579c9fef0a76cdd381a6bc8e0b4aced3 Mon Sep 17 00:00:00 2001 From: rudrasohan Date: Tue, 24 Oct 2017 13:00:11 +0530 Subject: [PATCH 56/73] Changed Filename from A*.py to a_star.py --- Graphs/a_star.py | 101 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 101 insertions(+) create mode 100644 Graphs/a_star.py diff --git a/Graphs/a_star.py b/Graphs/a_star.py new file mode 100644 index 000000000..2ca9476e5 --- /dev/null +++ b/Graphs/a_star.py @@ -0,0 +1,101 @@ + +grid = [[0, 1, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0],#0 are free path whereas 1's are obstacles + [0, 1, 0, 0, 0, 0], + [0, 1, 0, 0, 1, 0], + [0, 0, 0, 0, 1, 0]] + +''' +heuristic = [[9, 8, 7, 6, 5, 4], + [8, 7, 6, 5, 4, 3], + [7, 6, 5, 4, 3, 2], + [6, 5, 4, 3, 2, 1], + [5, 4, 3, 2, 1, 0]]''' + +init = [0, 0] +goal = [len(grid)-1, len(grid[0])-1] #all coordinates are given in format [y,x] +cost = 1 + +#the cost map which pushes the path closer to the goal +heuristic = [[0 for row in range(len(grid[0]))] for col in range(len(grid))] +for i in range(len(grid)): + for j in range(len(grid[0])): + heuristic[i][j] = abs(i - goal[0]) + abs(j - goal[1]) + if grid[i][j] == 1: + heuristic[i][j] = 99 #added extra penalty in the heuristic map + + +#the actions we can take +delta = [[-1, 0 ], # go up + [ 0, -1], # go left + [ 1, 0 ], # go down + [ 0, 1 ]] # go right + + +#function to search the path +def search(grid,init,goal,cost,heuristic): + + closed = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]# the referrence grid + closed[init[0]][init[1]] = 1 + action = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]#the action grid + + x = init[0] + y = init[1] + g = 0 + f = g + heuristic[init[0]][init[0]] + cell = [[f, g, x, y]] + + found = False # flag that is set when search is complete + resign = False # flag set if we can't find expand + + while not found and not resign: + if len(cell) == 0: + resign = True + return "FAIL" + else: + cell.sort()#to choose the least costliest action so as to move closer to the goal + cell.reverse() + next = cell.pop() + x = next[2] + y = next[3] + g = next[1] + f = next[0] + + + if x == goal[0] and y == goal[1]: + found = True + else: + for i in range(len(delta)):#to try out different valid actions + x2 = x + delta[i][0] + y2 = y + delta[i][1] + if x2 >= 0 and x2 < len(grid) and y2 >=0 and y2 < len(grid[0]): + if closed[x2][y2] == 0 and grid[x2][y2] == 0: + g2 = g + cost + f2 = g2 + heuristic[x2][y2] + cell.append([f2, g2, x2, y2]) + closed[x2][y2] = 1 + action[x2][y2] = i + invpath = [] + x = goal[0] + y = goal[1] + invpath.append([x, y])#we get the reverse path from here + while x != init[0] or y != init[1]: + x2 = x - delta[action[x][y]][0] + y2 = y - delta[action[x][y]][1] + x = x2 + y = y2 + invpath.append([x, y]) + + path = [] + for i in range(len(invpath)): + path.append(invpath[len(invpath) - 1 - i]) + print "ACTION MAP" + for i in range(len(action)): + print action[i] + + return path + +a = search(grid,init,goal,cost,heuristic) +for i in range(len(a)): + print a[i] + From 46c0c66a721ccee087917fb719346a5d74a327d8 Mon Sep 17 00:00:00 2001 From: Sachin Arora Date: Tue, 24 Oct 2017 19:52:03 +0530 Subject: [PATCH 57/73] deleted A*.py Duplicate File --- Graphs/A*.py | 101 --------------------------------------------------- 1 file changed, 101 deletions(-) delete mode 100644 Graphs/A*.py diff --git a/Graphs/A*.py b/Graphs/A*.py deleted file mode 100644 index 2ca9476e5..000000000 --- a/Graphs/A*.py +++ /dev/null @@ -1,101 +0,0 @@ - -grid = [[0, 1, 0, 0, 0, 0], - [0, 1, 0, 0, 0, 0],#0 are free path whereas 1's are obstacles - [0, 1, 0, 0, 0, 0], - [0, 1, 0, 0, 1, 0], - [0, 0, 0, 0, 1, 0]] - -''' -heuristic = [[9, 8, 7, 6, 5, 4], - [8, 7, 6, 5, 4, 3], - [7, 6, 5, 4, 3, 2], - [6, 5, 4, 3, 2, 1], - [5, 4, 3, 2, 1, 0]]''' - -init = [0, 0] -goal = [len(grid)-1, len(grid[0])-1] #all coordinates are given in format [y,x] -cost = 1 - -#the cost map which pushes the path closer to the goal -heuristic = [[0 for row in range(len(grid[0]))] for col in range(len(grid))] -for i in range(len(grid)): - for j in range(len(grid[0])): - heuristic[i][j] = abs(i - goal[0]) + abs(j - goal[1]) - if grid[i][j] == 1: - heuristic[i][j] = 99 #added extra penalty in the heuristic map - - -#the actions we can take -delta = [[-1, 0 ], # go up - [ 0, -1], # go left - [ 1, 0 ], # go down - [ 0, 1 ]] # go right - - -#function to search the path -def search(grid,init,goal,cost,heuristic): - - closed = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]# the referrence grid - closed[init[0]][init[1]] = 1 - action = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]#the action grid - - x = init[0] - y = init[1] - g = 0 - f = g + heuristic[init[0]][init[0]] - cell = [[f, g, x, y]] - - found = False # flag that is set when search is complete - resign = False # flag set if we can't find expand - - while not found and not resign: - if len(cell) == 0: - resign = True - return "FAIL" - else: - cell.sort()#to choose the least costliest action so as to move closer to the goal - cell.reverse() - next = cell.pop() - x = next[2] - y = next[3] - g = next[1] - f = next[0] - - - if x == goal[0] and y == goal[1]: - found = True - else: - for i in range(len(delta)):#to try out different valid actions - x2 = x + delta[i][0] - y2 = y + delta[i][1] - if x2 >= 0 and x2 < len(grid) and y2 >=0 and y2 < len(grid[0]): - if closed[x2][y2] == 0 and grid[x2][y2] == 0: - g2 = g + cost - f2 = g2 + heuristic[x2][y2] - cell.append([f2, g2, x2, y2]) - closed[x2][y2] = 1 - action[x2][y2] = i - invpath = [] - x = goal[0] - y = goal[1] - invpath.append([x, y])#we get the reverse path from here - while x != init[0] or y != init[1]: - x2 = x - delta[action[x][y]][0] - y2 = y - delta[action[x][y]][1] - x = x2 - y = y2 - invpath.append([x, y]) - - path = [] - for i in range(len(invpath)): - path.append(invpath[len(invpath) - 1 - i]) - print "ACTION MAP" - for i in range(len(action)): - print action[i] - - return path - -a = search(grid,init,goal,cost,heuristic) -for i in range(len(a)): - print a[i] - From 848432c6fef0b3e64c864d99cd26f3dbf3f89780 Mon Sep 17 00:00:00 2001 From: Sachin Arora Date: Tue, 24 Oct 2017 20:19:14 +0530 Subject: [PATCH 58/73] Project Euler Problems Added. --- Project Euler/README.md | 39 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 39 insertions(+) create mode 100644 Project Euler/README.md diff --git a/Project Euler/README.md b/Project Euler/README.md new file mode 100644 index 000000000..072203a41 --- /dev/null +++ b/Project Euler/README.md @@ -0,0 +1,39 @@ +# ProjectEuler + +Problems are taken from https://projecteuler.net/. + +Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical +insights to solve. Project Euler is ideal for mathematicians who are learning to code. + +Here the efficiency of your code is also checked. +I've tried to provide all the best possible solutions. + +PROBLEMS: + +1. If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3,5,6 and 9. The sum of these multiples is 23. + Find the sum of all the multiples of 3 or 5 below N. + +2. Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, + the first 10 terms will be: + 1,2,3,5,8,13,21,34,55,89,.. + By considering the terms in the Fibonacci sequence whose values do not exceed n, find the sum of the even-valued terms. + e.g. for n=10, we have {2,8}, sum is 10. + +3. The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor of a given number N? + e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17. + +4. A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. + Find the largest palindrome made from the product of two 3-digit numbers which is less than N. + +5. 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. + What is the smallest positive number that is evenly divisible(divisible with no remainder) by all of the numbers from 1 to N? + +6. The sum of the squares of the first ten natural numbers is, + 1^2 + 2^2 + ... + 10^2 = 385 + The square of the sum of the first ten natural numbers is, + (1 + 2 + ... + 10)^2 = 552 = 3025 + Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640. + Find the difference between the sum of the squares of the first N natural numbers and the square of the sum. + +7. By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. + What is the Nth prime number? From 7284714d0d6fcf65ad9519d4491fba80b07bac59 Mon Sep 17 00:00:00 2001 From: Sachin Arora Date: Tue, 24 Oct 2017 21:11:19 +0530 Subject: [PATCH 59/73] Project Euler Solutions Added. --- Project Euler/Problem 01/sol1.py | 12 +++++++++ Project Euler/Problem 01/sol2.py | 15 ++++++++++++ Project Euler/Problem 01/sol3.py | 42 ++++++++++++++++++++++++++++++++ Project Euler/Problem 02/sol1.py | 18 ++++++++++++++ Project Euler/Problem 03/sol1.py | 38 +++++++++++++++++++++++++++++ Project Euler/Problem 03/sol2.py | 16 ++++++++++++ Project Euler/Problem 04/sol1.py | 15 ++++++++++++ Project Euler/Problem 04/sol2.py | 18 ++++++++++++++ Project Euler/Problem 05/sol1.py | 20 +++++++++++++++ Project Euler/Problem 06/sol1.py | 19 +++++++++++++++ Project Euler/Problem 06/sol2.py | 15 ++++++++++++ Project Euler/Problem 07/sol1.py | 29 ++++++++++++++++++++++ 12 files changed, 257 insertions(+) create mode 100644 Project Euler/Problem 01/sol1.py create mode 100644 Project Euler/Problem 01/sol2.py create mode 100644 Project Euler/Problem 01/sol3.py create mode 100644 Project Euler/Problem 02/sol1.py create mode 100644 Project Euler/Problem 03/sol1.py create mode 100644 Project Euler/Problem 03/sol2.py create mode 100644 Project Euler/Problem 04/sol1.py create mode 100644 Project Euler/Problem 04/sol2.py create mode 100644 Project Euler/Problem 05/sol1.py create mode 100644 Project Euler/Problem 06/sol1.py create mode 100644 Project Euler/Problem 06/sol2.py create mode 100644 Project Euler/Problem 07/sol1.py diff --git a/Project Euler/Problem 01/sol1.py b/Project Euler/Problem 01/sol1.py new file mode 100644 index 000000000..512154e29 --- /dev/null +++ b/Project Euler/Problem 01/sol1.py @@ -0,0 +1,12 @@ +''' +Problem Statement: +If we list all the natural numbers below 10 that are multiples of 3 or 5, +we get 3,5,6 and 9. The sum of these multiples is 23. +Find the sum of all the multiples of 3 or 5 below N. +''' +n = int(raw_input().strip()) +sum=0; +for a in range(3,n): + if(a%3==0 or a%5==0): + sum+=a +print sum; \ No newline at end of file diff --git a/Project Euler/Problem 01/sol2.py b/Project Euler/Problem 01/sol2.py new file mode 100644 index 000000000..5e368c220 --- /dev/null +++ b/Project Euler/Problem 01/sol2.py @@ -0,0 +1,15 @@ +''' +Problem Statement: +If we list all the natural numbers below 10 that are multiples of 3 or 5, +we get 3,5,6 and 9. The sum of these multiples is 23. +Find the sum of all the multiples of 3 or 5 below N. +''' +n = int(raw_input().strip()) +sum = 0 +terms = (n-1)/3 +sum+= ((terms)*(6+(terms-1)*3))/2 #sum of an A.P. +terms = (n-1)/5 +sum+= ((terms)*(10+(terms-1)*5))/2 +terms = (n-1)/15 +sum-= ((terms)*(30+(terms-1)*15))/2 +print sum \ No newline at end of file diff --git a/Project Euler/Problem 01/sol3.py b/Project Euler/Problem 01/sol3.py new file mode 100644 index 000000000..0caa30a53 --- /dev/null +++ b/Project Euler/Problem 01/sol3.py @@ -0,0 +1,42 @@ +''' +Problem Statement: +If we list all the natural numbers below 10 that are multiples of 3 or 5, +we get 3,5,6 and 9. The sum of these multiples is 23. +Find the sum of all the multiples of 3 or 5 below N. +''' +''' +This solution is based on the pattern that the successive numbers in the series follow: 0+3,+2,+1,+3,+1,+2,+3. +''' +n = int(raw_input().strip()) +sum=0; +num=0; +while(1): + num+=3 + if(num>=n): + break + sum+=num + num+=2 + if(num>=n): + break + sum+=num + num+=1 + if(num>=n): + break + sum+=num + num+=3 + if(num>=n): + break + sum+=num + num+=1 + if(num>=n): + break + sum+=num + num+=2 + if(num>=n): + break + sum+=num + num+=3 + if(num>=n): + break + sum+=num +print sum; \ No newline at end of file diff --git a/Project Euler/Problem 02/sol1.py b/Project Euler/Problem 02/sol1.py new file mode 100644 index 000000000..6cf520767 --- /dev/null +++ b/Project Euler/Problem 02/sol1.py @@ -0,0 +1,18 @@ +''' +Problem: +Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, +the first 10 terms will be: + 1,2,3,5,8,13,21,34,55,89,.. +By considering the terms in the Fibonacci sequence whose values do not exceed n, find the sum of the even-valued terms. +e.g. for n=10, we have {2,8}, sum is 10. +''' + +n = int(raw_input().strip()) +i=1; j=2; sum=0 +while(j<=n): + if((j&1)==0): #can also use (j%2==0) + sum+=j + temp=i + i=j + j=temp+i +print sum \ No newline at end of file diff --git a/Project Euler/Problem 03/sol1.py b/Project Euler/Problem 03/sol1.py new file mode 100644 index 000000000..bd3e237e7 --- /dev/null +++ b/Project Euler/Problem 03/sol1.py @@ -0,0 +1,38 @@ +''' +Problem: +The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor of a given number N? +e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17. +''' + +import math + +def isprime(no): + if(no==2): + return True + elif (no%2==0): + return False + sq = int(math.sqrt(no))+1 + for i in range(3,sq,2): + if(no%i==0): + return False + return True + +max=0 +n=int(input()) +if(isprime(n)): + print n +else: + while (n%2==0): + n=n/2 + if(isprime(n)): + print n + else: + n1 = int(math.sqrt(n))+1 + for i in range(3,n1,2): + if(n%i==0): + if(isprime(n/i)): + max=n/i + break + elif(isprime(i)): + max=i + print max diff --git a/Project Euler/Problem 03/sol2.py b/Project Euler/Problem 03/sol2.py new file mode 100644 index 000000000..2577892c4 --- /dev/null +++ b/Project Euler/Problem 03/sol2.py @@ -0,0 +1,16 @@ +''' +Problem: +The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor of a given number N? +e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17. +''' +n=int(input()) +prime=1 +i=2 +while(i*i<=n): + while(n%i==0): + prime=i + n/=i + i+=1 +if(n>1): + prime=n +print prime diff --git a/Project Euler/Problem 04/sol1.py b/Project Euler/Problem 04/sol1.py new file mode 100644 index 000000000..f8ed832d8 --- /dev/null +++ b/Project Euler/Problem 04/sol1.py @@ -0,0 +1,15 @@ +''' +Problem: +A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99. +Find the largest palindrome made from the product of two 3-digit numbers which is less than N. +''' +n=int(input()) +for i in range(n-1,10000,-1): + temp=str(i) + if(temp==temp[::-1]): + j=999 + while(j!=99): + if((i%j==0) and (len(str(i/j))==3)): + print i + exit(0) + j-=1 diff --git a/Project Euler/Problem 04/sol2.py b/Project Euler/Problem 04/sol2.py new file mode 100644 index 000000000..4d2006242 --- /dev/null +++ b/Project Euler/Problem 04/sol2.py @@ -0,0 +1,18 @@ +''' +Problem: +A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99. +Find the largest palindrome made from the product of two 3-digit numbers which is less than N. +''' +arr = [] +for i in range(999,100,-1): + for j in range(999,100,-1): + t = str(i*j) + if t == t[::-1]: + arr.append(i*j) +arr.sort() + +n=int(input()) +for i in arr[::-1]: + if(i Date: Wed, 25 Oct 2017 01:37:11 +0530 Subject: [PATCH 60/73] Added Dequeue in Python --- .gitignore | 91 + Graphs/a_star.py | 101 + Graphs/basic-graphs.py | 267 + License | 21 + Neural_Network/convolution_neural_network.py | 305 + Neural_Network/neuralnetwork_bp3.py | 152 + Neural_Network/perceptron.py | 123 + README.md | 174 + ciphers/Prehistoric Men.txt | 7193 + ciphers/affine_cipher.py | 76 + ciphers/brute-force_caesar_cipher.py | 53 + ciphers/caesar_cipher.py | 44 + ciphers/cryptomath_module.py | 14 + ciphers/playfair_cipher.py | 102 + ciphers/rabin_miller.py | 63 + ciphers/rsa_cipher.py | 124 + ciphers/rsa_key_generator.py | 45 + ciphers/simple_substitution_cipher.py | 70 + ciphers/transposition_cipher.py | 53 + ...ansposition_cipher_encrypt-decrypt_file.py | 35 + ciphers/vigenere_cipher.py | 60 + data_structures/AVL/AVL.py | 180 + data_structures/Arrays | 1 + data_structures/Binary Tree/FenwickTree.py | 28 + .../Binary Tree/LazySegmentTree.py | 90 + data_structures/Binary Tree/SegmentTree.py | 64 + .../Binary Tree/binary_seach_tree.py | 103 + data_structures/Graph/BreadthFirstSearch.py | 61 + data_structures/Graph/DepthFirstSearch.py | 61 + data_structures/Graph/Graph.py | 40 + data_structures/Graph/Graph_list.py | 28 + data_structures/Graph/Graph_matrix.py | 29 + data_structures/Graph/dijkstra_algorithm.py | 211 + data_structures/Heap/heap.py | 83 + .../LinkedList/DoublyLinkedList.py | 73 + data_structures/LinkedList/__init__.py | 22 + .../LinkedList/singly_LinkedList.py | 50 + data_structures/Queue/DeQueue.py | 39 + data_structures/Queue/QueueOnList.py | 45 + data_structures/Queue/QueueOnPseudoStack.py | 50 + data_structures/Queue/__init__.py | 0 data_structures/Stacks/__init__.py | 23 + .../Stacks/balanced_parentheses.py | 21 + .../Stacks/infix_to_postfix_conversion.py | 62 + data_structures/Stacks/next.py | 16 + data_structures/Stacks/stack.py | 68 + data_structures/Trie/Trie.py | 75 + data_structures/__init__.py | 0 dynamic_programming/FloydWarshall.py | 37 + dynamic_programming/edit_distance.py | 74 + dynamic_programming/fastfibonacci.py | 42 + dynamic_programming/fibonacci.py | 57 + .../k_means_clustering_tensorflow.py | 141 + dynamic_programming/knapsack.py | 14 + .../longest common subsequence.py | 48 + .../longest_increasing_subsequence.py | 41 + ...longest_increasing_subsequence_O(nlogn).py | 40 + dynamic_programming/longest_sub_array.py | 32 + dynamic_programming/max_sub_array.py | 59 + dynamic_programming/minimum_partition.py | 28 + hashes/md5.py | 107 + machine_learning/decision_tree.py | 139 + machine_learning/gradient_descent.py | 121 + machine_learning/k_means_clust.py | 172 + machine_learning/linear_regression.py | 108 + machine_learning/perceptron.py | 123 + machine_learning/scoring_functions.py | 63 + other/Dictionary.txt | 45333 +++ other/FindingPrimes.py | 18 + other/LinearCongruentialGenerator.py | 34 + other/anagrams.py | 28 + other/binary_exponentiation.py | 49 + other/binary_exponentiation_2.py | 50 + other/detecting_english_programmatically.py | 55 + other/euclidean_gcd.py | 18 + other/frequency_finder.py | 68 + other/nested_brackets.py | 49 + other/password_generator.py | 14 + other/tower_of_hanoi.py | 25 + other/word_patterns.py | 38 + other/words | 235886 +++++++++++++++ searches/binary_search.py | 162 + searches/interpolation_search.py | 102 + searches/linear_search.py | 62 + searches/quick_select.py | 47 + searches/ternary_search.py | 112 + sorts/bogosort.py | 53 + sorts/bubble_sort.py | 53 + sorts/bucket_sort.py | 56 + sorts/cocktail_shaker_sort.py | 36 + sorts/counting_sort.py | 72 + sorts/gnome_sort.py | 34 + sorts/heap_sort.py | 65 + sorts/insertion_sort.py | 53 + sorts/merge_sort.py | 76 + sorts/normal_distribution_QuickSort_README.md | 76 + sorts/quick_sort.py | 54 + sorts/radix_sort.py | 27 + sorts/random_normaldistribution_quicksort.py | 66 + sorts/selection_sort.py | 56 + sorts/shell_sort.py | 57 + sorts/sortinggraphs.png | Bin 0 -> 10362 bytes sorts/timsort.py | 81 + sorts/topological_sort.py | 32 + traversals/binary_tree_traversals.py | 109 + 105 files changed, 295341 insertions(+) create mode 100644 .gitignore create mode 100644 Graphs/a_star.py create mode 100644 Graphs/basic-graphs.py create mode 100644 License create mode 100644 Neural_Network/convolution_neural_network.py create mode 100644 Neural_Network/neuralnetwork_bp3.py create mode 100644 Neural_Network/perceptron.py create mode 100644 README.md create mode 100644 ciphers/Prehistoric Men.txt create mode 100644 ciphers/affine_cipher.py create mode 100644 ciphers/brute-force_caesar_cipher.py create mode 100644 ciphers/caesar_cipher.py create mode 100644 ciphers/cryptomath_module.py create mode 100644 ciphers/playfair_cipher.py create mode 100644 ciphers/rabin_miller.py create mode 100644 ciphers/rsa_cipher.py create mode 100644 ciphers/rsa_key_generator.py create mode 100644 ciphers/simple_substitution_cipher.py create mode 100644 ciphers/transposition_cipher.py create mode 100644 ciphers/transposition_cipher_encrypt-decrypt_file.py create mode 100644 ciphers/vigenere_cipher.py create mode 100644 data_structures/AVL/AVL.py create mode 100644 data_structures/Arrays create mode 100644 data_structures/Binary Tree/FenwickTree.py create mode 100644 data_structures/Binary Tree/LazySegmentTree.py create mode 100644 data_structures/Binary Tree/SegmentTree.py create mode 100644 data_structures/Binary Tree/binary_seach_tree.py create mode 100644 data_structures/Graph/BreadthFirstSearch.py create mode 100644 data_structures/Graph/DepthFirstSearch.py create mode 100644 data_structures/Graph/Graph.py create mode 100644 data_structures/Graph/Graph_list.py create mode 100644 data_structures/Graph/Graph_matrix.py create mode 100644 data_structures/Graph/dijkstra_algorithm.py create mode 100644 data_structures/Heap/heap.py create mode 100644 data_structures/LinkedList/DoublyLinkedList.py create mode 100644 data_structures/LinkedList/__init__.py create mode 100644 data_structures/LinkedList/singly_LinkedList.py create mode 100644 data_structures/Queue/DeQueue.py create mode 100644 data_structures/Queue/QueueOnList.py create mode 100644 data_structures/Queue/QueueOnPseudoStack.py create mode 100644 data_structures/Queue/__init__.py create mode 100644 data_structures/Stacks/__init__.py create mode 100644 data_structures/Stacks/balanced_parentheses.py create mode 100644 data_structures/Stacks/infix_to_postfix_conversion.py create mode 100644 data_structures/Stacks/next.py create mode 100644 data_structures/Stacks/stack.py create mode 100644 data_structures/Trie/Trie.py create mode 100644 data_structures/__init__.py create mode 100644 dynamic_programming/FloydWarshall.py create mode 100644 dynamic_programming/edit_distance.py create mode 100644 dynamic_programming/fastfibonacci.py create mode 100644 dynamic_programming/fibonacci.py create mode 100644 dynamic_programming/k_means_clustering_tensorflow.py create mode 100644 dynamic_programming/knapsack.py create mode 100644 dynamic_programming/longest common subsequence.py create mode 100644 dynamic_programming/longest_increasing_subsequence.py create mode 100644 dynamic_programming/longest_increasing_subsequence_O(nlogn).py create mode 100644 dynamic_programming/longest_sub_array.py create mode 100644 dynamic_programming/max_sub_array.py create mode 100644 dynamic_programming/minimum_partition.py create mode 100644 hashes/md5.py create mode 100644 machine_learning/decision_tree.py create mode 100644 machine_learning/gradient_descent.py create mode 100644 machine_learning/k_means_clust.py create mode 100644 machine_learning/linear_regression.py create mode 100644 machine_learning/perceptron.py create mode 100644 machine_learning/scoring_functions.py create mode 100644 other/Dictionary.txt create mode 100644 other/FindingPrimes.py create mode 100644 other/LinearCongruentialGenerator.py create mode 100644 other/anagrams.py create mode 100644 other/binary_exponentiation.py create mode 100644 other/binary_exponentiation_2.py create mode 100644 other/detecting_english_programmatically.py create mode 100644 other/euclidean_gcd.py create mode 100644 other/frequency_finder.py create mode 100644 other/nested_brackets.py create mode 100644 other/password_generator.py create mode 100644 other/tower_of_hanoi.py create mode 100644 other/word_patterns.py create mode 100644 other/words create mode 100644 searches/binary_search.py create mode 100644 searches/interpolation_search.py create mode 100644 searches/linear_search.py create mode 100644 searches/quick_select.py create mode 100644 searches/ternary_search.py create mode 100644 sorts/bogosort.py create mode 100644 sorts/bubble_sort.py create mode 100644 sorts/bucket_sort.py create mode 100644 sorts/cocktail_shaker_sort.py create mode 100644 sorts/counting_sort.py create mode 100644 sorts/gnome_sort.py create mode 100644 sorts/heap_sort.py create mode 100644 sorts/insertion_sort.py create mode 100644 sorts/merge_sort.py create mode 100644 sorts/normal_distribution_QuickSort_README.md create mode 100644 sorts/quick_sort.py create mode 100644 sorts/radix_sort.py create mode 100644 sorts/random_normaldistribution_quicksort.py create mode 100644 sorts/selection_sort.py create mode 100644 sorts/shell_sort.py create mode 100644 sorts/sortinggraphs.png create mode 100644 sorts/timsort.py create mode 100644 sorts/topological_sort.py create mode 100644 traversals/binary_tree_traversals.py diff --git a/.gitignore b/.gitignore new file mode 100644 index 000000000..96422cb2e --- /dev/null +++ b/.gitignore @@ -0,0 +1,91 @@ +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +env/ +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +*.egg-info/ +.installed.cfg +*.egg + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*,cover +.hypothesis/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# IPython Notebook +.ipynb_checkpoints + +# pyenv +.python-version + +# celery beat schedule file +celerybeat-schedule + +# dotenv +.env + +# virtualenv +venv/ +ENV/ + +# Spyder project settings +.spyderproject + +# Rope project settings +.ropeproject +.idea +.DS_Store \ No newline at end of file diff --git a/Graphs/a_star.py b/Graphs/a_star.py new file mode 100644 index 000000000..2ca9476e5 --- /dev/null +++ b/Graphs/a_star.py @@ -0,0 +1,101 @@ + +grid = [[0, 1, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0],#0 are free path whereas 1's are obstacles + [0, 1, 0, 0, 0, 0], + [0, 1, 0, 0, 1, 0], + [0, 0, 0, 0, 1, 0]] + +''' +heuristic = [[9, 8, 7, 6, 5, 4], + [8, 7, 6, 5, 4, 3], + [7, 6, 5, 4, 3, 2], + [6, 5, 4, 3, 2, 1], + [5, 4, 3, 2, 1, 0]]''' + +init = [0, 0] +goal = [len(grid)-1, len(grid[0])-1] #all coordinates are given in format [y,x] +cost = 1 + +#the cost map which pushes the path closer to the goal +heuristic = [[0 for row in range(len(grid[0]))] for col in range(len(grid))] +for i in range(len(grid)): + for j in range(len(grid[0])): + heuristic[i][j] = abs(i - goal[0]) + abs(j - goal[1]) + if grid[i][j] == 1: + heuristic[i][j] = 99 #added extra penalty in the heuristic map + + +#the actions we can take +delta = [[-1, 0 ], # go up + [ 0, -1], # go left + [ 1, 0 ], # go down + [ 0, 1 ]] # go right + + +#function to search the path +def search(grid,init,goal,cost,heuristic): + + closed = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]# the referrence grid + closed[init[0]][init[1]] = 1 + action = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]#the action grid + + x = init[0] + y = init[1] + g = 0 + f = g + heuristic[init[0]][init[0]] + cell = [[f, g, x, y]] + + found = False # flag that is set when search is complete + resign = False # flag set if we can't find expand + + while not found and not resign: + if len(cell) == 0: + resign = True + return "FAIL" + else: + cell.sort()#to choose the least costliest action so as to move closer to the goal + cell.reverse() + next = cell.pop() + x = next[2] + y = next[3] + g = next[1] + f = next[0] + + + if x == goal[0] and y == goal[1]: + found = True + else: + for i in range(len(delta)):#to try out different valid actions + x2 = x + delta[i][0] + y2 = y + delta[i][1] + if x2 >= 0 and x2 < len(grid) and y2 >=0 and y2 < len(grid[0]): + if closed[x2][y2] == 0 and grid[x2][y2] == 0: + g2 = g + cost + f2 = g2 + heuristic[x2][y2] + cell.append([f2, g2, x2, y2]) + closed[x2][y2] = 1 + action[x2][y2] = i + invpath = [] + x = goal[0] + y = goal[1] + invpath.append([x, y])#we get the reverse path from here + while x != init[0] or y != init[1]: + x2 = x - delta[action[x][y]][0] + y2 = y - delta[action[x][y]][1] + x = x2 + y = y2 + invpath.append([x, y]) + + path = [] + for i in range(len(invpath)): + path.append(invpath[len(invpath) - 1 - i]) + print "ACTION MAP" + for i in range(len(action)): + print action[i] + + return path + +a = search(grid,init,goal,cost,heuristic) +for i in range(len(a)): + print a[i] + diff --git a/Graphs/basic-graphs.py b/Graphs/basic-graphs.py new file mode 100644 index 000000000..fc78e5652 --- /dev/null +++ b/Graphs/basic-graphs.py @@ -0,0 +1,267 @@ +# Accept No. of Nodes and edges +n, m = map(int, raw_input().split(" ")) + +# Initialising Dictionary of edges +g = {} +for i in xrange(n): + g[i + 1] = [] + +""" +-------------------------------------------------------------------------------- + Accepting edges of Unweighted Directed Graphs +-------------------------------------------------------------------------------- +""" +for _ in xrange(m): + x, y = map(int, raw_input().split(" ")) + g[x].append(y) + +""" +-------------------------------------------------------------------------------- + Accepting edges of Unweighted Undirected Graphs +-------------------------------------------------------------------------------- +""" +for _ in xrange(m): + x, y = map(int, raw_input().split(" ")) + g[x].append(y) + g[y].append(x) + +""" +-------------------------------------------------------------------------------- + Accepting edges of Weighted Undirected Graphs +-------------------------------------------------------------------------------- +""" +for _ in xrange(m): + x, y, r = map(int, raw_input().split(" ")) + g[x].append([y, r]) + g[y].append([x, r]) + +""" +-------------------------------------------------------------------------------- + Depth First Search. + Args : G - Dictionary of edges + s - Starting Node + Vars : vis - Set of visited nodes + S - Traversal Stack +-------------------------------------------------------------------------------- +""" + + +def dfs(G, s): + vis, S = set([s]), [s] + print s + while S: + flag = 0 + for i in G[S[-1]]: + if i not in vis: + S.append(i) + vis.add(i) + flag = 1 + print i + break + if not flag: + S.pop() + + +""" +-------------------------------------------------------------------------------- + Breadth First Search. + Args : G - Dictionary of edges + s - Starting Node + Vars : vis - Set of visited nodes + Q - Traveral Stack +-------------------------------------------------------------------------------- +""" +from collections import deque + + +def bfs(G, s): + vis, Q = set([s]), deque([s]) + print s + while Q: + u = Q.popleft() + for v in G[u]: + if v not in vis: + vis.add(v) + Q.append(v) + print v + + +""" +-------------------------------------------------------------------------------- + Dijkstra's shortest path Algorithm + Args : G - Dictionary of edges + s - Starting Node + Vars : dist - Dictionary storing shortest distance from s to every other node + known - Set of knows nodes + path - Preceding node in path +-------------------------------------------------------------------------------- +""" + + +def dijk(G, s): + dist, known, path = {s: 0}, set(), {s: 0} + while True: + if len(known) == len(G) - 1: + break + mini = 100000 + for i in dist: + if i not in known and dist[i] < mini: + mini = dist[i] + u = i + known.add(u) + for v in G[u]: + if v[0] not in known: + if dist[u] + v[1] < dist.get(v[0], 100000): + dist[v[0]] = dist[u] + v[1] + path[v[0]] = u + for i in dist: + if i != s: + print dist[i] + + +""" +-------------------------------------------------------------------------------- + Topological Sort +-------------------------------------------------------------------------------- +""" +from collections import deque + + +def topo(G, ind=None, Q=[1]): + if ind == None: + ind = [0] * (len(G) + 1) # SInce oth Index is ignored + for u in G: + for v in G[u]: + ind[v] += 1 + Q = deque() + for i in G: + if ind[i] == 0: + Q.append(i) + if len(Q) == 0: + return + v = Q.popleft() + print v + for w in G[v]: + ind[w] -= 1 + if ind[w] == 0: + Q.append(w) + topo(G, ind, Q) + + +""" +-------------------------------------------------------------------------------- + Reading an Adjacency matrix +-------------------------------------------------------------------------------- +""" + + +def adjm(): + n, a = input(), [] + for i in xrange(n): + a.append(map(int, raw_input().split())) + return a, n + + +""" +-------------------------------------------------------------------------------- + Floyd Warshall's algorithm + Args : G - Dictionary of edges + s - Starting Node + Vars : dist - Dictionary storing shortest distance from s to every other node + known - Set of knows nodes + path - Preceding node in path + +-------------------------------------------------------------------------------- +""" + + +def floy((A, n)): + dist = list(A) + path = [[0] * n for i in xrange(n)] + for k in xrange(n): + for i in xrange(n): + for j in xrange(n): + if dist[i][j] > dist[i][k] + dist[k][j]: + dist[i][j] = dist[i][k] + dist[k][j] + path[i][k] = k + print dist + + +""" +-------------------------------------------------------------------------------- + Prim's MST Algorithm + Args : G - Dictionary of edges + s - Starting Node + Vars : dist - Dictionary storing shortest distance from s to nearest node + known - Set of knows nodes + path - Preceding node in path +-------------------------------------------------------------------------------- +""" + + +def prim(G, s): + dist, known, path = {s: 0}, set(), {s: 0} + while True: + if len(known) == len(G) - 1: + break + mini = 100000 + for i in dist: + if i not in known and dist[i] < mini: + mini = dist[i] + u = i + known.add(u) + for v in G[u]: + if v[0] not in known: + if v[1] < dist.get(v[0], 100000): + dist[v[0]] = v[1] + path[v[0]] = u + + +""" +-------------------------------------------------------------------------------- + Accepting Edge list + Vars : n - Number of nodes + m - Number of edges + Returns : l - Edge list + n - Number of Nodes +-------------------------------------------------------------------------------- +""" + + +def edglist(): + n, m = map(int, raw_input().split(" ")) + l = [] + for i in xrange(m): + l.append(map(int, raw_input().split(' '))) + return l, n + + +""" +-------------------------------------------------------------------------------- + Kruskal's MST Algorithm + Args : E - Edge list + n - Number of Nodes + Vars : s - Set of all nodes as unique disjoint sets (initially) +-------------------------------------------------------------------------------- +""" + + +def krusk((E, n)): + # Sort edges on the basis of distance + E.sort(reverse=True, key=lambda x: x[2]) + s = [set([i]) for i in range(1, n + 1)] + while True: + if len(s) == 1: + break + print s + x = E.pop() + for i in xrange(len(s)): + if x[0] in s[i]: + break + for j in xrange(len(s)): + if x[1] in s[j]: + if i == j: + break + s[j].update(s[i]) + s.pop(i) + break diff --git a/License b/License new file mode 100644 index 000000000..c84ae570c --- /dev/null +++ b/License @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2016 The Algorithms + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/Neural_Network/convolution_neural_network.py b/Neural_Network/convolution_neural_network.py new file mode 100644 index 000000000..d8ab0d2e5 --- /dev/null +++ b/Neural_Network/convolution_neural_network.py @@ -0,0 +1,305 @@ +#-*- coding: utf-8 -*- + +''' + - - - - - -- - - - - - - - - - - - - - - - - - - - - - - + Name - - CNN - Convolution Neural Network For Photo Recognizing + Goal - - Recognize Handing Writting Word Photo + Detail：Total 5 layers neural network + * Convolution layer + * Pooling layer + * Input layer layer of BP + * Hiden layer of BP + * Output layer of BP + Author: Stephen Lee + Github: 245885195@qq.com + Date: 2017.9.20 + - - - - - -- - - - - - - - - - - - - - - - - - - - - - - + ''' + +import numpy as np +import matplotlib.pyplot as plt + +class CNN(): + + def __init__(self,conv1_get,size_p1,bp_num1,bp_num2,bp_num3,rate_w=0.2,rate_t=0.2): + ''' + :param conv1_get: [a,c,d]，size, number, step of convolution kernel + :param size_p1: pooling size + :param bp_num1: units number of flatten layer + :param bp_num2: units number of hidden layer + :param bp_num3: units number of output layer + :param rate_w: rate of weight learning + :param rate_t: rate of threshold learning + ''' + self.num_bp1 = bp_num1 + self.num_bp2 = bp_num2 + self.num_bp3 = bp_num3 + self.conv1 = conv1_get[:2] + self.step_conv1 = conv1_get[2] + self.size_pooling1 = size_p1 + self.rate_weight = rate_w + self.rate_thre = rate_t + self.w_conv1 = [np.mat(-1*np.random.rand(self.conv1[0],self.conv1[0])+0.5) for i in range(self.conv1[1])] + self.wkj = np.mat(-1 * np.random.rand(self.num_bp3, self.num_bp2) + 0.5) + self.vji = np.mat(-1*np.random.rand(self.num_bp2, self.num_bp1)+0.5) + self.thre_conv1 = -2*np.random.rand(self.conv1[1])+1 + self.thre_bp2 = -2*np.random.rand(self.num_bp2)+1 + self.thre_bp3 = -2*np.random.rand(self.num_bp3)+1 + + + def save_model(self,save_path): + #save model dict with pickle + import pickle + model_dic = {'num_bp1':self.num_bp1, + 'num_bp2':self.num_bp2, + 'num_bp3':self.num_bp3, + 'conv1':self.conv1, + 'step_conv1':self.step_conv1, + 'size_pooling1':self.size_pooling1, + 'rate_weight':self.rate_weight, + 'rate_thre':self.rate_thre, + 'w_conv1':self.w_conv1, + 'wkj':self.wkj, + 'vji':self.vji, + 'thre_conv1':self.thre_conv1, + 'thre_bp2':self.thre_bp2, + 'thre_bp3':self.thre_bp3} + with open(save_path, 'wb') as f: + pickle.dump(model_dic, f) + + print('Model saved： %s'% save_path) + + @classmethod + def ReadModel(cls,model_path): + #read saved model + import pickle + with open(model_path, 'rb') as f: + model_dic = pickle.load(f) + + conv_get= model_dic.get('conv1') + conv_get.append(model_dic.get('step_conv1')) + size_p1 = model_dic.get('size_pooling1') + bp1 = model_dic.get('num_bp1') + bp2 = model_dic.get('num_bp2') + bp3 = model_dic.get('num_bp3') + r_w = model_dic.get('rate_weight') + r_t = model_dic.get('rate_thre') + #create model instance + conv_ins = CNN(conv_get,size_p1,bp1,bp2,bp3,r_w,r_t) + #modify model parameter + conv_ins.w_conv1 = model_dic.get('w_conv1') + conv_ins.wkj = model_dic.get('wkj') + conv_ins.vji = model_dic.get('vji') + conv_ins.thre_conv1 = model_dic.get('thre_conv1') + conv_ins.thre_bp2 = model_dic.get('thre_bp2') + conv_ins.thre_bp3 = model_dic.get('thre_bp3') + return conv_ins + + + def sig(self,x): + return 1 / (1 + np.exp(-1*x)) + + def do_round(self,x): + return round(x, 3) + + def convolute(self,data,convs,w_convs,thre_convs,conv_step): + #convolution process + size_conv = convs[0] + num_conv =convs[1] + size_data = np.shape(data)[0] + #get the data slice of original image data, data_focus + data_focus = [] + for i_focus in range(0, size_data - size_conv + 1, conv_step): + for j_focus in range(0, size_data - size_conv + 1, conv_step): + focus = data[i_focus:i_focus + size_conv, j_focus:j_focus + size_conv] + data_focus.append(focus) + #caculate the feature map of every single kernel, and saved as list of matrix + data_featuremap = [] + Size_FeatureMap = int((size_data - size_conv) / conv_step + 1) + for i_map in range(num_conv): + featuremap = [] + for i_focus in range(len(data_focus)): + net_focus = np.sum(np.multiply(data_focus[i_focus], w_convs[i_map])) - thre_convs[i_map] + featuremap.append(self.sig(net_focus)) + featuremap = np.asmatrix(featuremap).reshape(Size_FeatureMap, Size_FeatureMap) + data_featuremap.append(featuremap) + + #expanding the data slice to One dimenssion + focus1_list = [] + for each_focus in data_focus: + focus1_list.extend(self.Expand_Mat(each_focus)) + focus_list = np.asarray(focus1_list) + return focus_list,data_featuremap + + def pooling(self,featuremaps,size_pooling,type='average_pool'): + #pooling process + size_map = len(featuremaps[0]) + size_pooled = int(size_map/size_pooling) + featuremap_pooled = [] + for i_map in range(len(featuremaps)): + map = featuremaps[i_map] + map_pooled = [] + for i_focus in range(0,size_map,size_pooling): + for j_focus in range(0, size_map, size_pooling): + focus = map[i_focus:i_focus + size_pooling, j_focus:j_focus + size_pooling] + if type == 'average_pool': + #average pooling + map_pooled.append(np.average(focus)) + elif type == 'max_pooling': + #max pooling + map_pooled.append(np.max(focus)) + map_pooled = np.asmatrix(map_pooled).reshape(size_pooled,size_pooled) + featuremap_pooled.append(map_pooled) + return featuremap_pooled + + def _expand(self,datas): + #expanding three dimension data to one dimension list + data_expanded = [] + for i in range(len(datas)): + shapes = np.shape(datas[i]) + data_listed = datas[i].reshape(1,shapes[0]*shapes[1]) + data_listed = data_listed.getA().tolist()[0] + data_expanded.extend(data_listed) + data_expanded = np.asarray(data_expanded) + return data_expanded + + def _expand_mat(self,data_mat): + #expanding matrix to one dimension list + data_mat = np.asarray(data_mat) + shapes = np.shape(data_mat) + data_expanded = data_mat.reshape(1,shapes[0]*shapes[1]) + return data_expanded + + def _calculate_gradient_from_pool(self,out_map,pd_pool,num_map,size_map,size_pooling): + ''' + calcluate the gradient from the data slice of pool layer + pd_pool: list of matrix + out_map: the shape of data slice(size_map*size_map) + return: pd_all: list of matrix, [num, size_map, size_map] + ''' + pd_all = [] + i_pool = 0 + for i_map in range(num_map): + pd_conv1 = np.ones((size_map, size_map)) + for i in range(0, size_map, size_pooling): + for j in range(0, size_map, size_pooling): + pd_conv1[i:i + size_pooling, j:j + size_pooling] = pd_pool[i_pool] + i_pool = i_pool + 1 + pd_conv2 = np.multiply(pd_conv1,np.multiply(out_map[i_map],(1-out_map[i_map]))) + pd_all.append(pd_conv2) + return pd_all + + def trian(self,patterns,datas_train, datas_teach, n_repeat, error_accuracy,draw_e = bool): + #model traning + print('----------------------Start Training-------------------------') + print(' - - Shape: Train_Data ',np.shape(datas_train)) + print(' - - Shape: Teach_Data ',np.shape(datas_teach)) + rp = 0 + all_mse = [] + mse = 10000 + while rp < n_repeat and mse >= error_accuracy: + alle = 0 + print('-------------Learning Time %d--------------'%rp) + for p in range(len(datas_train)): + #print('------------Learning Image: %d--------------'%p) + data_train = np.asmatrix(datas_train[p]) + data_teach = np.asarray(datas_teach[p]) + data_focus1,data_conved1 = self.convolute(data_train,self.conv1,self.w_conv1, + self.thre_conv1,conv_step=self.step_conv1) + data_pooled1 = self.pooling(data_conved1,self.size_pooling1) + shape_featuremap1 = np.shape(data_conved1) + ''' + print(' -----original shape ', np.shape(data_train)) + print(' ---- after convolution ',np.shape(data_conv1)) + print(' -----after pooling ',np.shape(data_pooled1)) + ''' + data_bp_input = self._expand(data_pooled1) + bp_out1 = data_bp_input + + bp_net_j = np.dot(bp_out1,self.vji.T) - self.thre_bp2 + bp_out2 = self.sig(bp_net_j) + bp_net_k = np.dot(bp_out2 ,self.wkj.T) - self.thre_bp3 + bp_out3 = self.sig(bp_net_k) + + #--------------Model Leaning ------------------------ + # calcluate error and gradient--------------- + pd_k_all = np.multiply((data_teach - bp_out3), np.multiply(bp_out3, (1 - bp_out3))) + pd_j_all = np.multiply(np.dot(pd_k_all,self.wkj), np.multiply(bp_out2, (1 - bp_out2))) + pd_i_all = np.dot(pd_j_all,self.vji) + + pd_conv1_pooled = pd_i_all / (self.size_pooling1*self.size_pooling1) + pd_conv1_pooled = pd_conv1_pooled.T.getA().tolist() + pd_conv1_all = self._calculate_gradient_from_pool(data_conved1,pd_conv1_pooled,shape_featuremap1[0], + shape_featuremap1[1],self.size_pooling1) + #weight and threshold learning process--------- + #convolution layer + for k_conv in range(self.conv1[1]): + pd_conv_list = self._expand_mat(pd_conv1_all[k_conv]) + delta_w = self.rate_weight * np.dot(pd_conv_list,data_focus1) + + self.w_conv1[k_conv] = self.w_conv1[k_conv] + delta_w.reshape((self.conv1[0],self.conv1[0])) + + self.thre_conv1[k_conv] = self.thre_conv1[k_conv] - np.sum(pd_conv1_all[k_conv]) * self.rate_thre + #all connected layer + self.wkj = self.wkj + pd_k_all.T * bp_out2 * self.rate_weight + self.vji = self.vji + pd_j_all.T * bp_out1 * self.rate_weight + self.thre_bp3 = self.thre_bp3 - pd_k_all * self.rate_thre + self.thre_bp2 = self.thre_bp2 - pd_j_all * self.rate_thre + # calculate the sum error of all single image + errors = np.sum(abs((data_teach - bp_out3))) + alle = alle + errors + #print(' ----Teach ',data_teach) + #print(' ----BP_output ',bp_out3) + rp = rp + 1 + mse = alle/patterns + all_mse.append(mse) + def draw_error(): + yplot = [error_accuracy for i in range(int(n_repeat * 1.2))] + plt.plot(all_mse, '+-') + plt.plot(yplot, 'r--') + plt.xlabel('Learning Times') + plt.ylabel('All_mse') + plt.grid(True, alpha=0.5) + plt.show() + print('------------------Training Complished---------------------') + print(' - - Training epoch: ', rp, ' - - Mse: %.6f' % mse) + if draw_e: + draw_error() + return mse + + def predict(self,datas_test): + #model predict + produce_out = [] + print('-------------------Start Testing-------------------------') + print(' - - Shape: Test_Data ',np.shape(datas_test)) + for p in range(len(datas_test)): + data_test = np.asmatrix(datas_test[p]) + data_focus1, data_conved1 = self.convolute(data_test, self.conv1, self.w_conv1, + self.thre_conv1, conv_step=self.step_conv1) + data_pooled1 = self.pooling(data_conved1, self.size_pooling1) + data_bp_input = self._expand(data_pooled1) + + bp_out1 = data_bp_input + bp_net_j = bp_out1 * self.vji.T - self.thre_bp2 + bp_out2 = self.sig(bp_net_j) + bp_net_k = bp_out2 * self.wkj.T - self.thre_bp3 + bp_out3 = self.sig(bp_net_k) + produce_out.extend(bp_out3.getA().tolist()) + res = [list(map(self.do_round,each)) for each in produce_out] + return np.asarray(res) + + def convolution(self,data): + #return the data of image after convoluting process so we can check it out + data_test = np.asmatrix(data) + data_focus1, data_conved1 = self.convolute(data_test, self.conv1, self.w_conv1, + self.thre_conv1, conv_step=self.step_conv1) + data_pooled1 = self.pooling(data_conved1, self.size_pooling1) + + return data_conved1,data_pooled1 + + +if __name__ == '__main__': + pass + ''' + I will put the example on other file + ''' \ No newline at end of file diff --git a/Neural_Network/neuralnetwork_bp3.py b/Neural_Network/neuralnetwork_bp3.py new file mode 100644 index 000000000..896411a5d --- /dev/null +++ b/Neural_Network/neuralnetwork_bp3.py @@ -0,0 +1,152 @@ +#-*- coding:utf-8 -*- +''' +Author: Stephen Lee +Date: 2017.9.21 + +BP neural network with three layers +''' + +import numpy as np +import matplotlib.pyplot as plt + +class Bpnn(): + + def __init__(self,n_layer1,n_layer2,n_layer3,rate_w=0.3,rate_t=0.3): + ''' + :param n_layer1: number of input layer + :param n_layer2: number of hiden layer + :param n_layer3: number of output layer + :param rate_w: rate of weight learning + :param rate_t: rate of threshold learning + ''' + self.num1 = n_layer1 + self.num2 = n_layer2 + self.num3 = n_layer3 + self.rate_weight = rate_w + self.rate_thre = rate_t + self.thre2 = -2*np.random.rand(self.num2)+1 + self.thre3 = -2*np.random.rand(self.num3)+1 + self.vji = np.mat(-2*np.random.rand(self.num2, self.num1)+1) + self.wkj = np.mat(-2*np.random.rand(self.num3, self.num2)+1) + + def sig(self,x): + return 1 / (1 + np.exp(-1*x)) + + def sig_plain(self,x): + return 1 / (1 + np.exp(-1*x)) + + def do_round(self,x): + return round(x, 3) + + def trian(self,patterns,data_train, data_teach, n_repeat, error_accuracy, draw_e=False): + ''' + :param patterns: the number of patterns + :param data_train: training data x; numpy.ndarray + :param data_teach: training data y; numpy.ndarray + :param n_repeat: echoes + :param error_accuracy: error accuracy + :return: None + ''' + data_train = np.asarray(data_train) + data_teach = np.asarray(data_teach) + # print('-------------------Start Training-------------------------') + # print(' - - Shape: Train_Data ',np.shape(data_train)) + # print(' - - Shape: Teach_Data ',np.shape(data_teach)) + rp = 0 + all_mse = [] + mse = 10000 + while rp < n_repeat and mse >= error_accuracy: + alle = 0 + final_out = [] + for g in range(np.shape(data_train)[0]): + net_i = data_train[g] + out1 = net_i + + net_j = out1 * self.vji.T - self.thre2 + out2=self.sig(net_j) + + net_k = out2 * self.wkj.T - self.thre3 + out3 = self.sig(net_k) + + # learning process + pd_k_all = np.multiply(np.multiply(out3,(1 - out3)),(data_teach[g]-out3)) + pd_j_all = np.multiply(pd_k_all * self.wkj,np.multiply(out2,1-out2)) + #upgrade weight + self.wkj = self.wkj + pd_k_all.T * out2 *self.rate_weight + self.vji = self.vji + pd_j_all.T * out1 * self.rate_weight + #upgrade threshold + self.thre3 = self.thre3 - pd_k_all * self.rate_thre + self.thre2 = self.thre2 - pd_j_all * self.rate_thre + #calculate sum of error + errors = np.sum(abs((data_teach[g] - out3))) + + alle = alle + errors + final_out.extend(out3.getA().tolist()) + final_out3 = [list(map(self.do_round,each)) for each in final_out] + + rp = rp + 1 + mse = alle/patterns + all_mse.append(mse) + def draw_error(): + yplot = [error_accuracy for i in range(int(n_repeat * 1.2))] + plt.plot(all_mse, '+-') + plt.plot(yplot, 'r--') + plt.xlabel('Learning Times') + plt.ylabel('All_mse') + plt.grid(True,alpha = 0.7) + plt.show() + # print('------------------Training Complished---------------------') + # print(' - - Training epoch: ', rp, ' - - Mse: %.6f'%mse) + # print(' - - Last Output: ', final_out3) + if draw_e: + draw_error() + + def predict(self,data_test): + ''' + :param data_test: data test, numpy.ndarray + :return: predict output data + ''' + data_test = np.asarray(data_test) + produce_out = [] + # print('-------------------Start Testing-------------------------') + # print(' - - Shape: Test_Data ',np.shape(data_test)) + # print(np.shape(data_test)) + for g in range(np.shape(data_test)[0]): + + net_i = data_test[g] + out1 = net_i + + net_j = out1 * self.vji.T - self.thre2 + out2 = self.sig(net_j) + + net_k = out2 * self.wkj.T - self.thre3 + out3 = self.sig(net_k) + produce_out.extend(out3.getA().tolist()) + res = [list(map(self.do_round,each)) for each in produce_out] + return np.asarray(res) + + +def main(): + #example data + data_x = [[1,2,3,4], + [5,6,7,8], + [2,2,3,4], + [7,7,8,8]] + data_y = [[1,0,0,0], + [0,1,0,0], + [0,0,1,0], + [0,0,0,1]] + + test_x = [[1,2,3,4], + [3,2,3,4]] + + #building network model + model = Bpnn(4,10,4) + #training the model + model.trian(patterns=4,data_train=data_x,data_teach=data_y, + n_repeat=100,error_accuracy=0.1,draw_e=True) + #predicting data + model.predict(test_x) + +if __name__ == '__main__': + main() diff --git a/Neural_Network/perceptron.py b/Neural_Network/perceptron.py new file mode 100644 index 000000000..0cd89df16 --- /dev/null +++ b/Neural_Network/perceptron.py @@ -0,0 +1,123 @@ +''' + + Perceptron + w = w + N * (d(k) - y) * x(k) + + Using perceptron network for oil analysis, + with Measuring of 3 parameters that represent chemical characteristics we can classify the oil, in p1 or p2 + p1 = -1 + p2 = 1 + +''' + +import random + + +class Perceptron: + def __init__(self, sample, exit, learn_rate=0.01, epoch_number=1000, bias=-1): + self.sample = sample + self.exit = exit + self.learn_rate = learn_rate + self.epoch_number = epoch_number + self.bias = bias + self.number_sample = len(sample) + self.col_sample = len(sample[0]) + self.weight = [] + + def trannig(self): + for sample in self.sample: + sample.insert(0, self.bias) + + for i in range(self.col_sample): + self.weight.append(random.random()) + + self.weight.insert(0, self.bias) + + epoch_count = 0 + + while True: + erro = False + for i in range(self.number_sample): + u = 0 + for j in range(self.col_sample + 1): + u = u + self.weight[j] * self.sample[i][j] + y = self.sign(u) + if y != self.exit[i]: + + for j in range(self.col_sample + 1): + + self.weight[j] = self.weight[j] + self.learn_rate * (self.exit[i] - y) * self.sample[i][j] + erro = True + #print('Epoch: \n',epoch_count) + epoch_count = epoch_count + 1 + # if you want controle the epoch or just by erro + if erro == False: + print('\nEpoch:\n',epoch_count) + print('------------------------\n') + #if epoch_count > self.epoch_number or not erro: + break + + def sort(self, sample): + sample.insert(0, self.bias) + u = 0 + for i in range(self.col_sample + 1): + u = u + self.weight[i] * sample[i] + + y = self.sign(u) + + if y == -1: + print('Sample: ', sample) + print('classification: P1') + else: + print('Sample: ', sample) + print('classification: P2') + + def sign(self, u): + return 1 if u >= 0 else -1 + + +samples = [ + [-0.6508, 0.1097, 4.0009], + [-1.4492, 0.8896, 4.4005], + [2.0850, 0.6876, 12.0710], + [0.2626, 1.1476, 7.7985], + [0.6418, 1.0234, 7.0427], + [0.2569, 0.6730, 8.3265], + [1.1155, 0.6043, 7.4446], + [0.0914, 0.3399, 7.0677], + [0.0121, 0.5256, 4.6316], + [-0.0429, 0.4660, 5.4323], + [0.4340, 0.6870, 8.2287], + [0.2735, 1.0287, 7.1934], + [0.4839, 0.4851, 7.4850], + [0.4089, -0.1267, 5.5019], + [1.4391, 0.1614, 8.5843], + [-0.9115, -0.1973, 2.1962], + [0.3654, 1.0475, 7.4858], + [0.2144, 0.7515, 7.1699], + [0.2013, 1.0014, 6.5489], + [0.6483, 0.2183, 5.8991], + [-0.1147, 0.2242, 7.2435], + [-0.7970, 0.8795, 3.8762], + [-1.0625, 0.6366, 2.4707], + [0.5307, 0.1285, 5.6883], + [-1.2200, 0.7777, 1.7252], + [0.3957, 0.1076, 5.6623], + [-0.1013, 0.5989, 7.1812], + [2.4482, 0.9455, 11.2095], + [2.0149, 0.6192, 10.9263], + [0.2012, 0.2611, 5.4631] + +] + +exit = [-1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1] + +network = Perceptron(sample=samples, exit = exit, learn_rate=0.01, epoch_number=1000, bias=-1) + +network.trannig() + +while True: + sample = [] + for i in range(3): + sample.insert(i, float(input('value: '))) + network.sort(sample) \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 000000000..70077e98f --- /dev/null +++ b/README.md @@ -0,0 +1,174 @@ +# The Algorithms - Python + +### All algorithms implemented in Python (for education) + +These are for demonstration purposes only. There are many implementations of sorts in the Python standard library that are much better for performance reasons. + +## Sort Algorithms + + +### Bubble +![alt text][bubble-image] + +From [Wikipedia][bubble-wiki]: Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the list to be sorted, compares each pair of adjacent items and swaps them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the list is sorted. + +__Properties__ +* Worst case performance O(n^2) +* Best case performance O(n) +* Average case performance O(n^2) + +###### View the algorithm in [action][bubble-toptal] + + + +### Insertion +![alt text][insertion-image] + +From [Wikipedia][insertion-wiki]: Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. + +__Properties__ +* Worst case performance O(n^2) +* Best case performance O(n) +* Average case performance O(n^2) + +###### View the algorithm in [action][insertion-toptal] + + +### Merge +![alt text][merge-image] + +From [Wikipedia][merge-wiki]: In computer science, merge sort (also commonly spelled mergesort) is an efficient, general-purpose, comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. Mergesort is a divide and conquer algorithm that was invented by John von Neumann in 1945. + +__Properties__ +* Worst case performance O(n log n) +* Best case performance O(n) +* Average case performance O(n) + + +###### View the algorithm in [action][merge-toptal] + +### Quick +![alt text][quick-image] + +From [Wikipedia][quick-wiki]: Quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order. + +__Properties__ +* Worst case performance O(n^2) +* Best case performance O(n log n) or O(n) with three-way partition +* Average case performance O(n^2) + +###### View the algorithm in [action][quick-toptal] + +### Selection +![alt text][selection-image] + +From [Wikipedia][selection-wiki]: The algorithm divides the input list into two parts: the sublist of items already sorted, which is built up from left to right at the front (left) of the list, and the sublist of items remaining to be sorted that occupy the rest of the list. Initially, the sorted sublist is empty and the unsorted sublist is the entire input list. The algorithm proceeds by finding the smallest (or largest, depending on sorting order) element in the unsorted sublist, exchanging (swapping) it with the leftmost unsorted element (putting it in sorted order), and moving the sublist boundaries one element to the right. + +__Properties__ +* Worst case performance O(n^2) +* Best case performance O(n^2) +* Average case performance O(n^2) + +###### View the algorithm in [action][selection-toptal] + +### Shell +![alt text][shell-image] + +From [Wikipedia][shell-wiki]: Shellsort is a generalization of insertion sort that allows the exchange of items that are far apart. The idea is to arrange the list of elements so that, starting anywhere, considering every nth element gives a sorted list. Such a list is said to be h-sorted. Equivalently, it can be thought of as h interleaved lists, each individually sorted. + +__Properties__ +* Worst case performance O(nlog2 2n) +* Best case performance O(n log n) +* Average case performance depends on gap sequence + +###### View the algorithm in [action][shell-toptal] + +### Time-Compexity Graphs + +Comparing the complexity of sorting algorithms (Bubble Sort, Insertion Sort, Selection Sort) + +[Complexity Graphs](https://github.com/prateekiiest/Python/blob/master/sorts/sortinggraphs.png) + +---------------------------------------------------------------------------------- + +## Search Algorithms + +### Linear +![alt text][linear-image] + +From [Wikipedia][linear-wiki]: linear search or sequential search is a method for finding a target value within a list. It sequentially checks each element of the list for the target value until a match is found or until all the elements have been searched. + Linear search runs in at worst linear time and makes at most n comparisons, where n is the length of the list. + +__Properties__ +* Worst case performance O(n) +* Best case performance O(1) +* Average case performance O(n) +* Worst case space complexity O(1) iterative + +### Binary +![alt text][binary-image] + +From [Wikipedia][binary-wiki]: Binary search, also known as half-interval search or logarithmic search, is a search algorithm that finds the position of a target value within a sorted array. It compares the target value to the middle element of the array; if they are unequal, the half in which the target cannot lie is eliminated and the search continues on the remaining half until it is successful. + +__Properties__ +* Worst case performance O(log n) +* Best case performance O(1) +* Average case performance O(log n) +* Worst case space complexity O(1) + +---------------------------------------------------------------------------------------------------------------------- + +## Ciphers + +### Caesar +![alt text][caesar]
+In cryptography, a **Caesar cipher**, also known as Caesar's cipher, the shift cipher, Caesar's code or Caesar shift, is one of the simplest and most widely known encryption techniques.
+It is **a type of substitution cipher** in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. For example, with a left shift of 3, D would be replaced by A, E would become B, and so on.
+The method is named after **Julius Caesar**, who used it in his private correspondence.
+The encryption step performed by a Caesar cipher is often incorporated as part of more complex schemes, such as the Vigenère cipher, and still has modern application in the ROT13 system. As with all single-alphabet substitution ciphers, the Caesar cipher is easily broken and in modern practice offers essentially no communication security. +###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Caesar_cipher) + +### Vigenère +The **Vigenère cipher** is a method of encrypting alphabetic text by using a series of **interwoven Caesar ciphers** based on the letters of a keyword. It is **a form of polyalphabetic substitution**.
+The Vigenère cipher has been reinvented many times. The method was originally described by Giovan Battista Bellaso in his 1553 book La cifra del. Sig. Giovan Battista Bellaso; however, the scheme was later misattributed to Blaise de Vigenère in the 19th century, and is now widely known as the "Vigenère cipher".
+Though the cipher is easy to understand and implement, for three centuries it resisted all attempts to break it; this earned it the description **le chiffre indéchiffrable**(French for 'the indecipherable cipher'). +Many people have tried to implement encryption schemes that are essentially Vigenère ciphers. Friedrich Kasiski was the first to publish a general method of deciphering a Vigenère cipher in 1863. +###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher) + +### Transposition +In cryptography, a **transposition cipher** is a method of encryption by which the positions held by units of plaintext (which are commonly characters or groups of characters) are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext. That is, the order of the units is changed (the plaintext is reordered).
+Mathematically a bijective function is used on the characters' positions to encrypt and an inverse function to decrypt. +###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Transposition_cipher) + +[bubble-toptal]: https://www.toptal.com/developers/sorting-algorithms/bubble-sort +[bubble-wiki]: https://en.wikipedia.org/wiki/Bubble_sort +[bubble-image]: https://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Bubblesort-edited-color.svg/220px-Bubblesort-edited-color.svg.png "Bubble Sort" + +[insertion-toptal]: https://www.toptal.com/developers/sorting-algorithms/insertion-sort +[insertion-wiki]: https://en.wikipedia.org/wiki/Insertion_sort +[insertion-image]: https://upload.wikimedia.org/wikipedia/commons/7/7e/Insertionsort-edited.png "Insertion Sort" + +[quick-toptal]: https://www.toptal.com/developers/sorting-algorithms/quick-sort +[quick-wiki]: https://en.wikipedia.org/wiki/Quicksort +[quick-image]: https://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif "Quick Sort" + +[merge-toptal]: https://www.toptal.com/developers/sorting-algorithms/merge-sort +[merge-wiki]: https://en.wikipedia.org/wiki/Merge_sort +[merge-image]: https://upload.wikimedia.org/wikipedia/commons/c/cc/Merge-sort-example-300px.gif "Merge Sort" + +[selection-toptal]: https://www.toptal.com/developers/sorting-algorithms/selection-sort +[selection-wiki]: https://en.wikipedia.org/wiki/Selection_sort +[selection-image]: https://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Selection_sort_animation.gif/250px-Selection_sort_animation.gif "Selection Sort Sort" + +[shell-toptal]: https://www.toptal.com/developers/sorting-algorithms/shell-sort +[shell-wiki]: https://en.wikipedia.org/wiki/Shellsort +[shell-image]: https://upload.wikimedia.org/wikipedia/commons/d/d8/Sorting_shellsort_anim.gif "Shell Sort" + +[linear-wiki]: https://en.wikipedia.org/wiki/Linear_search +[linear-image]: http://www.tutorialspoint.com/data_structures_algorithms/images/linear_search.gif + +[binary-wiki]: https://en.wikipedia.org/wiki/Binary_search_algorithm +[binary-image]: https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_search_into_array.png + + +[caesar]: https://upload.wikimedia.org/wikipedia/commons/4/4a/Caesar_cipher_left_shift_of_3.svg diff --git a/ciphers/Prehistoric Men.txt b/ciphers/Prehistoric Men.txt new file mode 100644 index 000000000..86c4de821 --- /dev/null +++ b/ciphers/Prehistoric Men.txt @@ -0,0 +1,7193 @@ +The Project Gutenberg eBook, Prehistoric Men, by Robert J. (Robert John) +Braidwood, Illustrated by Susan T. Richert + + +This eBook is for the use of anyone anywhere in the United States and most +other parts of the world at no cost and with almost no restrictions +whatsoever. You may copy it, give it away or re-use it under the terms of +the Project Gutenberg License included with this eBook or online at +www.gutenberg.org. If you are not located in the United States, you'll have +to check the laws of the country where you are located before using this ebook. + + +Title: Prehistoric Men +Author: Robert J. (Robert John) Braidwood +Release Date: July 28, 2016 [eBook #52664] +Language: English +Character set encoding: UTF-8 + + +***START OF THE PROJECT GUTENBERG EBOOK PREHISTORIC MEN*** + + +E-text prepared by Stephen Hutcheson, Dave Morgan, Charlie Howard, and the +Online Distributed Proofreading Team (http://www.pgdp.net) + + + +Note: Project Gutenberg also has an HTML version of this + file which includes the original illustrations. + See 52664-h.htm or 52664-h.zip: + (http://www.gutenberg.org/files/52664/52664-h/52664-h.htm) + or + (http://www.gutenberg.org/files/52664/52664-h.zip) + + +Transcriber's note: + + Some characters might not display in this UTF-8 text + version. If so, the reader should consult the HTML + version referred to above. One example of this might + occur in the second paragraph under "Choppers and + Adze-like Tools", page 46, which contains the phrase + an adze cutting edge is ? shaped. The symbol before + shaped looks like a sharply-italicized sans-serif L. + Devices that cannot display that symbol may substitute + a question mark, a square, or other symbol. + + +PREHISTORIC MEN + +by + +ROBERT J. BRAIDWOOD + +Research Associate, Old World Prehistory + +Professor +Oriental Institute and Department of Anthropology +University of Chicago + +Drawings by Susan T. Richert + + +[Illustration] + +Chicago Natural History Museum +Popular Series +Anthropology, Number 37 + +Third Edition Issued in Co-operation with +The Oriental Institute, The University of Chicago + +Edited by Lillian A. Ross + +Printed in the United States of America +by Chicago Natural History Museum Press + +Copyright 1948, 1951, and 1957 by Chicago Natural History Museum + +First edition 1948 +Second edition 1951 +Third edition 1957 +Fourth edition 1959 + + +Preface + +[Illustration] + + +Like the writing of most professional archeologists, mine has been +confined to so-called learned papers. Good, bad, or indifferent, these +papers were in a jargon that only my colleagues and a few advanced +students could understand. Hence, when I was asked to do this little +book, I soon found it extremely difficult to say what I meant in simple +fashion. The style is new to me, but I hope the reader will not find it +forced or pedantic; at least I have done my very best to tell the story +simply and clearly. + +Many friends have aided in the preparation of the book. The whimsical +charm of Miss Susan Richerts illustrations add enormously to the +spirit I wanted. She gave freely of her own time on the drawings and +in planning the book with me. My colleagues at the University of +Chicago, especially Professor Wilton M. Krogman (now of the University +of Pennsylvania), and also Mrs. Linda Braidwood, Associate of the +Oriental Institute, and Professors Fay-Cooper Cole and Sol Tax, of +the Department of Anthropology, gave me counsel in matters bearing on +their special fields, and the Department of Anthropology bore some of +the expense of the illustrations. From Mrs. Irma Hunter and Mr. Arnold +Maremont, who are not archeologists at all and have only an intelligent +laymans notion of archeology, I had sound advice on how best to tell +the story. I am deeply indebted to all these friends. + +While I was preparing the second edition, I had the great fortune +to be able to rework the third chapter with Professor Sherwood L. +Washburn, now of the Department of Anthropology of the University of +California, and the fourth, fifth, and sixth chapters with Professor +Hallum L. Movius, Jr., of the Peabody Museum, Harvard University. The +book has gained greatly in accuracy thereby. In matters of dating, +Professor Movius and the indications of Professor W. F. Libbys Carbon +14 chronology project have both encouraged me to choose the lowest +dates now current for the events of the Pleistocene Ice Age. There is +still no certain way of fixing a direct chronology for most of the +Pleistocene, but Professor Libbys method appears very promising for +its end range and for proto-historic dates. In any case, this book +names periods, and new dates may be written in against mine, if new +and better dating systems appear. + +I wish to thank Dr. Clifford C. Gregg, Director of Chicago Natural +History Museum, for the opportunity to publish this book. My old +friend, Dr. Paul S. Martin, Chief Curator in the Department of +Anthropology, asked me to undertake the job and inspired me to complete +it. I am also indebted to Miss Lillian A. Ross, Associate Editor of +Scientific Publications, and to Mr. George I. Quimby, Curator of +Exhibits in Anthropology, for all the time they have given me in +getting the manuscript into proper shape. + + ROBERT J. BRAIDWOOD + _June 15, 1950_ + + + + +Preface to the Third Edition + + +In preparing the enlarged third edition, many of the above mentioned +friends have again helped me. I have picked the brains of Professor F. +Clark Howell of the Department of Anthropology of the University of +Chicago in reworking the earlier chapters, and he was very patient in +the matter, which I sincerely appreciate. + +All of Mrs. Susan Richert Allens original drawings appear, but a few +necessary corrections have been made in some of the charts and some new +drawings have been added by Mr. John Pfiffner, Staff Artist, Chicago +Natural History Museum. + + ROBERT J. BRAIDWOOD + _March 1, 1959_ + + + + +Contents + + + PAGE + How We Learn about Prehistoric Men 7 + + The Changing World in Which Prehistoric Men Lived 17 + + Prehistoric Men Themselves 22 + + Cultural Beginnings 38 + + More Evidence of Culture 56 + + Early Moderns 70 + + End and Prelude 92 + + The First Revolution 121 + + The Conquest of Civilization 144 + + End of Prehistory 162 + + Summary 176 + + List of Books 180 + + Index 184 + + + + +HOW WE LEARN about Prehistoric Men + +[Illustration] + + +Prehistory means the time before written history began. Actually, more +than 99 per cent of mans story is prehistory. Man is at least half a +million years old, but he did not begin to write history (or to write +anything) until about 5,000 years ago. + +The men who lived in prehistoric times left us no history books, but +they did unintentionally leave a record of their presence and their way +of life. This record is studied and interpreted by different kinds of +scientists. + + +SCIENTISTS WHO FIND OUT ABOUT PREHISTORIC MEN + +The scientists who study the bones and teeth and any other parts +they find of the bodies of prehistoric men, are called _physical +anthropologists_. Physical anthropologists are trained, much like +doctors, to know all about the human body. They study living people, +too; they know more about the biological facts of human races than +anybody else. If the police find a badly decayed body in a trunk, +they ask a physical anthropologist to tell them what the person +originally looked like. The physical anthropologists who specialize in +prehistoric men work with fossils, so they are sometimes called _human +paleontologists_. + + +ARCHEOLOGISTS + +There is a kind of scientist who studies the things that prehistoric +men made and did. Such a scientist is called an _archeologist_. It is +the archeologists business to look for the stone and metal tools, the +pottery, the graves, and the caves or huts of the men who lived before +history began. + +But there is more to archeology than just looking for things. In +Professor V. Gordon Childes words, archeology furnishes a sort of +history of human activity, provided always that the actions have +produced concrete results and left recognizable material traces. You +will see that there are at least three points in what Childe says: + + 1. The archeologists have to find the traces of things left behind by + ancient man, and + + 2. Only a few objects may be found, for most of these were probably + too soft or too breakable to last through the years. However, + + 3. The archeologist must use whatever he can find to tell a story--to + make a sort of history--from the objects and living-places and + graves that have escaped destruction. + +What I mean is this: Let us say you are walking through a dump yard, +and you find a rusty old spark plug. If you want to think about what +the spark plug means, you quickly remember that it is a part of an +automobile motor. This tells you something about the man who threw +the spark plug on the dump. He either had an automobile, or he knew +or lived near someone who did. He cant have lived so very long ago, +youll remember, because spark plugs and automobiles are only about +sixty years old. + +When you think about the old spark plug in this way you have +just been making the beginnings of what we call an archeological +_interpretation_; you have been making the spark plug tell a story. +It is the same way with the man-made things we archeologists find +and put in museums. Usually, only a few of these objects are pretty +to look at; but each of them has some sort of story to tell. Making +the interpretation of his finds is the most important part of the +archeologists job. It is the way he gets at the sort of history of +human activity which is expected of archeology. + + +SOME OTHER SCIENTISTS + +There are many other scientists who help the archeologist and the +physical anthropologist find out about prehistoric men. The geologists +help us tell the age of the rocks or caves or gravel beds in which +human bones or man-made objects are found. There are other scientists +with names which all begin with paleo (the Greek word for old). The +_paleontologists_ study fossil animals. There are also, for example, +such scientists as _paleobotanists_ and _paleoclimatologists_, who +study ancient plants and climates. These scientists help us to know +the kinds of animals and plants that were living in prehistoric times +and so could be used for food by ancient man; what the weather was +like; and whether there were glaciers. Also, when I tell you that +prehistoric men did not appear until long after the great dinosaurs had +disappeared, I go on the say-so of the paleontologists. They know that +fossils of men and of dinosaurs are not found in the same geological +period. The dinosaur fossils come in early periods, the fossils of men +much later. + +Since World War II even the atomic scientists have been helping the +archeologists. By testing the amount of radioactivity left in charcoal, +wood, or other vegetable matter obtained from archeological sites, they +have been able to date the sites. Shell has been used also, and even +the hair of Egyptian mummies. The dates of geological and climatic +events have also been discovered. Some of this work has been done from +drillings taken from the bottom of the sea. + +This dating by radioactivity has considerably shortened the dates which +the archeologists used to give. If you find that some of the dates +I give here are more recent than the dates you see in other books +on prehistory, it is because I am using one of the new lower dating +systems. + +[Illustration: RADIOCARBON CHART + +The rate of disappearance of radioactivity as time passes.[1]] + + [1] It is important that the limitations of the radioactive carbon + dating system be held in mind. As the statistics involved in + the system are used, there are two chances in three that the + date of the sample falls within the range given as plus or + minus an added number of years. For example, the date for the + Jarmo village (see chart), given as 6750 200 B.C., really + means that there are only two chances in three that the real + date of the charcoal sampled fell between 6950 and 6550 B.C. + We have also begun to suspect that there are ways in which the + samples themselves may have become contaminated, either on + the early or on the late side. We now tend to be suspicious of + single radioactive carbon determinations, or of determinations + from one site alone. But as a fabric of consistent + determinations for several or more sites of one archeological + period, we gain confidence in the dates. + + +HOW THE SCIENTISTS FIND OUT + +So far, this chapter has been mainly about the people who find out +about prehistoric men. We also need a word about _how_ they find out. + +All our finds came by accident until about a hundred years ago. Men +digging wells, or digging in caves for fertilizer, often turned up +ancient swords or pots or stone arrowheads. People also found some odd +pieces of stone that didnt look like natural forms, but they also +didnt look like any known tool. As a result, the people who found them +gave them queer names; for example, thunderbolts. The people thought +the strange stones came to earth as bolts of lightning. We know now +that these strange stones were prehistoric stone tools. + +Many important finds still come to us by accident. In 1935, a British +dentist, A. T. Marston, found the first of two fragments of a very +important fossil human skull, in a gravel pit at Swanscombe, on the +River Thames, England. He had to wait nine months, until the face of +the gravel pit had been dug eight yards farther back, before the second +fragment appeared. They fitted! Then, twenty years later, still another +piece appeared. In 1928 workmen who were blasting out rock for the +breakwater in the port of Haifa began to notice flint tools. Thus the +story of cave men on Mount Carmel, in Palestine, began to be known. + +Planned archeological digging is only about a century old. Even before +this, however, a few men realized the significance of objects they dug +from the ground; one of these early archeologists was our own Thomas +Jefferson. The first real mound-digger was a German grocers clerk, +Heinrich Schliemann. Schliemann made a fortune as a merchant, first +in Europe and then in the California gold-rush of 1849. He became an +American citizen. Then he retired and had both money and time to test +an old idea of his. He believed that the heroes of ancient Troy and +Mycenae were once real Trojans and Greeks. He proved it by going to +Turkey and Greece and digging up the remains of both cities. + +Schliemann had the great good fortune to find rich and spectacular +treasures, and he also had the common sense to keep notes and make +descriptions of what he found. He proved beyond doubt that many ancient +city mounds can be _stratified_. This means that there may be the +remains of many towns in a mound, one above another, like layers in a +cake. + +You might like to have an idea of how mounds come to be in layers. +The original settlers may have chosen the spot because it had a good +spring and there were good fertile lands nearby, or perhaps because +it was close to some road or river or harbor. These settlers probably +built their town of stone and mud-brick. Finally, something would have +happened to the town--a flood, or a burning, or a raid by enemies--and +the walls of the houses would have fallen in or would have melted down +as mud in the rain. Nothing would have remained but the mud and debris +of a low mound of _one_ layer. + +The second settlers would have wanted the spot for the same reasons +the first settlers did--good water, land, and roads. Also, the second +settlers would have found a nice low mound to build their houses on, +a protection from floods. But again, something would finally have +happened to the second town, and the walls of _its_ houses would have +come tumbling down. This makes the _second_ layer. And so on.... + +In Syria I once had the good fortune to dig on a large mound that had +no less than fifteen layers. Also, most of the layers were thick, and +there were signs of rebuilding and repairs within each layer. The mound +was more than a hundred feet high. In each layer, the building material +used had been a soft, unbaked mud-brick, and most of the debris +consisted of fallen or rain-melted mud from these mud-bricks. + +This idea of _stratification_, like the cake layers, was already a +familiar one to the geologists by Schliemanns time. They could show +that their lowest layer of rock was oldest or earliest, and that the +overlying layers became more recent as one moved upward. Schliemanns +digging proved the same thing at Troy. His first (lowest and earliest) +city had at least nine layers above it; he thought that the second +layer contained the remains of Homers Troy. We now know that Homeric +Troy was layer VIIa from the bottom; also, we count eleven layers or +sub-layers in total. + +Schliemanns work marks the beginnings of modern archeology. Scholars +soon set out to dig on ancient sites, from Egypt to Central America. + + +ARCHEOLOGICAL INFORMATION + +As time went on, the study of archeological materials--found either +by accident or by digging on purpose--began to show certain things. +Archeologists began to get ideas as to the kinds of objects that +belonged together. If you compared a mail-order catalogue of 1890 with +one of today, you would see a lot of differences. If you really studied +the two catalogues hard, you would also begin to see that certain +objects go together. Horseshoes and metal buggy tires and pieces of +harness would begin to fit into a picture with certain kinds of coal +stoves and furniture and china dishes and kerosene lamps. Our friend +the spark plug, and radios and electric refrigerators and light bulbs +would fit into a picture with different kinds of furniture and dishes +and tools. You wont be old enough to remember the kind of hats that +women wore in 1890, but youve probably seen pictures of them, and you +know very well they couldnt be worn with the fashions of today. + +This is one of the ways that archeologists study their materials. +The various tools and weapons and jewelry, the pottery, the kinds +of houses, and even the ways of burying the dead tend to fit into +pictures. Some archeologists call all of the things that go together to +make such a picture an _assemblage_. The assemblage of the first layer +of Schliemanns Troy was as different from that of the seventh layer as +our 1900 mail-order catalogue is from the one of today. + +The archeologists who came after Schliemann began to notice other +things and to compare them with occurrences in modern times. The +idea that people will buy better mousetraps goes back into very +ancient times. Today, if we make good automobiles or radios, we can +sell some of them in Turkey or even in Timbuktu. This means that a +few present-day types of American automobiles and radios form part +of present-day assemblages in both Turkey and Timbuktu. The total +present-day assemblage of Turkey is quite different from that of +Timbuktu or that of America, but they have at least some automobiles +and some radios in common. + +Now these automobiles and radios will eventually wear out. Let us +suppose we could go to some remote part of Turkey or to Timbuktu in a +dream. We dont know what the date is, in our dream, but we see all +sorts of strange things and ways of living in both places. Nobody +tells us what the date is. But suddenly we see a 1936 Ford; so we +know that in our dream it has to be at least the year 1936, and only +as many years after that as we could reasonably expect a Ford to keep +in running order. The Ford would probably break down in twenty years +time, so the Turkish or Timbuktu assemblage were seeing in our dream +has to date at about A.D. 1936-56. + +Archeologists not only date their ancient materials in this way; they +also see over what distances and between which peoples trading was +done. It turns out that there was a good deal of trading in ancient +times, probably all on a barter and exchange basis. + + +EVERYTHING BEGINS TO FIT TOGETHER + +Now we need to pull these ideas all together and see the complicated +structure the archeologists can build with their materials. + +Even the earliest archeologists soon found that there was a very long +range of prehistoric time which would yield only very simple things. +For this very long early part of prehistory, there was little to be +found but the flint tools which wandering, hunting and gathering +people made, and the bones of the wild animals they ate. Toward the +end of prehistoric time there was a general settling down with the +coming of agriculture, and all sorts of new things began to be made. +Archeologists soon got a general notion of what ought to appear with +what. Thus, it would upset a French prehistorian digging at the bottom +of a very early cave if he found a fine bronze sword, just as much as +it would upset him if he found a beer bottle. The people of his very +early cave layer simply could not have made bronze swords, which came +later, just as do beer bottles. Some accidental disturbance of the +layers of his cave must have happened. + +With any luck, archeologists do their digging in a layered, stratified +site. They find the remains of everything that would last through +time, in several different layers. They know that the assemblage in +the bottom layer was laid down earlier than the assemblage in the next +layer above, and so on up to the topmost layer, which is the latest. +They look at the results of other digs and find that some other +archeologist 900 miles away has found ax-heads in his lowest layer, +exactly like the ax-heads of their fifth layer. This means that their +fifth layer must have been lived in at about the same time as was the +first layer in the site 200 miles away. It also may mean that the +people who lived in the two layers knew and traded with each other. Or +it could mean that they didnt necessarily know each other, but simply +that both traded with a third group at about the same time. + +You can see that the more we dig and find, the more clearly the main +facts begin to stand out. We begin to be more sure of which people +lived at the same time, which earlier and which later. We begin to +know who traded with whom, and which peoples seemed to live off by +themselves. We begin to find enough skeletons in burials so that the +physical anthropologists can tell us what the people looked like. We +get animal bones, and a paleontologist may tell us they are all bones +of wild animals; or he may tell us that some or most of the bones are +those of domesticated animals, for instance, sheep or cattle, and +therefore the people must have kept herds. + +More important than anything else--as our structure grows more +complicated and our materials increase--is the fact that a sort +of history of human activity does begin to appear. The habits or +traditions that men formed in the making of their tools and in the +ways they did things, begin to stand out for us. How characteristic +were these habits and traditions? What areas did they spread over? +How long did they last? We watch the different tools and the traces +of the way things were done--how the burials were arranged, what +the living-places were like, and so on. We wonder about the people +themselves, for the traces of habits and traditions are useful to us +only as clues to the men who once had them. So we ask the physical +anthropologists about the skeletons that we found in the burials. The +physical anthropologists tell us about the anatomy and the similarities +and differences which the skeletons show when compared with other +skeletons. The physical anthropologists are even working on a +method--chemical tests of the bones--that will enable them to discover +what the blood-type may have been. One thing is sure. We have never +found a group of skeletons so absolutely similar among themselves--so +cast from a single mould, so to speak--that we could claim to have a +pure race. I am sure we never shall. + +We become particularly interested in any signs of change--when new +materials and tool types and ways of doing things replace old ones. We +watch for signs of social change and progress in one way or another. + +We must do all this without one word of written history to aid us. +Everything we are concerned with goes back to the time _before_ men +learned to write. That is the prehistorians job--to find out what +happened before history began. + + + + +THE CHANGING WORLD in which Prehistoric Men Lived + +[Illustration] + + +Mankind, well say, is at least a half million years old. It is very +hard to understand how long a time half a million years really is. +If we were to compare this whole length of time to one day, wed get +something like this: The present time is midnight, and Jesus was +born just five minutes and thirty-six seconds ago. Earliest history +began less than fifteen minutes ago. Everything before 11:45 was in +prehistoric time. + +Or maybe we can grasp the length of time better in terms of +generations. As you know, primitive peoples tend to marry and have +children rather early in life. So suppose we say that twenty years +will make an average generation. At this rate there would be 25,000 +generations in a half-million years. But our United States is much less +than ten generations old, twenty-five generations take us back before +the time of Columbus, Julius Caesar was alive just 100 generations ago, +David was king of Israel less than 150 generations ago, 250 generations +take us back to the beginning of written history. And there were 24,750 +generations of men before written history began! + +I should probably tell you that there is a new method of prehistoric +dating which would cut the earliest dates in my reckoning almost +in half. Dr. Cesare Emiliani, combining radioactive (C14) and +chemical (oxygen isotope) methods in the study of deep-sea borings, +has developed a system which would lower the total range of human +prehistory to about 300,000 years. The system is still too new to have +had general examination and testing. Hence, I have not used it in this +book; it would mainly affect the dates earlier than 25,000 years ago. + + +CHANGES IN ENVIRONMENT + +The earth probably hasnt changed much in the last 5,000 years (250 +generations). Men have built things on its surface and dug into it and +drawn boundaries on maps of it, but the places where rivers, lakes, +seas, and mountains now stand have changed very little. + +In earlier times the earth looked very different. Geologists call the +last great geological period the _Pleistocene_. It began somewhere +between a half million and a million years ago, and was a time of great +changes. Sometimes we call it the Ice Age, for in the Pleistocene +there were at least three or four times when large areas of earth +were covered with glaciers. The reason for my uncertainty is that +while there seem to have been four major mountain or alpine phases of +glaciation, there may only have been three general continental phases +in the Old World.[2] + + [2] This is a complicated affair and I do not want to bother you + with its details. Both the alpine and the continental ice sheets + seem to have had minor fluctuations during their _main_ phases, + and the advances of the later phases destroyed many of the + traces of the earlier phases. The general textbooks have tended + to follow the names and numbers established for the Alps early + in this century by two German geologists. I will not bother you + with the names, but there were _four_ major phases. It is the + second of these alpine phases which seems to fit the traces of + the earliest of the great continental glaciations. In this book, + I will use the four-part system, since it is the most familiar, + but will add the word _alpine_ so you may remember to make the + transition to the continental system if you wish to do so. + +Glaciers are great sheets of ice, sometimes over a thousand feet +thick, which are now known only in Greenland and Antarctica and in +high mountains. During several of the glacial periods in the Ice Age, +the glaciers covered most of Canada and the northern United States and +reached down to southern England and France in Europe. Smaller ice +sheets sat like caps on the Rockies, the Alps, and the Himalayas. The +continental glaciation only happened north of the equator, however, so +remember that Ice Age is only half true. + +As you know, the amount of water on and about the earth does not vary. +These large glaciers contained millions of tons of water frozen into +ice. Because so much water was frozen and contained in the glaciers, +the water level of lakes and oceans was lowered. Flooded areas were +drained and appeared as dry land. There were times in the Ice Age when +there was no English Channel, so that England was not an island, and a +land bridge at the Dardanelles probably divided the Mediterranean from +the Black Sea. + +A very important thing for people living during the time of a +glaciation was the region adjacent to the glacier. They could not, of +course, live on the ice itself. The questions would be how close could +they live to it, and how would they have had to change their way of +life to do so. + + +GLACIERS CHANGE THE WEATHER + +Great sheets of ice change the weather. When the front of a glacier +stood at Milwaukee, the weather must have been bitterly cold in +Chicago. The climate of the whole world would have been different, and +you can see how animals and men would have been forced to move from one +place to another in search of food and warmth. + +On the other hand, it looks as if only a minor proportion of the whole +Ice Age was really taken up by times of glaciation. In between came +the _interglacial_ periods. During these times the climate around +Chicago was as warm as it is now, and sometimes even warmer. It may +interest you to know that the last great glacier melted away less than +10,000 years ago. Professor Ernst Antevs thinks we may be living in an +interglacial period and that the Ice Age may not be over yet. So if you +want to make a killing in real estate for your several hundred times +great-grandchildren, you might buy some land in the Arizona desert or +the Sahara. + +We do not yet know just why the glaciers appeared and disappeared, as +they did. It surely had something to do with an increase in rainfall +and a fall in temperature. It probably also had to do with a general +tendency for the land to rise at the beginning of the Pleistocene. We +know there was some mountain-building at that time. Hence, rain-bearing +winds nourished the rising and cooler uplands with snow. An increase +in all three of these factors--if they came together--would only have +needed to be slight. But exactly why this happened we do not know. + +The reason I tell you about the glaciers is simply to remind you of the +changing world in which prehistoric men lived. Their surroundings--the +animals and plants they used for food, and the weather they had to +protect themselves from--were always changing. On the other hand, this +change happened over so long a period of time and was so slow that +individual people could not have noticed it. Glaciers, about which they +probably knew nothing, moved in hundreds of miles to the north of them. +The people must simply have wandered ever more southward in search +of the plants and animals on which they lived. Or some men may have +stayed where they were and learned to hunt different animals and eat +different foods. Prehistoric men had to keep adapting themselves to new +environments and those who were most adaptive were most successful. + + +OTHER CHANGES + +Changes took place in the men themselves as well as in the ways they +lived. As time went on, they made better tools and weapons. Then, too, +we begin to find signs of how they started thinking of other things +than food and the tools to get it with. We find that they painted on +the walls of caves, and decorated their tools; we find that they buried +their dead. + +At about the time when the last great glacier was finally melting away, +men in the Near East made the first basic change in human economy. +They began to plant grain, and they learned to raise and herd certain +animals. This meant that they could store food in granaries and on the +hoof against the bad times of the year. This first really basic change +in mans way of living has been called the food-producing revolution. +By the time it happened, a modern kind of climate was beginning. Men +had already grown to look as they do now. Know-how in ways of living +had developed and progressed, slowly but surely, up to a point. It was +impossible for men to go beyond that point if they only hunted and +fished and gathered wild foods. Once the basic change was made--once +the food-producing revolution became effective--technology leaped ahead +and civilization and written history soon began. + + + + +Prehistoric Men THEMSELVES + +[Illustration] + + +DO WE KNOW WHERE MAN ORIGINATED? + +For a long time some scientists thought the cradle of mankind was in +central Asia. Other scientists insisted it was in Africa, and still +others said it might have been in Europe. Actually, we dont know +where it was. We dont even know that there was only _one_ cradle. +If we had to choose a cradle at this moment, we would probably say +Africa. But the southern portions of Asia and Europe may also have been +included in the general area. The scene of the early development of +mankind was certainly the Old World. It is pretty certain men didnt +reach North or South America until almost the end of the Ice Age--had +they done so earlier we would certainly have found some trace of them +by now. + +The earliest tools we have yet found come from central and south +Africa. By the dating system Im using, these tools must be over +500,000 years old. There are now reports that a few such early tools +have been found--at the Sterkfontein cave in South Africa--along with +the bones of small fossil men called australopithecines. + +Not all scientists would agree that the australopithecines were men, +or would agree that the tools were made by the australopithecines +themselves. For these sticklers, the earliest bones of men come from +the island of Java. The date would be about 450,000 years ago. So far, +we have not yet found the tools which we suppose these earliest men in +the Far East must have made. + +Let me say it another way. How old are the earliest traces of men we +now have? Over half a million years. This was a time when the first +alpine glaciation was happening in the north. What has been found so +far? The tools which the men of those times made, in different parts +of Africa. It is now fairly generally agreed that the men who made +the tools were the australopithecines. There is also a more man-like +jawbone at Kanam in Kenya, but its find-spot has been questioned. The +next earliest bones we have were found in Java, and they may be almost +a hundred thousand years younger than the earliest African finds. We +havent yet found the tools of these early Javanese. Our knowledge of +tool-using in Africa spreads quickly as time goes on: soon after the +appearance of tools in the south we shall have them from as far north +as Algeria. + +Very soon after the earliest Javanese come the bones of slightly more +developed people in Java, and the jawbone of a man who once lived in +what is now Germany. The same general glacial beds which yielded the +later Javanese bones and the German jawbone also include tools. These +finds come from the time of the second alpine glaciation. + +So this is the situation. By the time of the end of the second alpine +or first continental glaciation (say 400,000 years ago) we have traces +of men from the extremes of the more southerly portions of the Old +World--South Africa, eastern Asia, and western Europe. There are also +some traces of men in the middle ground. In fact, Professor Franz +Weidenreich believed that creatures who were the immediate ancestors +of men had already spread over Europe, Africa, and Asia by the time +the Ice Age began. We certainly have no reason to disbelieve this, but +fortunate accidents of discovery have not yet given us the evidence to +prove it. + + +MEN AND APES + +Many people used to get extremely upset at the ill-formed notion +that man descended from the apes. Such words were much more likely +to start fights or monkey trials than the correct notion that all +living animals, including man, ascended or evolved from a single-celled +organism which lived in the primeval seas hundreds of millions of years +ago. Men are mammals, of the order called Primates, and mans living +relatives are the great apes. Men didnt descend from the apes or +apes from men, and mankind must have had much closer relatives who have +since become extinct. + +Men stand erect. They also walk and run on their two feet. Apes are +happiest in trees, swinging with their arms from branch to branch. +Few branches of trees will hold the mighty gorilla, although he still +manages to sleep in trees. Apes cant stand really erect in our sense, +and when they have to run on the ground, they use the knuckles of their +hands as well as their feet. + +A key group of fossil bones here are the south African +australopithecines. These are called the _Australopithecinae_ or +man-apes or sometimes even ape-men. We do not _know_ that they were +directly ancestral to men but they can hardly have been so to apes. +Presently Ill describe them a bit more. The reason I mention them +here is that while they had brains no larger than those of apes, their +hipbones were enough like ours so that they must have stood erect. +There is no good reason to think they couldnt have walked as we do. + + +BRAINS, HANDS, AND TOOLS + +Whether the australopithecines were our ancestors or not, the proper +ancestors of men must have been able to stand erect and to walk on +their two feet. Three further important things probably were involved, +next, before they could become men proper. These are: + + 1. The increasing size and development of the brain. + + 2. The increasing usefulness (specialization) of the thumb and hand. + + 3. The use of tools. + +Nobody knows which of these three is most important, or which came +first. Most probably the growth of all three things was very much +blended together. If you think about each of the things, you will see +what I mean. Unless your hand is more flexible than a paw, and your +thumb will work against (or oppose) your fingers, you cant hold a tool +very well. But you wouldnt get the idea of using a tool unless you had +enough brain to help you see cause and effect. And it is rather hard to +see how your hand and brain would develop unless they had something to +practice on--like using tools. In Professor Krogmans words, the hand +must become the obedient servant of the eye and the brain. It is the +_co-ordination_ of these things that counts. + +Many other things must have been happening to the bodies of the +creatures who were the ancestors of men. Our ancestors had to develop +organs of speech. More than that, they had to get the idea of letting +_certain sounds_ made with these speech organs have _certain meanings_. + +All this must have gone very slowly. Probably everything was developing +little by little, all together. Men became men very slowly. + + +WHEN SHALL WE CALL MEN MEN? + +What do I mean when I say men? People who looked pretty much as we +do, and who used different tools to do different things, are men to me. +Well probably never know whether the earliest ones talked or not. They +probably had vocal cords, so they could make sounds, but did they know +how to make sounds work as symbols to carry meanings? But if the fossil +bones look like our skeletons, and if we find tools which well agree +couldnt have been made by nature or by animals, then Id say we had +traces of _men_. + +The australopithecine finds of the Transvaal and Bechuanaland, in +south Africa, are bound to come into the discussion here. Ive already +told you that the australopithecines could have stood upright and +walked on their two hind legs. They come from the very base of the +Pleistocene or Ice Age, and a few coarse stone tools have been found +with the australopithecine fossils. But there are three varieties +of the australopithecines and they last on until a time equal to +that of the second alpine glaciation. They are the best suggestion +we have yet as to what the ancestors of men _may_ have looked like. +They were certainly closer to men than to apes. Although their brain +size was no larger than the brains of modern apes their body size and +stature were quite small; hence, relative to their small size, their +brains were large. We have not been able to prove without doubt that +the australopithecines were _tool-making_ creatures, even though the +recent news has it that tools have been found with australopithecine +bones. The doubt as to whether the australopithecines used the tools +themselves goes like this--just suppose some man-like creature (whose +bones we have not yet found) made the tools and used them to kill +and butcher australopithecines. Hence a few experts tend to let +australopithecines still hang in limbo as man-apes. + + +THE EARLIEST MEN WE KNOW + +Ill postpone talking about the tools of early men until the next +chapter. The men whose bones were the earliest of the Java lot have +been given the name _Meganthropus_. The bones are very fragmentary. We +would not understand them very well unless we had the somewhat later +Javanese lot--the more commonly known _Pithecanthropus_ or Java +man--against which to refer them for study. One of the less well-known +and earliest fragments, a piece of lower jaw and some teeth, rather +strongly resembles the lower jaws and teeth of the australopithecine +type. Was _Meganthropus_ a sort of half-way point between the +australopithecines and _Pithecanthropus_? It is still too early to say. +We shall need more finds before we can be definite one way or the other. + +Java man, _Pithecanthropus_, comes from geological beds equal in age +to the latter part of the second alpine glaciation; the _Meganthropus_ +finds refer to beds of the beginning of this glaciation. The first +finds of Java man were made in 1891-92 by Dr. Eugene Dubois, a Dutch +doctor in the colonial service. Finds have continued to be made. There +are now bones enough to account for four skulls. There are also four +jaws and some odd teeth and thigh bones. Java man, generally speaking, +was about five feet six inches tall, and didnt hold his head very +erect. His skull was very thick and heavy and had room for little more +than two-thirds as large a brain as we have. He had big teeth and a big +jaw and enormous eyebrow ridges. + +No tools were found in the geological deposits where bones of Java man +appeared. There are some tools in the same general area, but they come +a bit later in time. One reason we accept the Java man as man--aside +from his general anatomical appearance--is that these tools probably +belonged to his near descendants. + +Remember that there are several varieties of men in the whole early +Java lot, at least two of which are earlier than the _Pithecanthropus_, +Java man. Some of the earlier ones seem to have gone in for +bigness, in tooth-size at least. _Meganthropus_ is one of these +earlier varieties. As we said, he _may_ turn out to be a link to +the australopithecines, who _may_ or _may not_ be ancestral to men. +_Meganthropus_ is best understandable in terms of _Pithecanthropus_, +who appeared later in the same general area. _Pithecanthropus_ is +pretty well understandable from the bones he left us, and also because +of his strong resemblance to the fully tool-using cave-dwelling Peking +man, _Sinanthropus_, about whom we shall talk next. But you can see +that the physical anthropologists and prehistoric archeologists still +have a lot of work to do on the problem of earliest men. + + +PEKING MEN AND SOME EARLY WESTERNERS + +The earliest known Chinese are called _Sinanthropus_, or Peking man, +because the finds were made near that city. In World War II, the United +States Marine guard at our Embassy in Peking tried to help get the +bones out of the city before the Japanese attack. Nobody knows where +these bones are now. The Red Chinese accuse us of having stolen them. +They were last seen on a dock-side at a Chinese port. But should you +catch a Marine with a sack of old bones, perhaps we could achieve peace +in Asia by returning them! Fortunately, there is a complete set of +casts of the bones. + +Peking man lived in a cave in a limestone hill, made tools, cracked +animal bones to get the marrow out, and used fire. Incidentally, the +bones of Peking man were found because Chinese dig for what they call +dragon bones and dragon teeth. Uneducated Chinese buy these things +in their drug stores and grind them into powder for medicine. The +dragon teeth and bones are really fossils of ancient animals, and +sometimes of men. The people who supply the drug stores have learned +where to dig for strange bones and teeth. Paleontologists who get to +China go to the drug stores to buy fossils. In a roundabout way, this +is how the fallen-in cave of Peking man at Choukoutien was discovered. + +Peking man was not quite as tall as Java man but he probably stood +straighter. His skull looked very much like that of the Java skull +except that it had room for a slightly larger brain. His face was less +brutish than was Java mans face, but this isnt saying much. + +Peking man dates from early in the interglacial period following the +second alpine glaciation. He probably lived close to 350,000 years +ago. There are several finds to account for in Europe by about this +time, and one from northwest Africa. The very large jawbone found +near Heidelberg in Germany is doubtless even earlier than Peking man. +The beds where it was found are of second alpine glacial times, and +recently some tools have been said to have come from the same beds. +There is not much I need tell you about the Heidelberg jaw save that it +seems certainly to have belonged to an early man, and that it is very +big. + +Another find in Germany was made at Steinheim. It consists of the +fragmentary skull of a man. It is very important because of its +relative completeness, but it has not yet been fully studied. The bone +is thick, but the back of the head is neither very low nor primitive, +and the face is also not primitive. The forehead does, however, have +big ridges over the eyes. The more fragmentary skull from Swanscombe in +England (p. 11) has been much more carefully studied. Only the top and +back of that skull have been found. Since the skull rounds up nicely, +it has been assumed that the face and forehead must have been quite +modern. Careful comparison with Steinheim shows that this was not +necessarily so. This is important because it bears on the question of +how early truly modern man appeared. + +Recently two fragmentary jaws were found at Ternafine in Algeria, +northwest Africa. They look like the jaws of Peking man. Tools were +found with them. Since no jaws have yet been found at Steinheim or +Swanscombe, but the time is the same, one wonders if these people had +jaws like those of Ternafine. + + +WHAT HAPPENED TO JAVA AND PEKING MEN + +Professor Weidenreich thought that there were at least a dozen ways in +which the Peking man resembled the modern Mongoloids. This would seem +to indicate that Peking man was really just a very early Chinese. + +Several later fossil men have been found in the Java-Australian area. +The best known of these is the so-called Solo man. There are some finds +from Australia itself which we now know to be quite late. But it looks +as if we may assume a line of evolution from Java man down to the +modern Australian natives. During parts of the Ice Age there was a land +bridge all the way from Java to Australia. + + +TWO ENGLISHMEN WHO WERENT OLD + +The older textbooks contain descriptions of two English finds which +were thought to be very old. These were called Piltdown (_Eoanthropus +dawsoni_) and Galley Hill. The skulls were very modern in appearance. +In 1948-49, British scientists began making chemical tests which proved +that neither of these finds is very old. It is now known that both +Piltdown man and the tools which were said to have been found with +him were part of an elaborate fake! + + +TYPICAL CAVE MEN + +The next men we have to talk about are all members of a related group. +These are the Neanderthal group. Neanderthal man himself was found in +the Neander Valley, near Dsseldorf, Germany, in 1856. He was the first +human fossil to be recognized as such. + +[Illustration: PRINCIPAL KNOWN TYPES OF FOSSIL MEN + + CRO-MAGNON + NEANDERTHAL + MODERN SKULL + COMBE-CAPELLE + SINANTHROPUS + PITHECANTHROPUS] + +Some of us think that the neanderthaloids proper are only those people +of western Europe who didnt get out before the beginning of the last +great glaciation, and who found themselves hemmed in by the glaciers +in the Alps and northern Europe. Being hemmed in, they intermarried +a bit too much and developed into a special type. Professor F. Clark +Howell sees it this way. In Europe, the earliest trace of men we +now know is the Heidelberg jaw. Evolution continued in Europe, from +Heidelberg through the Swanscombe and Steinheim types to a group of +pre-neanderthaloids. There are traces of these pre-neanderthaloids +pretty much throughout Europe during the third interglacial period--say +100,000 years ago. The pre-neanderthaloids are represented by such +finds as the ones at Ehringsdorf in Germany and Saccopastore in Italy. +I wont describe them for you, since they are simply less extreme than +the neanderthaloids proper--about half way between Steinheim and the +classic Neanderthal people. + +Professor Howell believes that the pre-neanderthaloids who happened to +get caught in the pocket of the southwest corner of Europe at the onset +of the last great glaciation became the classic Neanderthalers. Out in +the Near East, Howell thinks, it is possible to see traces of people +evolving from the pre-neanderthaloid type toward that of fully modern +man. Certainly, we dont see such extreme cases of neanderthaloidism +outside of western Europe. + +There are at least a dozen good examples in the main or classic +Neanderthal group in Europe. They date to just before and in the +earlier part of the last great glaciation (85,000 to 40,000 years ago). +Many of the finds have been made in caves. The cave men the movies +and the cartoonists show you are probably meant to be Neanderthalers. +Im not at all sure they dragged their women by the hair; the women +were probably pretty tough, too! + +Neanderthal men had large bony heads, but plenty of room for brains. +Some had brain cases even larger than the average for modern man. Their +faces were heavy, and they had eyebrow ridges of bone, but the ridges +were not as big as those of Java man. Their foreheads were very low, +and they didnt have much chin. They were about five feet three inches +tall, but were heavy and barrel-chested. But the Neanderthalers didnt +slouch as much as theyve been blamed for, either. + +One important thing about the Neanderthal group is that there is a fair +number of them to study. Just as important is the fact that we know +something about how they lived, and about some of the tools they made. + + +OTHER MEN CONTEMPORARY WITH THE NEANDERTHALOIDS + +We have seen that the neanderthaloids seem to be a specialization +in a corner of Europe. What was going on elsewhere? We think that +the pre-neanderthaloid type was a generally widespread form of men. +From this type evolved other more or less extreme although generally +related men. The Solo finds in Java form one such case. Another was the +Rhodesian man of Africa, and the more recent Hopefield finds show more +of the general Rhodesian type. It is more confusing than it needs to be +if these cases outside western Europe are called neanderthaloids. They +lived during the same approximate time range but they were all somewhat +different-looking people. + + +EARLY MODERN MEN + +How early is modern man (_Homo sapiens_), the wise man? Some people +have thought that he was very early, a few still think so. Piltdown +and Galley Hill, which were quite modern in anatomical appearance and +_supposedly_ very early in date, were the best evidence for very +early modern men. Now that Piltdown has been liquidated and Galley Hill +is known to be very late, what is left of the idea? + +The backs of the skulls of the Swanscombe and Steinheim finds look +rather modern. Unless you pay attention to the face and forehead of the +Steinheim find--which not many people have--and perhaps also consider +the Ternafine jaws, you might come to the conclusion that the crown of +the Swanscombe head was that of a modern-like man. + +Two more skulls, again without faces, are available from a French +cave site, Fontchevade. They come from the time of the last great +interglacial, as did the pre-neanderthaloids. The crowns of the +Fontchevade skulls also look quite modern. There is a bit of the +forehead preserved on one of these skulls and the brow-ridge is not +heavy. Nevertheless, there is a suggestion that the bones belonged to +an immature individual. In this case, his (or even more so, if _her_) +brow-ridges would have been weak anyway. The case for the Fontchevade +fossils, as modern type men, is little stronger than that for +Swanscombe, although Professor Vallois believes it a good case. + +It seems to add up to the fact that there were people living in +Europe--before the classic neanderthaloids--who looked more modern, +in some features, than the classic western neanderthaloids did. Our +best suggestion of what men looked like--just before they became fully +modern--comes from a cave on Mount Carmel in Palestine. + + +THE FIRST MODERNS + +Professor T. D. McCown and the late Sir Arthur Keith, who studied the +Mount Carmel bones, figured out that one of the two groups involved +was as much as 70 per cent modern. There were, in fact, two groups or +varieties of men in the Mount Carmel caves and in at least two other +Palestinian caves of about the same time. The time would be about that +of the onset of colder weather, when the last glaciation was beginning +in the north--say 75,000 years ago. + +The 70 per cent modern group came from only one cave, Mugharet es-Skhul +(cave of the kids). The other group, from several caves, had bones of +men of the type weve been calling pre-neanderthaloid which we noted +were widespread in Europe and beyond. The tools which came with each +of these finds were generally similar, and McCown and Keith, and other +scholars since their study, have tended to assume that both the Skhul +group and the pre-neanderthaloid group came from exactly the same time. +The conclusion was quite natural: here was a population of men in the +act of evolving in two different directions. But the time may not be +exactly the same. It is very difficult to be precise, within say 10,000 +years, for a time some 75,000 years ago. If the Skhul men are in fact +later than the pre-neanderthaloid group of Palestine, as some of us +think, then they show how relatively modern some men were--men who +lived at the same time as the classic Neanderthalers of the European +pocket. + +Soon after the first extremely cold phase of the last glaciation, we +begin to get a number of bones of completely modern men in Europe. +We also get great numbers of the tools they made, and their living +places in caves. Completely modern skeletons begin turning up in caves +dating back to toward 40,000 years ago. The time is about that of the +beginning of the second phase of the last glaciation. These skeletons +belonged to people no different from many people we see today. Like +people today, not everybody looked alike. (The positions of the more +important fossil men of later Europe are shown in the chart on page +72.) + + +DIFFERENCES IN THE EARLY MODERNS + +The main early European moderns have been divided into two groups, the +Cro-Magnon group and the Combe Capelle-Brnn group. Cro-Magnon people +were tall and big-boned, with large, long, and rugged heads. They +must have been built like many present-day Scandinavians. The Combe +Capelle-Brnn people were shorter; they had narrow heads and faces, and +big eyebrow-ridges. Of course we dont find the skin or hair of these +people. But there is little doubt they were Caucasoids (Whites). + +Another important find came in the Italian Riviera, near Monte Carlo. +Here, in a cave near Grimaldi, there was a grave containing a woman +and a young boy, buried together. The two skeletons were first called +Negroid because some features of their bones were thought to resemble +certain features of modern African Negro bones. But more recently, +Professor E. A. Hooton and other experts questioned the use of the word +Negroid in describing the Grimaldi skeletons. It is true that nothing +is known of the skin color, hair form, or any other fleshy feature of +the Grimaldi people, so that the word Negroid in its usual meaning is +not proper here. It is also not clear whether the features of the bones +claimed to be Negroid are really so at all. + +From a place called Wadjak, in Java, we have proto-Australoid skulls +which closely resemble those of modern Australian natives. Some of +the skulls found in South Africa, especially the Boskop skull, look +like those of modern Bushmen, but are much bigger. The ancestors of +the Bushmen seem to have once been very widespread south of the Sahara +Desert. True African Negroes were forest people who apparently expanded +out of the west central African area only in the last several thousand +years. Although dark in skin color, neither the Australians nor the +Bushmen are Negroes; neither the Wadjak nor the Boskop skulls are +Negroid. + +As weve already mentioned, Professor Weidenreich believed that Peking +man was already on the way to becoming a Mongoloid. Anyway, the +Mongoloids would seem to have been present by the time of the Upper +Cave at Choukoutien, the _Sinanthropus_ find-spot. + + +WHAT THE DIFFERENCES MEAN + +What does all this difference mean? It means that, at one moment in +time, within each different area, men tended to look somewhat alike. +From area to area, men tended to look somewhat different, just as +they do today. This is all quite natural. People _tended_ to mate +near home; in the anthropological jargon, they made up geographically +localized breeding populations. The simple continental division of +stocks--black = Africa, yellow = Asia, white = Europe--is too simple +a picture to fit the facts. People became accustomed to life in some +particular area within a continent (we might call it a natural area). +As they went on living there, they evolved towards some particular +physical variety. It would, of course, have been difficult to draw +a clear boundary between two adjacent areas. There must always have +been some mating across the boundaries in every case. One thing human +beings dont do, and never have done, is to mate for purity. It is +self-righteous nonsense when we try to kid ourselves into thinking that +they do. + +I am not going to struggle with the whole business of modern stocks and +races. This is a book about prehistoric men, not recent historic or +modern men. My physical anthropologist friends have been very patient +in helping me to write and rewrite this chapter--I am not going to +break their patience completely. Races are their business, not mine, +and they must do the writing about races. I shall, however, give two +modern definitions of race, and then make one comment. + + Dr. William G. Boyd, professor of Immunochemistry, School of + Medicine, Boston University: We may define a human race as a + population which differs significantly from other human populations + in regard to the frequency of one or more of the genes it + possesses. + + Professor Sherwood L. Washburn, professor of Physical Anthropology, + Department of Anthropology, the University of California: A race + is a group of genetically similar populations, and races intergrade + because there are always intermediate populations. + +My comment is that the ideas involved here are all biological: they +concern groups, _not_ individuals. Boyd and Washburn may differ a bit +on what they want to consider a population, but a population is a +group nevertheless, and genetics is biology to the hilt. Now a lot of +people still think of race in terms of how people dress or fix their +food or of other habits or customs they have. The next step is to talk +about racial purity. None of this has anything whatever to do with +race proper, which is a matter of the biology of groups. + +Incidentally, Im told that if man very carefully _controls_ +the breeding of certain animals over generations--dogs, cattle, +chickens--he might achieve a pure race of animals. But he doesnt do +it. Some unfortunate genetic trait soon turns up, so this has just as +carefully to be bred out again, and so on. + + +SUMMARY OF PRESENT KNOWLEDGE OF FOSSIL MEN + +The earliest bones of men we now have--upon which all the experts +would probably agree--are those of _Meganthropus_, from Java, of about +450,000 years ago. The earlier australopithecines of Africa were +possibly not tool-users and may not have been ancestral to men at all. +But there is an alternate and evidently increasingly stronger chance +that some of them may have been. The Kanam jaw from Kenya, another +early possibility, is not only very incomplete but its find-spot is +very questionable. + +Java man proper, _Pithecanthropus_, comes next, at about 400,000 years +ago, and the big Heidelberg jaw in Germany must be of about the same +date. Next comes Swanscombe in England, Steinheim in Germany, the +Ternafine jaws in Algeria, and Peking man, _Sinanthropus_. They all +date to the second great interglacial period, about 350,000 years ago. + +Piltdown and Galley Hill are out, and with them, much of the starch +in the old idea that there were two distinct lines of development +in human evolution: (1) a line of paleoanthropic development from +Heidelberg to the Neanderthalers where it became extinct, and (2) a +very early modern line, through Piltdown, Galley Hill, Swanscombe, to +us. Swanscombe, Steinheim, and Ternafine are just as easily cases of +very early pre-neanderthaloids. + +The pre-neanderthaloids were very widespread during the third +interglacial: Ehringsdorf, Saccopastore, some of the Mount Carmel +people, and probably Fontchevade are cases in point. A variety of +their descendants can be seen, from Java (Solo), Africa (Rhodesian +man), and about the Mediterranean and in western Europe. As the acute +cold of the last glaciation set in, the western Europeans found +themselves surrounded by water, ice, or bitter cold tundra. To vastly +over-simplify it, they bred in and became classic neanderthaloids. +But on Mount Carmel, the Skhul cave-find with its 70 per cent modern +features shows what could happen elsewhere at the same time. + +Lastly, from about 40,000 or 35,000 years ago--the time of the onset +of the second phase of the last glaciation--we begin to find the fully +modern skeletons of men. The modern skeletons differ from place to +place, just as different groups of men living in different places still +look different. + +What became of the Neanderthalers? Nobody can tell me for sure. Ive a +hunch they were simply bred out again when the cold weather was over. +Many Americans, as the years go by, are no longer ashamed to claim they +have Indian blood in their veins. Give us a few more generations +and there will not be very many other Americans left to whom we can +brag about it. It certainly isnt inconceivable to me to imagine a +little Cro-Magnon boy bragging to his friends about his tough, strong, +Neanderthaler great-great-great-great-grandfather! + + + + +Cultural BEGINNINGS + +[Illustration] + + +Men, unlike the lower animals, are made up of much more than flesh and +blood and bones; for men have culture. + + +WHAT IS CULTURE? + +Culture is a word with many meanings. The doctors speak of making a +culture of a certain kind of bacteria, and ants are said to have a +culture. Then there is the Emily Post kind of culture--you say a +person is cultured, or that he isnt, depending on such things as +whether or not he eats peas with his knife. + +The anthropologists use the word too, and argue heatedly over its finer +meanings; but they all agree that every human being is part of or has +some kind of culture. Each particular human group has a particular +culture; that is one of the ways in which we can tell one group of +men from another. In this sense, a CULTURE means the way the members +of a group of people think and believe and live, the tools they make, +and the way they do things. Professor Robert Redfield says a culture +is an organized or formalized body of conventional understandings. +Conventional understandings means the whole set of rules, beliefs, +and standards which a group of people lives by. These understandings +show themselves in art, and in the other things a people may make and +do. The understandings continue to last, through tradition, from one +generation to another. They are what really characterize different +human groups. + + +SOME CHARACTERISTICS OF CULTURE + +A culture lasts, although individual men in the group die off. On +the other hand, a culture changes as the different conventions and +understandings change. You could almost say that a culture lives in the +minds of the men who have it. But people are not born with it; they +get it as they grow up. Suppose a day-old Hungarian baby is adopted by +a family in Oshkosh, Wisconsin, and the child is not told that he is +Hungarian. He will grow up with no more idea of Hungarian culture than +anyone else in Oshkosh. + +So when I speak of ancient Egyptian culture, I mean the whole body +of understandings and beliefs and knowledge possessed by the ancient +Egyptians. I mean their beliefs as to why grain grew, as well as their +ability to make tools with which to reap the grain. I mean their +beliefs about life after death. What I am thinking about as culture is +a thing which lasted in time. If any one Egyptian, even the Pharaoh, +died, it didnt affect the Egyptian culture of that particular moment. + + +PREHISTORIC CULTURES + +For that long period of mans history that is all prehistory, we have +no written descriptions of cultures. We find only the tools men made, +the places where they lived, the graves in which they buried their +dead. Fortunately for us, these tools and living places and graves all +tell us something about the ways these men lived and the things they +believed. But the story we learn of the very early cultures must be +only a very small part of the whole, for we find so few things. The +rest of the story is gone forever. We have to do what we can with what +we find. + +For all of the time up to about 75,000 years ago, which was the time +of the classic European Neanderthal group of men, we have found few +cave-dwelling places of very early prehistoric men. First, there is the +fallen-in cave where Peking man was found, near Peking. Then there are +two or three other _early_, but not _very early_, possibilities. The +finds at the base of the French cave of Fontchevade, those in one of +the Makapan caves in South Africa, and several open sites such as Dr. +L. S. B. Leakeys Olorgesailie in Kenya doubtless all lie earlier than +the time of the main European Neanderthal group, but none are so early +as the Peking finds. + +You can see that we know very little about the home life of earlier +prehistoric men. We find different kinds of early stone tools, but we +cant even be really sure which tools may have been used together. + + +WHY LITTLE HAS LASTED FROM EARLY TIMES + +Except for the rare find-spots mentioned above, all our very early +finds come from geological deposits, or from the wind-blown surfaces +of deserts. Here is what the business of geological deposits really +means. Let us say that a group of people was living in England about +300,000 years ago. They made the tools they needed, lived in some sort +of camp, almost certainly built fires, and perhaps buried their dead. +While the climate was still warm, many generations may have lived in +the same place, hunting, and gathering nuts and berries; but after some +few thousand years, the weather began very gradually to grow colder. +These early Englishmen would not have known that a glacier was forming +over northern Europe. They would only have noticed that the animals +they hunted seemed to be moving south, and that the berries grew larger +toward the south. So they would have moved south, too. + +The camp site they left is the place we archeologists would really have +liked to find. All of the different tools the people used would have +been there together--many broken, some whole. The graves, and traces +of fire, and the tools would have been there. But the glacier got +there first! The front of this enormous sheet of ice moved down over +the country, crushing and breaking and plowing up everything, like a +gigantic bulldozer. You can see what happened to our camp site. + +Everything the glacier couldnt break, it pushed along in front of it +or plowed beneath it. Rocks were ground to gravel, and soil was caught +into the ice, which afterwards melted and ran off as muddy water. Hard +tools of flint sometimes remained whole. Human bones werent so hard; +its a wonder _any_ of them lasted. Gushing streams of melt water +flushed out the debris from underneath the glacier, and water flowed +off the surface and through great crevasses. The hard materials these +waters carried were even more rolled and ground up. Finally, such +materials were dropped by the rushing waters as gravels, miles from +the front of the glacier. At last the glacier reached its greatest +extent; then it melted backward toward the north. Debris held in the +ice was dropped where the ice melted, or was flushed off by more melt +water. When the glacier, leaving the land, had withdrawn to the sea, +great hunks of ice were broken off as icebergs. These icebergs probably +dropped the materials held in their ice wherever they floated and +melted. There must be many tools and fragmentary bones of prehistoric +men on the bottom of the Atlantic Ocean and the North Sea. + +Remember, too, that these glaciers came and went at least three or four +times during the Ice Age. Then you will realize why the earlier things +we find are all mixed up. Stone tools from one camp site got mixed up +with stone tools from many other camp sites--tools which may have been +made tens of thousands or more years apart. The glaciers mixed them +all up, and so we cannot say which particular sets of tools belonged +together in the first place. + + +EOLITHS + +But what sort of tools do we find earliest? For almost a century, +people have been picking up odd bits of flint and other stone in the +oldest Ice Age gravels in England and France. It is now thought these +odd bits of stone werent actually worked by prehistoric men. The +stones were given a name, _eoliths_, or dawn stones. You can see them +in many museums; but you can be pretty sure that very few of them were +actually fashioned by men. + +It is impossible to pick out eoliths that seem to be made in any +one _tradition_. By tradition I mean a set of habits for making one +kind of tool for some particular job. No two eoliths look very much +alike: tools made as part of some one tradition all look much alike. +Now its easy to suppose that the very earliest prehistoric men picked +up and used almost any sort of stone. This wouldnt be surprising; you +and I do it when we go camping. In other words, some of these eoliths +may actually have been used by prehistoric men. They must have used +anything that might be handy when they needed it. We could have figured +that out without the eoliths. + + +THE ROAD TO STANDARDIZATION + +Reasoning from what we know or can easily imagine, there should have +been three major steps in the prehistory of tool-making. The first step +would have been simple _utilization_ of what was at hand. This is the +step into which the eoliths would fall. The second step would have +been _fashioning_--the haphazard preparation of a tool when there was a +need for it. Probably many of the earlier pebble tools, which I shall +describe next, fall into this group. The third step would have been +_standardization_. Here, men began to make tools according to certain +set traditions. Counting the better-made pebble tools, there are four +such traditions or sets of habits for the production of stone tools in +earliest prehistoric times. Toward the end of the Pleistocene, a fifth +tradition appears. + + +PEBBLE TOOLS + +At the beginning of the last chapter, youll remember that I said there +were tools from very early geological beds. The earliest bones of men +have not yet been found in such early beds although the Sterkfontein +australopithecine cave approaches this early date. The earliest tools +come from Africa. They date back to the time of the first great +alpine glaciation and are at least 500,000 years old. The earliest +ones are made of split pebbles, about the size of your fist or a bit +bigger. They go under the name of pebble tools. There are many natural +exposures of early Pleistocene geological beds in Africa, and the +prehistoric archeologists of south and central Africa have concentrated +on searching for early tools. Other finds of early pebble tools have +recently been made in Algeria and Morocco. + +[Illustration: SOUTH AFRICAN PEBBLE TOOL] + +There are probably early pebble tools to be found in areas of the +Old World besides Africa; in fact, some prehistorians already claim +to have identified a few. Since the forms and the distinct ways of +making the earlier pebble tools had not yet sufficiently jelled into +a set tradition, they are difficult for us to recognize. It is not +so difficult, however, if there are great numbers of possibles +available. A little later in time the tradition becomes more clearly +set, and pebble tools are easier to recognize. So far, really large +collections of pebble tools have only been found and examined in Africa. + + +CORE-BIFACE TOOLS + +The next tradition well look at is the _core_ or biface one. The tools +are large pear-shaped pieces of stone trimmed flat on the two opposite +sides or faces. Hence biface has been used to describe these tools. +The front view is like that of a pear with a rather pointed top, and +the back view looks almost exactly the same. Look at them side on, and +you can see that the front and back faces are the same and have been +trimmed to a thin tip. The real purpose in trimming down the two faces +was to get a good cutting edge all around. You can see all this in the +illustration. + +[Illustration: ABBEVILLIAN BIFACE] + +We have very little idea of the way in which these core-bifaces were +used. They have been called hand axes, but this probably gives the +wrong idea, for an ax, to us, is not a pointed tool. All of these early +tools must have been used for a number of jobs--chopping, scraping, +cutting, hitting, picking, and prying. Since the core-bifaces tend to +be pointed, it seems likely that they were used for hitting, picking, +and prying. But they have rough cutting edges, so they could have been +used for chopping, scraping, and cutting. + + +FLAKE TOOLS + +The third tradition is the _flake_ tradition. The idea was to get a +tool with a good cutting edge by simply knocking a nice large flake off +a big block of stone. You had to break off the flake in such a way that +it was broad and thin, and also had a good sharp cutting edge. Once you +really got on to the trick of doing it, this was probably a simpler way +to make a good cutting tool than preparing a biface. You have to know +how, though; Ive tried it and have mashed my fingers more than once. + +The flake tools look as if they were meant mainly for chopping, +scraping, and cutting jobs. When one made a flake tool, the idea seems +to have been to produce a broad, sharp, cutting edge. + +[Illustration: CLACTONIAN FLAKE] + +The core-biface and the flake traditions were spread, from earliest +times, over much of Europe, Africa, and western Asia. The map on page +52 shows the general area. Over much of this great region there was +flint. Both of these traditions seem well adapted to flint, although +good core-bifaces and flakes were made from other kinds of stone, +especially in Africa south of the Sahara. + + +CHOPPERS AND ADZE-LIKE TOOLS + +The fourth early tradition is found in southern and eastern Asia, from +northwestern India through Java and Burma into China. Father Maringer +recently reported an early group of tools in Japan, which most resemble +those of Java, called Patjitanian. The prehistoric men in this general +area mostly used quartz and tuff and even petrified wood for their +stone tools (see illustration, p. 46). + +This fourth early tradition is called the _chopper-chopping tool_ +tradition. It probably has its earliest roots in the pebble tool +tradition of African type. There are several kinds of tools in this +tradition, but all differ from the western core-bifaces and flakes. +There are broad, heavy scrapers or cleavers, and tools with an +adze-like cutting edge. These last-named tools are called hand adzes, +just as the core-bifaces of the west have often been called hand +axes. The section of an adze cutting edge is ? shaped; the section of +an ax is < shaped. + +[Illustration: ANYATHIAN ADZE-LIKE TOOL] + +There are also pointed pebble tools. Thus the tool kit of these early +south and east Asiatic peoples seems to have included tools for doing +as many different jobs as did the tools of the Western traditions. + +Dr. H. L. Movius has emphasized that the tools which were found in the +Peking cave with Peking man belong to the chopper-tool tradition. This +is the only case as yet where the tools and the man have been found +together from very earliest times--if we except Sterkfontein. + + +DIFFERENCES WITHIN THE TOOL-MAKING TRADITIONS + +The latter three great traditions in the manufacture of stone +tools--and the less clear-cut pebble tools before them--are all we have +to show of the cultures of the men of those times. Changes happened in +each of the traditions. As time went on, the tools in each tradition +were better made. There could also be slight regional differences in +the tools within one tradition. Thus, tools with small differences, but +all belonging to one tradition, can be given special group (facies) +names. + +This naming of special groups has been going on for some time. Here are +some of these names, since you may see them used in museum displays +of flint tools, or in books. Within each tradition of tool-making +(save the chopper tools), the earliest tool type is at the bottom +of the list, just as it appears in the lowest beds of a geological +stratification.[3] + + [3] Archeologists usually make their charts and lists with the + earliest materials at the bottom and the latest on top, since + this is the way they find them in the ground. + + Chopper tool (all about equally early): + Anyathian (Burma) + Choukoutienian (China) + Patjitanian (Java) + Soan (India) + + Flake: + Typical Mousterian + Levalloiso-Mousterian + Levalloisian + Tayacian + Clactonian (localized in England) + + Core-biface: + Some blended elements in Mousterian + Micoquian (= Acheulean 6 and 7) + Acheulean + Abbevillian (once called Chellean) + + Pebble tool: + Oldowan + Ain Hanech + pre-Stellenbosch + Kafuan + +The core-biface and the flake traditions appear in the chart (p. 65). + +The early archeologists had many of the tool groups named before they +ever realized that there were broader tool preparation traditions. This +was understandable, for in dealing with the mixture of things that come +out of glacial gravels the easiest thing to do first is to isolate +individual types of tools into groups. First you put a bushel-basketful +of tools on a table and begin matching up types. Then you give names to +the groups of each type. The groups and the types are really matters of +the archeologists choice; in real life, they were probably less exact +than the archeologists lists of them. We now know pretty well in which +of the early traditions the various early groups belong. + + +THE MEANING OF THE DIFFERENT TRADITIONS + +What do the traditions really mean? I see them as the standardization +of ways to make tools for particular jobs. We may not know exactly what +job the maker of a particular core-biface or flake tool had in mind. We +can easily see, however, that he already enjoyed a know-how, a set of +persistent habits of tool preparation, which would always give him the +same type of tool when he wanted to make it. Therefore, the traditions +show us that persistent habits already existed for the preparation of +one type of tool or another. + +This tells us that one of the characteristic aspects of human culture +was already present. There must have been, in the minds of these +early men, a notion of the ideal type of tool for a particular job. +Furthermore, since we find so many thousands upon thousands of tools +of one type or another, the notion of the ideal types of tools _and_ +the know-how for the making of each type must have been held in common +by many men. The notions of the ideal types and the know-how for their +production must have been passed on from one generation to another. + +I could even guess that the notions of the ideal type of one or the +other of these tools stood out in the minds of men of those times +somewhat like a symbol of perfect tool for good job. If this were +so--remember its only a wild guess of mine--then men were already +symbol users. Now lets go on a further step to the fact that the words +men speak are simply sounds, each different sound being a symbol for a +different meaning. If standardized tool-making suggests symbol-making, +is it also possible that crude word-symbols were also being made? I +suppose that it is not impossible. + +There may, of course, be a real question whether tool-utilizing +creatures--our first step, on page 42--were actually men. Other +animals utilize things at hand as tools. The tool-fashioning creature +of our second step is more suggestive, although we may not yet feel +sure that many of the earlier pebble tools were man-made products. But +with the step to standardization and the appearance of the traditions, +I believe we must surely be dealing with the traces of culture-bearing +_men_. The conventional understandings which Professor Redfields +definition of culture suggests are now evidenced for us in the +persistent habits for the preparation of stone tools. Were we able to +see the other things these prehistoric men must have made--in materials +no longer preserved for the archeologist to find--I believe there would +be clear signs of further conventional understandings. The men may have +been physically primitive and pretty shaggy in appearance, but I think +we must surely call them men. + + +AN OLDER INTERPRETATION OF THE WESTERN TRADITIONS + +In the last chapter, I told you that many of the older archeologists +and human paleontologists used to think that modern man was very old. +The supposed ages of Piltdown and Galley Hill were given as evidence +of the great age of anatomically modern man, and some interpretations +of the Swanscombe and Fontchevade fossils were taken to support +this view. The conclusion was that there were two parallel lines or +phyla of men already present well back in the Pleistocene. The +first of these, the more primitive or paleoanthropic line, was +said to include Heidelberg, the proto-neanderthaloids and classic +Neanderthal. The more anatomically modern or neanthropic line was +thought to consist of Piltdown and the others mentioned above. The +Neanderthaler or paleoanthropic line was thought to have become extinct +after the first phase of the last great glaciation. Of course, the +modern or neanthropic line was believed to have persisted into the +present, as the basis for the worlds population today. But with +Piltdown liquidated, Galley Hill known to be very late, and Swanscombe +and Fontchevade otherwise interpreted, there is little left of the +so-called parallel phyla theory. + +While the theory was in vogue, however, and as long as the European +archeological evidence was looked at in one short-sighted way, the +archeological materials _seemed_ to fit the parallel phyla theory. It +was simply necessary to believe that the flake tools were made only +by the paleoanthropic Neanderthaler line, and that the more handsome +core-biface tools were the product of the neanthropic modern-man line. + +Remember that _almost_ all of the early prehistoric European tools +came only from the redeposited gravel beds. This means that the tools +were not normally found in the remains of camp sites or work shops +where they had actually been dropped by the men who made and used +them. The tools came, rather, from the secondary hodge-podge of the +glacial gravels. I tried to give you a picture of the bulldozing action +of glaciers (p. 40) and of the erosion and weathering that were +side-effects of a glacially conditioned climate on the earths surface. +As we said above, if one simply plucks tools out of the redeposited +gravels, his natural tendency is to type the tools by groups, and to +think that the groups stand for something _on their own_. + +In 1906, M. Victor Commont actually made a rare find of what seems +to have been a kind of workshop site, on a terrace above the Somme +river in France. Here, Commont realized, flake tools appeared clearly +in direct association with core-biface tools. Few prehistorians paid +attention to Commont or his site, however. It was easier to believe +that flake tools represented a distinct culture and that this +culture was that of the Neanderthaler or paleoanthropic line, and +that the core-bifaces stood for another culture which was that of the +supposed early modern or neanthropic line. Of course, I am obviously +skipping many details here. Some later sites with Neanderthal fossils +do seem to have only flake tools, but other such sites have both types +of tools. The flake tools which appeared _with_ the core-bifaces +in the Swanscombe gravels were never made much of, although it +was embarrassing for the parallel phyla people that Fontchevade +ran heavily to flake tools. All in all, the parallel phyla theory +flourished because it seemed so neat and easy to understand. + + +TRADITIONS ARE TOOL-MAKING HABITS, NOT CULTURES + +In case you think I simply enjoy beating a dead horse, look in any +standard book on prehistory written twenty (or even ten) years ago, or +in most encyclopedias. Youll find that each of the individual tool +types, of the West, at least, was supposed to represent a culture. +The cultures were believed to correspond to parallel lines of human +evolution. + +In 1937, Mr. Harper Kelley strongly re-emphasized the importance +of Commonts workshop site and the presence of flake tools with +core-bifaces. Next followed Dr. Movius clear delineation of the +chopper-chopping tool tradition of the Far East. This spoiled the nice +symmetry of the flake-tool = paleoanthropic, core-biface = neanthropic +equations. Then came increasing understanding of the importance of +the pebble tools in Africa, and the location of several more workshop +sites there, especially at Olorgesailie in Kenya. Finally came the +liquidation of Piltdown and the deflation of Galley Hills date. So it +is at last possible to picture an individual prehistoric man making a +flake tool to do one job and a core-biface tool to do another. Commont +showed us this picture in 1906, but few believed him. + +[Illustration: DISTRIBUTION OF TOOL-PREPARATION TRADITIONS + +Time approximately 100,000 years ago] + +There are certainly a few cases in which flake tools did appear with +few or no core-bifaces. The flake-tool group called Clactonian in +England is such a case. Another good, but certainly later case is +that of the cave on Mount Carmel in Palestine, where the blended +pre-neanderthaloid, 70 per cent modern-type skulls were found. Here, in +the same level with the skulls, were 9,784 flint tools. Of these, only +three--doubtless strays--were core-bifaces; all the rest were flake +tools or flake chips. We noted above how the Fontchevade cave ran to +flake tools. The only conclusion I would draw from this is that times +and circumstances did exist in which prehistoric men needed only flake +tools. So they only made flake tools for those particular times and +circumstances. + + +LIFE IN EARLIEST TIMES + +What do we actually know of life in these earliest times? In the +glacial gravels, or in the terrace gravels of rivers once swollen by +floods of melt water or heavy rains, or on the windswept deserts, we +find stone tools. The earliest and coarsest of these are the pebble +tools. We do not yet know what the men who made them looked like, +although the Sterkfontein australopithecines probably give us a good +hint. Then begin the more formal tool preparation traditions of the +west--the core-bifaces and the flake tools--and the chopper-chopping +tool series of the farther east. There is an occasional roughly worked +piece of bone. From the gravels which yield the Clactonian flakes of +England comes the fire-hardened point of a wooden spear. There are +also the chance finds of the fossil human bones themselves, of which +we spoke in the last chapter. Aside from the cave of Peking man, none +of the earliest tools have been found in caves. Open air or workshop +sites which do not seem to have been disturbed later by some geological +agency are very rare. + +The chart on page 65 shows graphically what the situation in +west-central Europe seems to have been. It is not yet certain whether +there were pebble tools there or not. The Fontchevade cave comes +into the picture about 100,000 years ago or more. But for the earlier +hundreds of thousands of years--below the red-dotted line on the +chart--the tools we find come almost entirely from the haphazard +mixture within the geological contexts. + +The stone tools of each of the earlier traditions are the simplest +kinds of all-purpose tools. Almost any one of them could be used for +hacking, chopping, cutting, and scraping; so the men who used them must +have been living in a rough and ready sort of way. They found or hunted +their food wherever they could. In the anthropological jargon, they +were food-gatherers, pure and simple. + +Because of the mixture in the gravels and in the materials they +carried, we cant be sure which animals these men hunted. Bones of +the larger animals turn up in the gravels, but they could just as +well belong to the animals who hunted the men, rather than the other +way about. We dont know. This is why camp sites like Commonts and +Olorgesailie in Kenya are so important when we do find them. The animal +bones at Olorgesailie belonged to various mammals of extremely large +size. Probably they were taken in pit-traps, but there are a number of +groups of three round stones on the site which suggest that the people +used bolas. The South American Indians used three-ball bolas, with the +stones in separate leather bags connected by thongs. These were whirled +and then thrown through the air so as to entangle the feet of a fleeing +animal. + +Professor F. Clark Howell recently returned from excavating another +important open air site at Isimila in Tanganyika. The site yielded +the bones of many fossil animals and also thousands of core-bifaces, +flakes, and choppers. But Howells reconstruction of the food-getting +habits of the Isimila people certainly suggests that the word hunting +is too dignified for what they did; scavenging would be much nearer +the mark. + +During a great part of this time the climate was warm and pleasant. The +second interglacial period (the time between the second and third great +alpine glaciations) lasted a long time, and during much of this time +the climate may have been even better than ours is now. We dont know +that earlier prehistoric men in Europe or Africa lived in caves. They +may not have needed to; much of the weather may have been so nice that +they lived in the open. Perhaps they didnt wear clothes, either. + + +WHAT THE PEKING CAVE-FINDS TELL US + +The one early cave-dwelling we have found is that of Peking man, in +China. Peking man had fire. He probably cooked his meat, or used +the fire to keep dangerous animals away from his den. In the cave +were bones of dangerous animals, members of the wolf, bear, and cat +families. Some of the cat bones belonged to beasts larger than tigers. +There were also bones of other wild animals: buffalo, camel, deer, +elephants, horses, sheep, and even ostriches. Seventy per cent of the +animals Peking man killed were fallow deer. Its much too cold and dry +in north China for all these animals to live there today. So this list +helps us know that the weather was reasonably warm, and that there was +enough rain to grow grass for the grazing animals. The list also helps +the paleontologists to date the find. + +Peking man also seems to have eaten plant food, for there are hackberry +seeds in the debris of the cave. His tools were made of sandstone and +quartz and sometimes of a rather bad flint. As weve already seen, they +belong in the chopper-tool tradition. It seems fairly clear that some +of the edges were chipped by right-handed people. There are also many +split pieces of heavy bone. Peking man probably split them so he could +eat the bone marrow, but he may have used some of them as tools. + +Many of these split bones were the bones of Peking men. Each one of the +skulls had already had the base broken out of it. In no case were any +of the bones resting together in their natural relation to one another. +There is nothing like a burial; all of the bones are scattered. Now +its true that animals could have scattered bodies that were not cared +for or buried. But splitting bones lengthwise and carefully removing +the base of a skull call for both the tools and the people to use them. +Its pretty clear who the people were. Peking man was a cannibal. + + * * * * * + +This rounds out about all we can say of the life and times of early +prehistoric men. In those days life was rough. You evidently had to +watch out not only for dangerous animals but also for your fellow men. +You ate whatever you could catch or find growing. But you had sense +enough to build fires, and you had already formed certain habits for +making the kinds of stone tools you needed. Thats about all we know. +But I think well have to admit that cultural beginnings had been made, +and that these early people were really _men_. + + + + +MORE EVIDENCE of Culture + +[Illustration] + + +While the dating is not yet sure, the material that we get from caves +in Europe must go back to about 100,000 years ago; the time of the +classic Neanderthal group followed soon afterwards. We dont know why +there is no earlier material in the caves; apparently they were not +used before the last interglacial phase (the period just before the +last great glaciation). We know that men of the classic Neanderthal +group were living in caves from about 75,000 to 45,000 years ago. +New radioactive carbon dates even suggest that some of the traces of +culture well describe in this chapter may have lasted to about 35,000 +years ago. Probably some of the pre-neanderthaloid types of men had +also lived in caves. But we have so far found their bones in caves only +in Palestine and at Fontchevade. + + +THE CAVE LAYERS + +In parts of France, some peasants still live in caves. In prehistoric +time, many generations of people lived in them. As a result, many +caves have deep layers of debris. The first people moved in and lived +on the rock floor. They threw on the floor whatever they didnt want, +and they tracked in mud; nobody bothered to clean house in those days. +Their debris--junk and mud and garbage and what not--became packed +into a layer. As time went on, and generations passed, the layer grew +thicker. Then there might have been a break in the occupation of the +cave for a while. Perhaps the game animals got scarce and the people +moved away; or maybe the cave became flooded. Later on, other people +moved in and began making a new layer of their own on top of the first +layer. Perhaps this process of layering went on in the same cave for a +hundred thousand years; you can see what happened. The drawing on this +page shows a section through such a cave. The earliest layer is on the +bottom, the latest one on top. They go in order from bottom to top, +earliest to latest. This is the _stratification_ we talked about (p. +12). + +[Illustration: SECTION OF SHELTER ON LOWER TERRACE, LE MOUSTIER] + +While we may find a mix-up in caves, its not nearly as bad as the +mixing up that was done by glaciers. The animal bones and shells, the +fireplaces, the bones of men, and the tools the men made all belong +together, if they come from one layer. Thats the reason why the cave +of Peking man is so important. It is also the reason why the caves in +Europe and the Near East are so important. We can get an idea of which +things belong together and which lot came earliest and which latest. + +In most cases, prehistoric men lived only in the mouths of caves. +They didnt like the dark inner chambers as places to live in. They +preferred rock-shelters, at the bases of overhanging cliffs, if there +was enough overhang to give shelter. When the weather was good, they no +doubt lived in the open air as well. Ill go on using the term cave +since its more familiar, but remember that I really mean rock-shelter, +as a place in which people actually lived. + +The most important European cave sites are in Spain, France, and +central Europe; there are also sites in England and Italy. A few caves +are known in the Near East and Africa, and no doubt more sites will be +found when the out-of-the-way parts of Europe, Africa, and Asia are +studied. + + +AN INDUSTRY DEFINED + +We have already seen that the earliest European cave materials are +those from the cave of Fontchevade. Movius feels certain that the +lowest materials here date back well into the third interglacial stage, +that which lay between the Riss (next to the last) and the Wrm I +(first stage of the last) alpine glaciations. This material consists +of an _industry_ of stone tools, apparently all made in the flake +tradition. This is the first time we have used the word industry. +It is useful to call all of the different tools found together in one +layer and made of _one kind of material_ an industry; that is, the +tools must be found together as men left them. Tools taken from the +glacial gravels (or from windswept desert surfaces or river gravels +or any geological deposit) are not together in this sense. We might +say the latter have only geological, not archeological context. +Archeological context means finding things just as men left them. We +can tell what tools go together in an industrial sense only if we +have archeological context. + +Up to now, the only things we could have called industries were the +worked stone industry and perhaps the worked (?) bone industry of the +Peking cave. We could add some of the very clear cases of open air +sites, like Olorgesailie. We couldnt use the term for the stone tools +from the glacial gravels, because we do not know which tools belonged +together. But when the cave materials begin to appear in Europe, we can +begin to speak of industries. Most of the European caves of this time +contain industries of flint tools alone. + + +THE EARLIEST EUROPEAN CAVE LAYERS + +Weve just mentioned the industry from what is said to be the oldest +inhabited cave in Europe; that is, the industry from the deepest layer +of the site at Fontchevade. Apparently it doesnt amount to much. The +tools are made of stone, in the flake tradition, and are very poorly +worked. This industry is called _Tayacian_. Its type tool seems to be +a smallish flake tool, but there are also larger flakes which seem to +have been fashioned for hacking. In fact, the type tool seems to be +simply a smaller edition of the Clactonian tool (pictured on p. 45). + +None of the Fontchevade tools are really good. There are scrapers, +and more or less pointed tools, and tools that may have been used +for hacking and chopping. Many of the tools from the earlier glacial +gravels are better made than those of this first industry we see in +a European cave. There is so little of this material available that +we do not know which is really typical and which is not. You would +probably find it hard to see much difference between this industry and +a collection of tools of the type called Clactonian, taken from the +glacial gravels, especially if the Clactonian tools were small-sized. + +The stone industry of the bottommost layer of the Mount Carmel cave, +in Palestine, where somewhat similar tools were found, has also been +called Tayacian. + +I shall have to bring in many unfamiliar words for the names of the +industries. The industries are usually named after the places where +they were first found, and since these were in most cases in France, +most of the names which follow will be of French origin. However, +the names have simply become handles and are in use far beyond the +boundaries of France. It would be better if we had a non-place-name +terminology, but archeologists have not yet been able to agree on such +a terminology. + + +THE ACHEULEAN INDUSTRY + +Both in France and in Palestine, as well as in some African cave +sites, the next layers in the deep caves have an industry in both the +core-biface and the flake traditions. The core-biface tools usually +make up less than half of all the tools in the industry. However, +the name of the biface type of tool is generally given to the whole +industry. It is called the _Acheulean_, actually a late form of it, as +Acheulean is also used for earlier core-biface tools taken from the +glacial gravels. In western Europe, the name used is _Upper Acheulean_ +or _Micoquian_. The same terms have been borrowed to name layers E and +F in the Tabun cave, on Mount Carmel in Palestine. + +The Acheulean core-biface type of tool is worked on two faces so as +to give a cutting edge all around. The outline of its front view may +be oval, or egg-shaped, or a quite pointed pear shape. The large +chip-scars of the Acheulean core-bifaces are shallow and flat. It is +suspected that this resulted from the removal of the chips with a +wooden club; the deep chip-scars of the earlier Abbevillian core-biface +came from beating the tool against a stone anvil. These tools are +really the best and also the final products of the core-biface +tradition. We first noticed the tradition in the early glacial gravels +(p. 43); now we see its end, but also its finest examples, in the +deeper cave levels. + +The flake tools, which really make up the greater bulk of this +industry, are simple scrapers and chips with sharp cutting edges. The +habits used to prepare them must have been pretty much the same as +those used for at least one of the flake industries we shall mention +presently. + +There is very little else in these early cave layers. We do not have +a proper industry of bone tools. There are traces of fire, and of +animal bones, and a few shells. In Palestine, there are many more +bones of deer than of gazelle in these layers; the deer lives in a +wetter climate than does the gazelle. In the European cave layers, the +animal bones are those of beasts that live in a warm climate. They +belonged in the last interglacial period. We have not yet found the +bones of fossil men definitely in place with this industry. + +[Illustration: ACHEULEAN BIFACE] + + +FLAKE INDUSTRIES FROM THE CAVES + +Two more stone industries--the _Levalloisian_ and the +_Mousterian_--turn up at approximately the same time in the European +cave layers. Their tools seem to be mainly in the flake tradition, +but according to some of the authorities their preparation also shows +some combination with the habits by which the core-biface tools were +prepared. + +Now notice that I dont tell you the Levalloisian and the Mousterian +layers are both above the late Acheulean layers. Look at the cave +section (p. 57) and youll find that some Mousterian of Acheulean +tradition appears above some typical Mousterian. This means that +there may be some kinds of Acheulean industries that are later than +some kinds of Mousterian. The same is true of the Levalloisian. + +There were now several different kinds of habits that men used in +making stone tools. These habits were based on either one or the other +of the two traditions--core-biface or flake--or on combinations of +the habits used in the preparation techniques of both traditions. All +were popular at about the same time. So we find that people who made +one kind of stone tool industry lived in a cave for a while. Then they +gave up the cave for some reason, and people with another industry +moved in. Then the first people came back--or at least somebody with +the same tool-making habits as the first people. Or maybe a third group +of tool-makers moved in. The people who had these different habits for +making their stone tools seem to have moved around a good deal. They no +doubt borrowed and exchanged tricks of the trade with each other. There +were no patent laws in those days. + +The extremely complicated interrelationships of the different habits +used by the tool-makers of this range of time are at last being +systematically studied. M. Franois Bordes has developed a statistical +method of great importance for understanding these tool preparation +habits. + + +THE LEVALLOISIAN AND MOUSTERIAN + +The easiest Levalloisian tool to spot is a big flake tool. The trick +in making it was to fashion carefully a big chunk of stone (called +the Levalloisian tortoise core, because it resembles the shape of +a turtle-shell) and then to whack this in such a way that a large +flake flew off. This large thin flake, with sharp cutting edges, is +the finished Levalloisian tool. There were various other tools in a +Levalloisian industry, but this is the characteristic _Levalloisian_ +tool. + +There are several typical Mousterian stone tools. Different from +the tools of the Levalloisian type, these were made from disc-like +cores. There are medium-sized flake side scrapers. There are also +some small pointed tools and some small hand axes. The last of these +tool types is often a flake worked on both of the flat sides (that +is, bifacially). There are also pieces of flint worked into the form +of crude balls. The pointed tools may have been fixed on shafts to +make short jabbing spears; the round flint balls may have been used as +bolas. Actually, we dont _know_ what either tool was used for. The +points and side scrapers are illustrated (pp. 64 and 66). + +[Illustration: LEVALLOIS FLAKE] + + +THE MIXING OF TRADITIONS + +Nowadays the archeologists are less and less sure of the importance +of any one specific tool type and name. Twenty years ago, they used +to speak simply of Acheulean or Levalloisian or Mousterian tools. +Now, more and more, _all_ of the tools from some one layer in a +cave are called an industry, which is given a mixed name. Thus we +have Levalloiso-Mousterian, and Acheuleo-Levalloisian, and even +Acheuleo-Mousterian (or Mousterian of Acheulean tradition). Bordes +systematic work is beginning to clear up some of our confusion. + +The time of these late Acheuleo-Levalloiso-Mousterioid industries +is from perhaps as early as 100,000 years ago. It may have lasted +until well past 50,000 years ago. This was the time of the first +phase of the last great glaciation. It was also the time that the +classic group of Neanderthal men was living in Europe. A number of +the Neanderthal fossil finds come from these cave layers. Before the +different habits of tool preparation were understood it used to be +popular to say Neanderthal man was Mousterian man. I think this is +wrong. What used to be called Mousterian is now known to be a variety +of industries with tools of both core-biface and flake habits, and +so mixed that the word Mousterian used alone really doesnt mean +anything. The Neanderthalers doubtless understood the tool preparation +habits by means of which Acheulean, Levalloisian and Mousterian type +tools were produced. We also have the more modern-like Mount Carmel +people, found in a cave layer of Palestine with tools almost entirely +in the flake tradition, called Levalloiso-Mousterian, and the +Fontchevade-Tayacian (p. 59). + +[Illustration: MOUSTERIAN POINT] + + +OTHER SUGGESTIONS OF LIFE IN THE EARLY CAVE LAYERS + +Except for the stone tools, what do we know of the way men lived in the +time range after 100,000 to perhaps 40,000 years ago or even later? +We know that in the area from Europe to Palestine, at least some of +the people (some of the time) lived in the fronts of caves and warmed +themselves over fires. In Europe, in the cave layers of these times, +we find the bones of different animals; the bones in the lowest layers +belong to animals that lived in a warm climate; above them are the +bones of those who could stand the cold, like the reindeer and mammoth. +Thus, the meat diet must have been changing, as the glacier crept +farther south. Shells and possibly fish bones have lasted in these +cave layers, but there is not a trace of the vegetable foods and the +nuts and berries and other wild fruits that must have been eaten when +they could be found. + +[Illustration: CHART SHOWING PRESENT UNDERSTANDING OF RELATIONSHIPS AND +SUCCESSION OF TOOL-PREPARATION TRADITIONS, INDUSTRIES, AND ASSEMBLAGES +OF WEST-CENTRAL EUROPE + +Wavy lines indicate transitions in industrial habits. These transitions +are not yet understood in detail. The glacial and climatic scheme shown +is the alpine one.] + +Bone tools have also been found from this period. Some are called +scrapers, and there are also long chisel-like leg-bone fragments +believed to have been used for skinning animals. Larger hunks of bone, +which seem to have served as anvils or chopping blocks, are fairly +common. + +Bits of mineral, used as coloring matter, have also been found. We +dont know what the color was used for. + +[Illustration: MOUSTERIAN SIDE SCRAPER] + +There is a small but certain number of cases of intentional burials. +These burials have been found on the floors of the caves; in other +words, the people dug graves in the places where they lived. The holes +made for the graves were small. For this reason (or perhaps for some +other?) the bodies were in a curled-up or contracted position. Flint or +bone tools or pieces of meat seem to have been put in with some of the +bodies. In several cases, flat stones had been laid over the graves. + + +TOOLS FROM AFRICA AND ASIA ABOUT 100,000 YEARS AGO + +Professor Movius characterizes early prehistoric Africa as a continent +showing a variety of stone industries. Some of these industries were +purely local developments and some were practically identical with +industries found in Europe at the same time. From northwest Africa +to Capetown--excepting the tropical rain forest region of the west +center--tools of developed Acheulean, Levalloisian, and Mousterian +types have been recognized. Often they are named after African place +names. + +In east and south Africa lived people whose industries show a +development of the Levalloisian technique. Such industries are +called Stillbay. Another industry, developed on the basis of the +Acheulean technique, is called Fauresmith. From the northwest comes +an industry with tanged points and flake-blades; this is called the +Aterian. The tropical rain forest region contained people whose stone +tools apparently show adjustment to this peculiar environment; the +so-called Sangoan industry includes stone picks, adzes, core-bifaces +of specialized Acheulean type, and bifacial points which were probably +spearheads. + +In western Asia, even as far as the east coast of India, the tools of +the Eurafrican core-biface and flake tool traditions continued to be +used. But in the Far East, as we noted in the last chapter, men had +developed characteristic stone chopper and chopping tools. This tool +preparation tradition--basically a pebble tool tradition--lasted to the +very end of the Ice Age. + +When more intact open air sites such as that of an earlier time at +Olorgesailie, and more stratified cave sites are found and excavated +in Asia and Africa, we shall be able to get a more complete picture. +So far, our picture of the general cultural level of the Old World at +about 100,000 years ago--and soon afterwards--is best from Europe, but +it is still far from complete there, too. + + +CULTURE AT THE BEGINNING OF THE LAST GREAT GLACIAL PERIOD + +The few things we have found must indicate only a very small part +of the total activities of the people who lived at the time. All of +the things they made of wood and bark, of skins, of anything soft, +are gone. The fact that burials were made, at least in Europe and +Palestine, is pretty clear proof that the people had some notion of a +life after death. But what this notion really was, or what gods (if +any) men believed in, we cannot know. Dr. Movius has also reminded me +of the so-called bear cults--cases in which caves have been found which +contain the skulls of bears in apparently purposeful arrangement. This +might suggest some notion of hoarding up the spirits or the strength of +bears killed in the hunt. Probably the people lived in small groups, +as hunting and food-gathering seldom provide enough food for large +groups of people. These groups probably had some kind of leader or +chief. Very likely the rude beginnings of rules for community life +and politics, and even law, were being made. But what these were, we +do not know. We can only guess about such things, as we can only guess +about many others; for example, how the idea of a family must have been +growing, and how there may have been witch doctors who made beginnings +in medicine or in art, in the materials they gathered for their trade. + +The stone tools help us most. They have lasted, and we can find +them. As they come to us, from this cave or that, and from this +layer or that, the tool industries show a variety of combinations +of the different basic habits or traditions of tool preparation. +This seems only natural, as the groups of people must have been very +small. The mixtures and blendings of the habits used in making stone +tools must mean that there were also mixtures and blends in many of +the other ideas and beliefs of these small groups. And what this +probably means is that there was no one _culture_ of the time. It is +certainly unlikely that there were simply three cultures, Acheulean, +Levalloisian, and Mousterian, as has been thought in the past. +Rather there must have been a great variety of loosely related cultures +at about the same stage of advancement. We could say, too, that here +we really begin to see, for the first time, that remarkable ability +of men to adapt themselves to a variety of conditions. We shall see +this adaptive ability even more clearly as time goes on and the record +becomes more complete. + +Over how great an area did these loosely related cultures reach in +the time 75,000 to 45,000 or even as late as 35,000 years ago? We +have described stone tools made in one or another of the flake and +core-biface habits, for an enormous area. It covers all of Europe, all +of Africa, the Near East, and parts of India. It is perfectly possible +that the flake and core-biface habits lasted on after 35,000 years ago, +in some places outside of Europe. In northern Africa, for example, we +are certain that they did (see chart, p. 72). + +On the other hand, in the Far East (China, Burma, Java) and in northern +India, the tools of the old chopper-tool tradition were still being +made. Out there, we must assume, there was a different set of loosely +related cultures. At least, there was a different set of loosely +related habits for the making of tools. But the men who made them must +have looked much like the men of the West. Their tools were different, +but just as useful. + +As to what the men of the West looked like, Ive already hinted at all +we know so far (pp. 29 ff.). The Neanderthalers were present at +the time. Some more modern-like men must have been about, too, since +fossils of them have turned up at Mount Carmel in Palestine, and at +Teshik Tash, in Trans-caspian Russia. It is still too soon to know +whether certain combinations of tools within industries were made +only by certain physical types of men. But since tools of both the +core-biface and the flake traditions, and their blends, turn up from +South Africa to England to India, it is most unlikely that only one +type of man used only one particular habit in the preparation of tools. +What seems perfectly clear is that men in Africa and men in India were +making just as good tools as the men who lived in western Europe. + + + + +EARLY MODERNS + +[Illustration] + + +From some time during the first inter-stadial of the last great +glaciation (say some time after about 40,000 years ago), we have +more accurate dates for the European-Mediterranean area and less +accurate ones for the rest of the Old World. This is probably +because the effects of the last glaciation have been studied in the +European-Mediterranean area more than they have been elsewhere. + + +A NEW TRADITION APPEARS + +Something new was probably beginning to happen in the +European-Mediterranean area about 40,000 years ago, though all the +rest of the Old World seems to have been going on as it had been. I +cant be sure of this because the information we are using as a basis +for dates is very inaccurate for the areas outside of Europe and the +Mediterranean. + +We can at least make a guess. In Egypt and north Africa, men were still +using the old methods of making stone tools. This was especially true +of flake tools of the Levalloisian type, save that they were growing +smaller and smaller as time went on. But at the same time, a new +tradition was becoming popular in westernmost Asia and in Europe. This +was the blade-tool tradition. + + +BLADE TOOLS + +A stone blade is really just a long parallel-sided flake, as the +drawing shows. It has sharp cutting edges, and makes a very useful +knife. The real trick is to be able to make one. It is almost +impossible to make a blade out of any stone but flint or a natural +volcanic glass called obsidian. And even if you have flint or obsidian, +you first have to work up a special cone-shaped blade-core, from +which to whack off blades. + +[Illustration: PLAIN BLADE] + +You whack with a hammer stone against a bone or antler punch which is +directed at the proper place on the blade-core. The blade-core has to +be well supported or gripped while this is going on. To get a good +flint blade tool takes a great deal of know-how. + +Remember that a tradition in stone tools means no more than that some +particular way of making the tools got started and lasted a long time. +Men who made some tools in one tradition or set of habits would also +make other tools for different purposes by means of another tradition +or set of habits. It was even possible for the two sets of habits to +become combined. + + +THE EARLIEST BLADE TOOLS + +The oldest blade tools we have found were deep down in the layers of +the Mount Carmel caves, in Tabun Eb and Ea. Similar tools have been +found in equally early cave levels in Syria; their popularity there +seems to fluctuate a bit. Some more or less parallel-sided flakes are +known in the Levalloisian industry in France, but they are probably +no earlier than Tabun E. The Tabun blades are part of a local late +Acheulean industry, which is characterized by core-biface hand +axes, but which has many flake tools as well. Professor F. E. +Zeuner believes that this industry may be more than 120,000 years old; +actually its date has not yet been fixed, but it is very old--older +than the fossil finds of modern-like men in the same caves. + +[Illustration: SUCCESSION OF ICE AGE FLINT TYPES, INDUSTRIES, AND +ASSEMBLAGES, AND OF FOSSIL MEN, IN NORTHWESTERN EURAFRASIA] + +For some reason, the habit of making blades in Palestine and Syria was +interrupted. Blades only reappeared there at about the same time they +were first made in Europe, some time after 45,000 years ago; that is, +after the first phase of the last glaciation was ended. + +[Illustration: BACKED BLADE] + +We are not sure just where the earliest _persisting_ habits for the +production of blade tools developed. Impressed by the very early +momentary appearance of blades at Tabun on Mount Carmel, Professor +Dorothy A. Garrod first favored the Near East as a center of origin. +She spoke of some as yet unidentified Asiatic centre, which she +thought might be in the highlands of Iran or just beyond. But more +recent work has been done in this area, especially by Professor Coon, +and the blade tools do not seem to have an early appearance there. When +the blade tools reappear in the Syro-Palestinian area, they do so in +industries which also include Levalloiso-Mousterian flake tools. From +the point of view of form and workmanship, the blade tools themselves +are not so fine as those which seem to be making their appearance +in western Europe about the same time. There is a characteristic +Syro-Palestinian flake point, possibly a projectile tip, called the +Emiran, which is not known from Europe. The appearance of blade tools, +together with Levalloiso-Mousterian flakes, continues even after the +Emiran point has gone out of use. + +It seems clear that the production of blade tools did not immediately +swamp the set of older habits in Europe, too; the use of flake +tools also continued there. This was not so apparent to the older +archeologists, whose attention was focused on individual tool types. It +is not, in fact, impossible--although it is certainly not proved--that +the technique developed in the preparation of the Levalloisian tortoise +core (and the striking of the Levalloisian flake from it) might have +followed through to the conical core and punch technique for the +production of blades. Professor Garrod is much impressed with the speed +of change during the later phases of the last glaciation, and its +probable consequences. She speaks of the greater number of industries +having enough individual character to be classified as distinct ... +since evolution now starts to outstrip diffusion. Her evolution here +is of course an industrial evolution rather than a biological one. +Certainly the people of Europe had begun to make blade tools during +the warm spell after the first phase of the last glaciation. By about +40,000 years ago blades were well established. The bones of the blade +tool makers weve found so far indicate that anatomically modern men +had now certainly appeared. Unfortunately, only a few fossil men have +so far been found from the very beginning of the blade tool range in +Europe (or elsewhere). What I certainly shall _not_ tell you is that +conquering bands of fine, strong, anatomically modern men, armed with +superior blade tools, came sweeping out of the East to exterminate the +lowly Neanderthalers. Even if we dont know exactly what happened, Id +lay a good bet it wasnt that simple. + +We do know a good deal about different blade industries in Europe. +Almost all of them come from cave layers. There is a great deal of +complication in what we find. The chart (p. 72) tries to simplify +this complication; in fact, it doubtless simplifies it too much. But +it may suggest all the complication of industries which is going +on at this time. You will note that the upper portion of my much +simpler chart (p. 65) covers the same material (in the section +marked Various Blade-Tool Industries). That chart is certainly too +simplified. + +You will realize that all this complication comes not only from +the fact that we are finding more material. It is due also to the +increasing ability of men to adapt themselves to a great variety of +situations. Their tools indicate this adaptiveness. We know there was +a good deal of climatic change at this time. The plants and animals +that men used for food were changing, too. The great variety of tools +and industries we now find reflect these changes and the ability of men +to keep up with the times. Now, for example, is the first time we are +sure that there are tools to _make_ other tools. They also show mens +increasing ability to adapt themselves. + + +SPECIAL TYPES OF BLADE TOOLS + +The most useful tools that appear at this time were made from blades. + + 1. The backed blade. This is a knife made of a flint blade, with + one edge purposely blunted, probably to save the users fingers + from being cut. There are several shapes of backed blades (p. + 73). + + [Illustration: TWO BURINS] + + 2. The _burin_ or graver. The burin was the original chisel. Its + cutting edge is _transverse_, like a chisels. Some burins are + made like a screw-driver, save that burins are sharp. Others have + edges more like the blade of a chisel or a push plane, with + only one bevel. Burins were probably used to make slots in wood + and bone; that is, to make handles or shafts for other tools. + They must also be the tools with which much of the engraving on + bone (see p. 83) was done. There is a bewildering variety of + different kinds of burins. + +[Illustration: TANGED POINT] + + 3. The tanged point. These stone points were used to tip arrows or + light spears. They were made from blades, and they had a long tang + at the bottom where they were fixed to the shaft. At the place + where the tang met the main body of the stone point, there was + a marked shoulder, the beginnings of a barb. Such points had + either one or two shoulders. + +[Illustration: NOTCHED BLADE] + + 4. The notched or strangulated blade. Along with the points for + arrows or light spears must go a tool to prepare the arrow or + spear shaft. Today, such a tool would be called a draw-knife or + a spoke-shave, and this is what the notched blades probably are. + Our spoke-shaves have sharp straight cutting blades and really + shave. Notched blades of flint probably scraped rather than cut. + + 5. The awl, drill, or borer. These blade tools are worked out + to a spike-like point. They must have been used for making holes + in wood, bone, shell, skin, or other things. + +[Illustration: DRILL OR AWL] + + 6. The end-scraper on a blade is a tool with one or both ends + worked so as to give a good scraping edge. It could have been used + to hollow out wood or bone, scrape hides, remove bark from trees, + and a number of other things (p. 78). + +There is one very special type of flint tool, which is best known from +western Europe in an industry called the Solutrean. These tools were +usually made of blades, but the best examples are so carefully worked +on both sides (bifacially) that it is impossible to see the original +blade. This tool is + + 7. The laurel leaf point. Some of these tools were long and + dagger-like, and must have been used as knives or daggers. Others + were small, called willow leaf, and must have been mounted on + spear or arrow shafts. Another typical Solutrean tool is the + shouldered point. Both the laurel leaf and shouldered point + types are illustrated (see above and p. 79). + +[Illustration: END-SCRAPER ON A BLADE] + +[Illustration: LAUREL LEAF POINT] + +The industries characterized by tools in the blade tradition also +yield some flake and core tools. We will end this list with two types +of tools that appear at this time. The first is made of a flake; the +second is a core tool. + +[Illustration: SHOULDERED POINT] + + 8. The keel-shaped round scraper is usually small and quite round, + and has had chips removed up to a peak in the center. It is called + keel-shaped because it is supposed to look (when upside down) + like a section through a boat. Actually, it looks more like a tent + or an umbrella. Its outer edges are sharp all the way around, and + it was probably a general purpose scraping tool (see illustration, + p. 81). + + 9. The keel-shaped nosed scraper is a much larger and heavier tool + than the round scraper. It was made on a core with a flat bottom, + and has one nicely worked end or nose. Such tools are usually + large enough to be easily grasped, and probably were used like + push planes (see illustration, p. 81). + +[Illustration: KEEL-SHAPED ROUND SCRAPER] + +[Illustration: KEEL-SHAPED NOSED SCRAPER] + +The stone tools (usually made of flint) we have just listed are among +the most easily recognized blade tools, although they show differences +in detail at different times. There are also many other kinds. Not +all of these tools appear in any one industry at one time. Thus the +different industries shown in the chart (p. 72) each have only some +of the blade tools weve just listed, and also a few flake tools. Some +industries even have a few core tools. The particular types of blade +tools appearing in one cave layer or another, and the frequency of +appearance of the different types, tell which industry we have in each +layer. + + +OTHER KINDS OF TOOLS + +By this time in Europe--say from about 40,000 to about 10,000 years +ago--we begin to find other kinds of material too. Bone tools begin +to appear. There are knives, pins, needles with eyes, and little +double-pointed straight bars of bone that were probably fish-hooks. The +fish-line would have been fastened in the center of the bar; when the +fish swallowed the bait, the bar would have caught cross-wise in the +fishs mouth. + +One quite special kind of bone tool is a long flat point for a light +spear. It has a deep notch cut up into the breadth of its base, and is +called a split-based bone point (p. 82). We know examples of bone +beads from these times, and of bone handles for flint tools. Pierced +teeth of some animals were worn as beads or pendants, but I am not sure +that elks teeth were worn this early. There are even spool-shaped +buttons or toggles. + +[Illustration: SPLIT-BASED BONE POINT] + +[Illustration: SPEAR-THROWER] + +[Illustration: BONE HARPOON] + +Antler came into use for tools, especially in central and western +Europe. We do not know the use of one particular antler tool that +has a large hole bored in one end. One suggestion is that it was +a thong-stropper used to strop or work up hide thongs (see +illustration, below); another suggestion is that it was an arrow-shaft +straightener. + +Another interesting tool, usually of antler, is the spear-thrower, +which is little more than a stick with a notch or hook on one end. +The hook fits into the butt end of the spear, and the length of the +spear-thrower allows you to put much more power into the throw (p. +82). It works on pretty much the same principle as the sling. + +Very fancy harpoons of antler were also made in the latter half of +the period in western Europe. These harpoons had barbs on one or both +sides and a base which would slip out of the shaft (p. 82). Some have +engraved decoration. + + +THE BEGINNING OF ART + +[Illustration: THONG-STROPPER] + +In western Europe, at least, the period saw the beginning of several +kinds of art work. It is handy to break the art down into two great +groups: the movable art, and the cave paintings and sculpture. The +movable art group includes the scratchings, engravings, and modeling +which decorate tools and weapons. Knives, stroppers, spear-throwers, +harpoons, and sometimes just plain fragments of bone or antler are +often carved. There is also a group of large flat pebbles which seem +almost to have served as sketch blocks. The surfaces of these various +objects may show animals, or rather abstract floral designs, or +geometric designs. + +[Illustration: VENUS FIGURINE FROM WILLENDORF] + +Some of the movable art is not done on tools. The most remarkable +examples of this class are little figures of women. These women seem to +be pregnant, and their most female characteristics are much emphasized. +It is thought that these Venus or Mother-goddess figurines may be +meant to show the great forces of nature--fertility and the birth of +life. + + +CAVE PAINTINGS + +In the paintings on walls and ceilings of caves we have some examples +that compare with the best art of any time. The subjects were usually +animals, the great cold-weather beasts of the end of the Ice Age: the +mammoth, the wooly rhinoceros, the bison, the reindeer, the wild horse, +the bear, the wild boar, and wild cattle. As in the movable art, there +are different styles in the cave art. The really great cave art is +pretty well restricted to southern France and Cantabrian (northwestern) +Spain. + +There are several interesting things about the Franco-Cantabrian cave +art. It was done deep down in the darkest and most dangerous parts of +the caves, although the men lived only in the openings of caves. If you +think what they must have had for lights--crude lamps of hollowed stone +have been found, which must have burned some kind of oil or grease, +with a matted hair or fiber wick--and of the animals that may have +lurked in the caves, youll understand the part about danger. Then, +too, were sure the pictures these people painted were not simply to be +looked at and admired, for they painted one picture right over other +pictures which had been done earlier. Clearly, it was the _act_ of +_painting_ that counted. The painter had to go way down into the most +mysterious depths of the earth and create an animal in paint. Possibly +he believed that by doing this he gained some sort of magic power over +the same kind of animal when he hunted it in the open air. It certainly +doesnt look as if he cared very much about the picture he painted--as +a finished product to be admired--for he or somebody else soon went +down and painted another animal right over the one he had done. + +The cave art of the Franco-Cantabrian style is one of the great +artistic achievements of all time. The subjects drawn are almost always +the larger animals of the time: the bison, wild cattle and horses, the +wooly rhinoceros, the mammoth, the wild boar, and the bear. In some of +the best examples, the beasts are drawn in full color and the paintings +are remarkably alive and charged with energy. They come from the hands +of men who knew the great animals well--knew the feel of their fur, the +tremendous drive of their muscles, and the danger one faced when he +hunted them. + +Another artistic style has been found in eastern Spain. It includes +lively drawings, often of people hunting with bow and arrow. The East +Spanish art is found on open rock faces and in rock-shelters. It is +less spectacular and apparently more recent than the Franco-Cantabrian +cave art. + + +LIFE AT THE END OF THE ICE AGE IN EUROPE + +Life in these times was probably as good as a hunter could expect it +to be. Game and fish seem to have been plentiful; berries and wild +fruits probably were, too. From France to Russia, great pits or +piles of animal bones have been found. Some of this killing was done +as our Plains Indians killed the buffalo--by stampeding them over +steep river banks or cliffs. There were also good tools for hunting, +however. In western Europe, people lived in the openings of caves and +under overhanging rocks. On the great plains of eastern Europe, very +crude huts were being built, half underground. The first part of this +time must have been cold, for it was the middle and end phases of the +last great glaciation. Northern Europe from Scotland to Scandinavia, +northern Germany and Russia, and also the higher mountains to the +south, were certainly covered with ice. But people had fire, and the +needles and tools that were used for scraping hides must mean that they +wore clothing. + +It is clear that men were thinking of a great variety of things beside +the tools that helped them get food and shelter. Such burials as we +find have more grave-gifts than before. Beads and ornaments and often +flint, bone, or antler tools are included in the grave, and sometimes +the body is sprinkled with red ochre. Red is the color of blood, which +means life, and of fire, which means heat. Professor Childe wonders if +the red ochre was a pathetic attempt at magic--to give back to the body +the heat that had gone from it. But pathetic or not, it is sure proof +that these people were already moved by death as men still are moved by +it. + +Their art is another example of the direction the human mind was +taking. And when I say human, I mean it in the fullest sense, for this +is the time in which fully modern man has appeared. On page 34, we +spoke of the Cro-Magnon group and of the Combe Capelle-Brnn group of +Caucasoids and of the Grimaldi Negroids, who are no longer believed +to be Negroid. I doubt that any one of these groups produced most of +the achievements of the times. Its not yet absolutely sure which +particular group produced the great cave art. The artists were almost +certainly a blend of several (no doubt already mixed) groups. The pair +of Grimaldians were buried in a grave with a sprinkling of red ochre, +and were provided with shell beads and ornaments and with some blade +tools of flint. Regardless of the different names once given them by +the human paleontologists, each of these groups seems to have shared +equally in the cultural achievements of the times, for all that the +archeologists can say. + + +MICROLITHS + +One peculiar set of tools seems to serve as a marker for the very last +phase of the Ice Age in southwestern Europe. This tool-making habit is +also found about the shore of the Mediterranean basin, and it moved +into northern Europe as the last glaciation pulled northward. People +began making blade tools of very small size. They learned how to chip +very slender and tiny blades from a prepared core. Then they made these +little blades into tiny triangles, half-moons (lunates), trapezoids, +and several other geometric forms. These little tools are called +microliths. They are so small that most of them must have been fixed +in handles or shafts. + +[Illustration: MICROLITHS + + BLADE FRAGMENT + BURIN + LUNATE + TRAPEZOID + SCALENE TRIANGLE + ARROWHEAD] + +We have found several examples of microliths mounted in shafts. In +northern Europe, where their use soon spread, the microlithic triangles +or lunates were set in rows down each side of a bone or wood point. +One corner of each little triangle stuck out, and the whole thing +made a fine barbed harpoon. In historic times in Egypt, geometric +trapezoidal microliths were still in use as arrowheads. They were +fastened--broad end out--on the end of an arrow shaft. It seems queer +to give an arrow a point shaped like a T. Actually, the little points +were very sharp, and must have pierced the hides of animals very +easily. We also think that the broader cutting edge of the point may +have caused more bleeding than a pointed arrowhead would. In hunting +fleet-footed animals like the gazelle, which might run for miles after +being shot with an arrow, it was an advantage to cause as much bleeding +as possible, for the animal would drop sooner. + +We are not really sure where the microliths were first invented. There +is some evidence that they appear early in the Near East. Their use +was very common in northwest Africa but this came later. The microlith +makers who reached south Russia and central Europe possibly moved up +out of the Near East. Or it may have been the other way around; we +simply dont yet know. + +Remember that the microliths we are talking about here were made from +carefully prepared little blades, and are often geometric in outline. +Each microlithic industry proper was made up, in good part, of such +tiny blade tools. But there were also some normal-sized blade tools and +even some flake scrapers, in most microlithic industries. I emphasize +this bladelet and the geometric character of the microlithic industries +of the western Old World, since there has sometimes been confusion in +the matter. Sometimes small flake chips, utilized as minute pointed +tools, have been called microliths. They may be _microlithic_ in size +in terms of the general meaning of the word, but they do not seem to +belong to the sub-tradition of the blade tool preparation habits which +we have been discussing here. + + +LATER BLADE-TOOL INDUSTRIES OF THE NEAR EAST AND AFRICA + +The blade-tool industries of normal size we talked about earlier spread +from Europe to central Siberia. We noted that blade tools were made +in western Asia too, and early, although Professor Garrod is no longer +sure that the whole tradition originated in the Near East. If you look +again at my chart (p. 72) you will note that in western Asia I list +some of the names of the western European industries, but with the +qualification -like (for example, Gravettian-like). The western +Asiatic blade-tool industries do vaguely recall some aspects of those +of western Europe, but we would probably be better off if we used +completely local names for them. The Emiran of my chart is such an +example; its industry includes a long spike-like blade point which has +no western European counterpart. + +When we last spoke of Africa (p. 66), I told you that stone tools +there were continuing in the Levalloisian flake tradition, and were +becoming smaller. At some time during this process, two new tool +types appeared in northern Africa: one was the Aterian point with +a tang (p. 67), and the other was a sort of laurel leaf point, +called the Sbaikian. These two tool types were both produced from +flakes. The Sbaikian points, especially, are roughly similar to some +of the Solutrean points of Europe. It has been suggested that both the +Sbaikian and Aterian points may be seen on their way to France through +their appearance in the Spanish cave deposits of Parpallo, but there is +also a rival pre-Solutrean in central Europe. We still do not know +whether there was any contact between the makers of these north African +tools and the Solutrean tool-makers. What does seem clear is that the +blade-tool tradition itself arrived late in northern Africa. + + +NETHER AFRICA + +Blade tools and laurel leaf points and some other probably late +stone tool types also appear in central and southern Africa. There +are geometric microliths on bladelets and even some coarse pottery in +east Africa. There is as yet no good way of telling just where these +items belong in time; in broad geological terms they are late. +Some people have guessed that they are as early as similar European +and Near Eastern examples, but I doubt it. The makers of small-sized +Levalloisian flake tools occupied much of Africa until very late in +time. + + +THE FAR EAST + +India and the Far East still seem to be going their own way. In India, +some blade tools have been found. These are not well dated, save that +we believe they must be post-Pleistocene. In the Far East it looks as +if the old chopper-tool tradition was still continuing. For Burma, +Dr. Movius feels this is fairly certain; for China he feels even more +certain. Actually, we know very little about the Far East at about the +time of the last glaciation. This is a shame, too, as you will soon +agree. + + +THE NEW WORLD BECOMES INHABITED + +At some time toward the end of the last great glaciation--almost +certainly after 20,000 years ago--people began to move over Bering +Strait, from Asia into America. As you know, the American Indians have +been assumed to be basically Mongoloids. New studies of blood group +types make this somewhat uncertain, but there is no doubt that the +ancestors of the American Indians came from Asia. + +The stone-tool traditions of Europe, Africa, the Near and Middle East, +and central Siberia, did _not_ move into the New World. With only a +very few special or late exceptions, there are _no_ core-bifaces, +flakes, or blade tools of the Old World. Such things just havent been +found here. + +This is why I say its a shame we dont know more of the end of the +chopper-tool tradition in the Far East. According to Weidenreich, +the Mongoloids were in the Far East long before the end of the last +glaciation. If the genetics of the blood group types do demand a +non-Mongoloid ancestry for the American Indians, who else may have been +in the Far East 25,000 years ago? We know a little about the habits +for making stone tools which these first people brought with them, +and these habits dont conform with those of the western Old World. +Wed better keep our eyes open for whatever happened to the end of +the chopper-tool tradition in northern China; already there are hints +that it lasted late there. Also we should watch future excavations +in eastern Siberia. Perhaps we shall find the chopper-tool tradition +spreading up that far. + + +THE NEW ERA + +Perhaps it comes in part from the way I read the evidence and perhaps +in part it is only intuition, but I feel that the materials of this +chapter suggest a new era in the ways of life. Before about 40,000 +years ago, people simply gathered their food, wandering over large +areas to scavenge or to hunt in a simple sort of way. But here we +have seen them settling-in more, perhaps restricting themselves in +their wanderings and adapting themselves to a given locality in more +intensive ways. This intensification might be suggested by the word +collecting. The ways of life we described in the earlier chapters +were food-gathering ways, but now an era of food-collecting has +begun. We shall see further intensifications of it in the next chapter. + + + + +End and PRELUDE + +[Illustration] + + +Up to the end of the last glaciation, we prehistorians have a +relatively comfortable time schedule. The farther back we go the less +exact we can be about time and details. Elbow-room of five, ten, +even fifty or more thousands of years becomes available for us to +maneuver in as we work backward in time. But now our story has come +forward to the point where more exact methods of dating are at hand. +The radioactive carbon method reaches back into the span of the last +glaciation. There are other methods, developed by the geologists and +paleobotanists, which supplement and extend the usefulness of the +radioactive carbon dates. And, happily, as our means of being more +exact increases, our story grows more exciting. There are also more +details of culture for us to deal with, which add to the interest. + + +CHANGES AT THE END OF THE ICE AGE + +The last great glaciation of the Ice Age was a two-part affair, with a +sub-phase at the end of the second part. In Europe the last sub-phase +of this glaciation commenced somewhere around 15,000 years ago. Then +the glaciers began to melt back, for the last time. Remember that +Professor Antevs (p. 19) isnt sure the Ice Age is over yet! This +melting sometimes went by fits and starts, and the weather wasnt +always changing for the better; but there was at least one time when +European weather was even better than it is now. + +The melting back of the glaciers and the weather fluctuations caused +other changes, too. We know a fair amount about these changes in +Europe. In an earlier chapter, we said that the whole Ice Age was a +matter of continual change over long periods of time. As the last +glaciers began to melt back some interesting things happened to mankind. + +In Europe, along with the melting of the last glaciers, geography +itself was changing. Britain and Ireland had certainly become islands +by 5000 B.C. The Baltic was sometimes a salt sea, sometimes a large +fresh-water lake. Forests began to grow where the glaciers had been, +and in what had once been the cold tundra areas in front of the +glaciers. The great cold-weather animals--the mammoth and the wooly +rhinoceros--retreated northward and finally died out. It is probable +that the efficient hunting of the earlier people of 20,000 or 25,000 +to about 12,000 years ago had helped this process along (see p. 86). +Europeans, especially those of the post-glacial period, had to keep +changing to keep up with the times. + +The archeological materials for the time from 10,000 to 6000 B.C. seem +simpler than those of the previous five thousand years. The great cave +art of France and Spain had gone; so had the fine carving in bone and +antler. Smaller, speedier animals were moving into the new forests. New +ways of hunting them, or ways of getting other food, had to be found. +Hence, new tools and weapons were necessary. Some of the people who +moved into northern Germany were successful reindeer hunters. Then the +reindeer moved off to the north, and again new sources of food had to +be found. + + +THE READJUSTMENTS COMPLETED IN EUROPE + +After a few thousand years, things began to look better. Or at least +we can say this: By about 6000 B.C. we again get hotter archeological +materials. The best of these come from the north European area: +Britain, Belgium, Holland, Denmark, north Germany, southern Norway and +Sweden. Much of this north European material comes from bogs and swamps +where it had become water-logged and has kept very well. Thus we have +much more complete _assemblages_[4] than for any time earlier. + + [4] Assemblage is a useful word when there are different kinds of + archeological materials belonging together, from one area and of + one time. An assemblage is made up of a number of industries + (that is, all the tools in chipped stone, all the tools in + bone, all the tools in wood, the traces of houses, etc.) and + everything else that manages to survive, such as the art, the + burials, the bones of the animals used as food, and the traces + of plant foods; in fact, everything that has been left to us + and can be used to help reconstruct the lives of the people to + whom it once belonged. Our own present-day assemblage would be + the sum total of all the objects in our mail-order catalogues, + department stores and supply houses of every sort, our churches, + our art galleries and other buildings, together with our roads, + canals, dams, irrigation ditches, and any other traces we might + leave of ourselves, from graves to garbage dumps. Not everything + would last, so that an archeologist digging us up--say 2,000 + years from now--would find only the most durable items in our + assemblage. + +The best known of these assemblages is the _Maglemosian_, named after a +great Danish peat-swamp where much has been found. + +[Illustration: SKETCH OF MAGLEMOSIAN ASSEMBLAGE + + CHIPPED STONE + HEMP + GROUND STONE + BONE AND ANTLER + WOOD] + +In the Maglemosian assemblage the flint industry was still very +important. Blade tools, tanged arrow points, and burins were still +made, but there were also axes for cutting the trees in the new +forests. Moreover, the tiny microlithic blades, in a variety of +geometric forms, are also found. Thus, a specialized tradition that +possibly began east of the Mediterranean had reached northern Europe. +There was also a ground stone industry; some axes and club-heads were +made by grinding and polishing rather than by chipping. The industries +in bone and antler show a great variety of tools: axes, fish-hooks, +fish spears, handles and hafts for other tools, harpoons, and clubs. +A remarkable industry in wood has been preserved. Paddles, sled +runners, handles for tools, and bark floats for fish-nets have been +found. There are even fish-nets made of plant fibers. Canoes of some +kind were no doubt made. Bone and antler tools were decorated with +simple patterns, and amber was collected. Wooden bows and arrows are +found. + +It seems likely that the Maglemosian bog finds are remains of summer +camps, and that in winter the people moved to higher and drier regions. +Childe calls them the Forest folk; they probably lived much the +same sort of life as did our pre-agricultural Indians of the north +central states. They hunted small game or deer; they did a great deal +of fishing; they collected what plant food they could find. In fact, +their assemblage shows us again that remarkable ability of men to adapt +themselves to change. They had succeeded in domesticating the dog; he +was still a very wolf-like dog, but his long association with mankind +had now begun. Professor Coon believes that these people were direct +descendants of the men of the glacial age and that they had much the +same appearance. He believes that most of the Ice Age survivors still +extant are living today in the northwestern European area. + + +SOUTH AND CENTRAL EUROPE PERHAPS AS READJUSTED AS THE NORTH + +There is always one trouble with things that come from areas where +preservation is exceptionally good: The very quantity of materials in +such an assemblage tends to make things from other areas look poor +and simple, although they may not have been so originally at all. The +assemblages of the people who lived to the south of the Maglemosian +area may also have been quite large and varied; but, unfortunately, +relatively little of the southern assemblages has lasted. The +water-logged sites of the Maglemosian area preserved a great deal +more. Hence the Maglemosian itself _looks_ quite advanced to us, when +we compare it with the few things that have happened to last in other +areas. If we could go back and wander over the Europe of eight thousand +years ago, we would probably find that the peoples of France, central +Europe, and south central Russia were just as advanced as those of the +north European-Baltic belt. + +South of the north European belt the hunting-food-collecting peoples +were living on as best they could during this time. One interesting +group, which seems to have kept to the regions of sandy soil and scrub +forest, made great quantities of geometric microliths. These are the +materials called _Tardenoisian_. The materials of the Forest folk of +France and central Europe generally are called _Azilian_; Dr. Movius +believes the term might best be restricted to the area south of the +Loire River. + + +HOW MUCH REAL CHANGE WAS THERE? + +You can see that no really _basic_ change in the way of life has yet +been described. Childe sees the problem that faced the Europeans of +10,000 to 3000 B.C. as a problem in readaptation to the post-glacial +forest environment. By 6000 B.C. some quite successful solutions of +the problem--like the Maglemosian--had been made. The upsets that came +with the melting of the last ice gradually brought about all sorts of +changes in the tools and food-getting habits, but the people themselves +were still just as much simple hunters, fishers, and food-collectors as +they had been in 25,000 B.C. It could be said that they changed just +enough so that they would not have to change. But there is a bit more +to it than this. + +Professor Mathiassen of Copenhagen, who knows the archeological remains +of this time very well, poses a question. He speaks of the material +as being neither rich nor progressive, in fact rather stagnant, but +he goes on to add that the people had a certain receptiveness and +were able to adapt themselves quickly when the next change did come. +My own understanding of the situation is that the Forest folk made +nothing as spectacular as had the producers of the earlier Magdalenian +assemblage and the Franco-Cantabrian art. On the other hand, they +_seem_ to have been making many more different kinds of tools for many +more different kinds of tasks than had their Ice Age forerunners. I +emphasize seem because the preservation in the Maglemosian bogs +is very complete; certainly we cannot list anywhere near as many +different things for earlier times as we did for the Maglemosians +(p. 94). I believe this experimentation with all kinds of new tools +and gadgets, this intensification of adaptiveness (p. 91), this +receptiveness, even if it is still only pointed toward hunting, +fishing, and food-collecting, is an important thing. + +Remember that the only marker we have handy for the _beginning_ of +this tendency toward receptiveness and experimentation is the +little microlithic blade tools of various geometric forms. These, we +saw, began before the last ice had melted away, and they lasted on +in use for a very long time. I wish there were a better marker than +the microliths but I do not know of one. Remember, too, that as yet +we can only use the microliths as a marker in Europe and about the +Mediterranean. + + +CHANGES IN OTHER AREAS? + +All this last section was about Europe. How about the rest of the world +when the last glaciers were melting away? + +We simply dont know much about this particular time in other parts +of the world except in Europe, the Mediterranean basin and the Middle +East. People were certainly continuing to move into the New World by +way of Siberia and the Bering Strait about this time. But for the +greater part of Africa and Asia, we do not know exactly what was +happening. Some day, we shall no doubt find out; today we are without +clear information. + + +REAL CHANGE AND PRELUDE IN THE NEAR EAST + +The appearance of the microliths and the developments made by the +Forest folk of northwestern Europe also mark an end. They show us +the terminal phase of the old food-collecting way of life. It grows +increasingly clear that at about the same time that the Maglemosian and +other Forest folk were adapting themselves to hunting, fishing, and +collecting in new ways to fit the post-glacial environment, something +completely new was being made ready in western Asia. + +Unfortunately, we do not have as much understanding of the climate and +environment of the late Ice Age in western Asia as we have for most +of Europe. Probably the weather was never so violent or life quite +so rugged as it was in northern Europe. We know that the microliths +made their appearance in western Asia at least by 10,000 B.C. and +possibly earlier, marking the beginning of the terminal phase of +food-collecting. Then, gradually, we begin to see the build-up towards +the first _basic change_ in human life. + +This change amounted to a revolution just as important as the +Industrial Revolution. In it, men first learned to domesticate +plants and animals. They began _producing_ their food instead of +simply gathering or collecting it. When their food-production +became reasonably effective, people could and did settle down in +village-farming communities. With the appearance of the little farming +villages, a new way of life was actually under way. Professor Childe +has good reason to speak of the food-producing revolution, for it was +indeed a revolution. + + +QUESTIONS ABOUT CAUSE + +We do not yet know _how_ and _why_ this great revolution took place. We +are only just beginning to put the questions properly. I suspect the +answers will concern some delicate and subtle interplay between man and +nature. Clearly, both the level of culture and the natural condition of +the environment must have been ready for the great change, before the +change itself could come about. + +It is going to take years of co-operative field work by both +archeologists and the natural scientists who are most helpful to them +before the _how_ and _why_ answers begin to appear. Anthropologically +trained archeologists are fascinated with the cultures of men in times +of great change. About ten or twelve thousand years ago, the general +level of culture in many parts of the world seems to have been ready +for change. In northwestern Europe, we saw that cultures changed +just enough so that they would not have to change. We linked this to +environmental changes with the coming of post-glacial times. + +In western Asia, we archeologists can prove that the food-producing +revolution actually took place. We can see _the_ important consequence +of effective domestication of plants and animals in the appearance of +the settled village-farming community. And within the village-farming +community was the seed of civilization. The way in which effective +domestication of plants and animals came about, however, must also be +linked closely with the natural environment. Thus the archeologists +will not solve the _how_ and _why_ questions alone--they will need the +help of interested natural scientists in the field itself. + + +PRECONDITIONS FOR THE REVOLUTION + +Especially at this point in our story, we must remember how culture and +environment go hand in hand. Neither plants nor animals domesticate +themselves; men domesticate them. Furthermore, men usually domesticate +only those plants and animals which are useful. There is a good +question here: What is cultural usefulness? But I shall side-step it to +save time. Men cannot domesticate plants and animals that do not exist +in the environment where the men live. Also, there are certainly some +animals and probably some plants that resist domestication, although +they might be useful. + +This brings me back again to the point that _both_ the level of culture +and the natural condition of the environment--with the proper plants +and animals in it--must have been ready before domestication could +have happened. But this is precondition, not cause. Why did effective +food-production happen first in the Near East? Why did it happen +independently in the New World slightly later? Why also in the Far +East? Why did it happen at all? Why are all human beings not still +living as the Maglemosians did? These are the questions we still have +to face. + + +CULTURAL RECEPTIVENESS AND PROMISING ENVIRONMENTS + +Until the archeologists and the natural scientists--botanists, +geologists, zoologists, and general ecologists--have spent many more +years on the problem, we shall not have full _how_ and _why_ answers. I +do think, however, that we are beginning to understand what to look for. + +We shall have to learn much more of what makes the cultures of men +receptive and experimental. Did change in the environment alone +force it? Was it simply a case of Professor Toynbees challenge and +response? I cannot believe the answer is quite that simple. Were it +so simple, we should want to know why the change hadnt come earlier, +along with earlier environmental changes. We shall not know the answer, +however, until we have excavated the traces of many more cultures of +the time in question. We shall doubtless also have to learn more about, +and think imaginatively about, the simpler cultures still left today. +The mechanics of culture in general will be bound to interest us. + +It will also be necessary to learn much more of the environments of +10,000 to 12,000 years ago. In which regions of the world were the +natural conditions most promising? Did this promise include plants and +animals which could be domesticated, or did it only offer new ways of +food-collecting? There is much work to do on this problem, but we are +beginning to get some general hints. + +Before I begin to detail the hints we now have from western Asia, I +want to do two things. First, I shall tell you of an old theory as to +how food-production might have appeared. Second, I will bother you with +some definitions which should help us in our thinking as the story goes +on. + + +AN OLD THEORY AS TO THE CAUSE OF THE REVOLUTION + +The idea that change would result, if the balance between nature +and culture became upset, is of course not a new one. For at least +twenty-five years, there has been a general theory as to _how_ the +food-producing revolution happened. This theory depends directly on the +idea of natural change in the environment. + +The five thousand years following about 10,000 B.C. must have been +very difficult ones, the theory begins. These were the years when +the most marked melting of the last glaciers was going on. While the +glaciers were in place, the climate to the south of them must have been +different from the climate in those areas today. You have no doubt read +that people once lived in regions now covered by the Sahara Desert. +This is true; just when is not entirely clear. The theory is that +during the time of the glaciers, there was a broad belt of rain winds +south of the glaciers. These rain winds would have kept north Africa, +the Nile Valley, and the Middle East green and fertile. But when the +glaciers melted back to the north, the belt of rain winds is supposed +to have moved north too. Then the people living south and east of the +Mediterranean would have found that their water supply was drying up, +that the animals they hunted were dying or moving away, and that the +plant foods they collected were dried up and scarce. + +According to the theory, all this would have been true except in the +valleys of rivers and in oases in the growing deserts. Here, in the +only places where water was left, the men and animals and plants would +have clustered. They would have been forced to live close to one +another, in order to live at all. Presently the men would have seen +that some animals were more useful or made better food than others, +and so they would have begun to protect these animals from their +natural enemies. The men would also have been forced to try new plant +foods--foods which possibly had to be prepared before they could be +eaten. Thus, with trials and errors, but by being forced to live close +to plants and animals, men would have learned to domesticate them. + + +THE OLD THEORY TOO SIMPLE FOR THE FACTS + +This theory was set up before we really knew anything in detail about +the later prehistory of the Near and Middle East. We now know that +the facts which have been found dont fit the old theory at all well. +Also, I have yet to find an American meteorologist who feels that we +know enough about the changes in the weather pattern to say that it can +have been so simple and direct. And, of course, the glacial ice which +began melting after 12,000 years ago was merely the last sub-phase of +the last great glaciation. There had also been three earlier periods +of great alpine glaciers, and long periods of warm weather in between. +If the rain belt moved north as the glaciers melted for the last time, +it must have moved in the same direction in earlier times. Thus, the +forced neighborliness of men, plants, and animals in river valleys and +oases must also have happened earlier. Why didnt domestication happen +earlier, then? + +Furthermore, it does not seem to be in the oases and river valleys +that we have our first or only traces of either food-production +or the earliest farming villages. These traces are also in the +hill-flanks of the mountains of western Asia. Our earliest sites of the +village-farmers do not seem to indicate a greatly different climate +from that which the same region now shows. In fact, everything we now +know suggests that the old theory was just too simple an explanation to +have been the true one. The only reason I mention it--beyond correcting +the ideas you may get in the general texts--is that it illustrates the +kind of thinking we shall have to do, even if it is doubtless wrong in +detail. + +We archeologists shall have to depend much more than we ever have on +the natural scientists who can really help us. I can tell you this from +experience. I had the great good fortune to have on my expedition staff +in Iraq in 1954-55, a geologist, a botanist, and a zoologist. Their +studies added whole new bands of color to my spectrum of thinking about +_how_ and _why_ the revolution took place and how the village-farming +community began. But it was only a beginning; as I said earlier, we are +just now learning to ask the proper questions. + + +ABOUT STAGES AND ERAS + +Now come some definitions, so I may describe my material more easily. +Archeologists have always loved to make divisions and subdivisions +within the long range of materials which they have found. They often +disagree violently about which particular assemblage of material +goes into which subdivision, about what the subdivisions should be +named, about what the subdivisions really mean culturally. Some +archeologists, probably through habit, favor an old scheme of Grecized +names for the subdivisions: paleolithic, mesolithic, neolithic. I +refuse to use these words myself. They have meant too many different +things to too many different people and have tended to hide some pretty +fuzzy thinking. Probably you havent even noticed my own scheme of +subdivision up to now, but Id better tell you in general what it is. + +I think of the earliest great group of archeological materials, from +which we can deduce only a food-gathering way of culture, as the +_food-gathering stage_. I say stage rather than age, because it +is not quite over yet; there are still a few primitive people in +out-of-the-way parts of the world who remain in the _food-gathering +stage_. In fact, Professor Julian Steward would probably prefer to call +it a food-gathering _level_ of existence, rather than a stage. This +would be perfectly acceptable to me. I also tend to find myself using +_collecting_, rather than _gathering_, for the more recent aspects or +era of the stage, as the word collecting appears to have more sense +of purposefulness and specialization than does gathering (see p. +91). + +Now, while I think we could make several possible subdivisions of the +food-gathering stage--I call my subdivisions of stages _eras_[5]--I +believe the only one which means much to us here is the last or +_terminal sub-era of food-collecting_ of the whole food-gathering +stage. The microliths seem to mark its approach in the northwestern +part of the Old World. It is really shown best in the Old World by +the materials of the Forest folk, the cultural adaptation to the +post-glacial environment in northwestern Europe. We talked about +the Forest folk at the beginning of this chapter, and I used the +Maglemosian assemblage of Denmark as an example. + + [5] It is difficult to find words which have a sequence or gradation + of meaning with respect to both development and a range of time + in the past, or with a range of time from somewhere in the past + which is perhaps not yet ended. One standard Webster definition + of _stage_ is: One of the steps into which the material + development of man ... is divided. I cannot find any dictionary + definition that suggests which of the words, _stage_ or _era_, + has the meaning of a longer span of time. Therefore, I have + chosen to let my eras be shorter, and to subdivide my stages + into eras. Webster gives _era_ as: A signal stage of history, + an epoch. When I want to subdivide my eras, I find myself using + _sub-eras_. Thus I speak of the _eras_ within a _stage_ and of + the _sub-eras_ within an _era_; that is, I do so when I feel + that I really have to, and when the evidence is clear enough to + allow it. + +The food-producing revolution ushers in the _food-producing stage_. +This stage began to be replaced by the _industrial stage_ only about +two hundred years ago. Now notice that my stage divisions are in terms +of technology and economics. We must think sharply to be sure that the +subdivisions of the stages, the eras, are in the same terms. This does +not mean that I think technology and economics are the only important +realms of culture. It is rather that for most of prehistoric time the +materials left to the archeologists tend to limit our deductions to +technology and economics. + +Im so soon out of my competence, as conventional ancient history +begins, that I shall only suggest the earlier eras of the +food-producing stage to you. This book is about prehistory, and Im not +a universal historian. + + +THE TWO EARLIEST ERAS OF THE FOOD-PRODUCING STAGE + +The food-producing stage seems to appear in western Asia with really +revolutionary suddenness. It is seen by the relative speed with which +the traces of new crafts appear in the earliest village-farming +community sites weve dug. It is seen by the spread and multiplication +of these sites themselves, and the remarkable growth in human +population we deduce from this increase in sites. Well look at some +of these sites and the archeological traces they yield in the next +chapter. When such village sites begin to appear, I believe we are in +the _era of the primary village-farming community_. I also believe this +is the second era of the food-producing stage. + +The first era of the food-producing stage, I believe, was an _era of +incipient cultivation and animal domestication_. I keep saying I +believe because the actual evidence for this earlier era is so slight +that one has to set it up mainly by playing a hunch for it. The reason +for playing the hunch goes about as follows. + +One thing we seem to be able to see, in the food-collecting era in +general, is a tendency for people to begin to settle down. This +settling down seemed to become further intensified in the terminal +era. How this is connected with Professor Mathiassens receptiveness +and the tendency to be experimental, we do not exactly know. The +evidence from the New World comes into play here as well as that from +the Old World. With this settling down in one place, the people of the +terminal era--especially the Forest folk whom we know best--began +making a great variety of new things. I remarked about this earlier in +the chapter. Dr. Robert M. Adams is of the opinion that this atmosphere +of experimentation with new tools--with new ways of collecting food--is +the kind of atmosphere in which one might expect trials at planting +and at animal domestication to have been made. We first begin to find +traces of more permanent life in outdoor camp sites, although caves +were still inhabited at the beginning of the terminal era. It is not +surprising at all that the Forest folk had already domesticated the +dog. In this sense, the whole era of food-collecting was becoming ready +and almost incipient for cultivation and animal domestication. + +Northwestern Europe was not the place for really effective beginnings +in agriculture and animal domestication. These would have had to take +place in one of those natural environments of promise, where a variety +of plants and animals, each possible of domestication, was available in +the wild state. Let me spell this out. Really effective food-production +must include a variety of items to make up a reasonably well-rounded +diet. The food-supply so produced must be trustworthy, even though +the food-producing peoples themselves might be happy to supplement +it with fish and wild strawberries, just as we do when such things +are available. So, as we said earlier, part of our problem is that +of finding a region with a natural environment which includes--and +did include, some ten thousand years ago--a variety of possibly +domesticable wild plants and animals. + + +NUCLEAR AREAS + +Now comes the last of my definitions. A region with a natural +environment which included a variety of wild plants and animals, +both possible and ready for domestication, would be a central +or core or _nuclear area_, that is, it would be when and _if_ +food-production took place within it. It is pretty hard for me to +imagine food-production having ever made an independent start outside +such a nuclear area, although there may be some possible nuclear areas +in which food-production never took place (possibly in parts of Africa, +for example). + +We know of several such nuclear areas. In the New World, Middle America +and the Andean highlands make up one or two; it is my understanding +that the evidence is not yet clear as to which. There seems to have +been a nuclear area somewhere in southeastern Asia, in the Malay +peninsula or Burma perhaps, connected with the early cultivation of +taro, breadfruit, the banana and the mango. Possibly the cultivation +of rice and the domestication of the chicken and of zebu cattle and +the water buffalo belong to this southeast Asiatic nuclear area. We +know relatively little about it archeologically, as yet. The nuclear +area which was the scene of the earliest experiment in effective +food-production was in western Asia. Since I know it best, I shall use +it as my example. + + +THE NUCLEAR NEAR EAST + +The nuclear area of western Asia is naturally the one of greatest +interest to people of the western cultural tradition. Our cultural +heritage began within it. The area itself is the region of the hilly +flanks of rain-watered grass-land which build up to the high mountain +ridges of Iran, Iraq, Turkey, Syria, and Palestine. The map on page +125 indicates the region. If you have a good atlas, try to locate the +zone which surrounds the drainage basin of the Tigris and Euphrates +Rivers at elevations of from approximately 2,000 to 5,000 feet. The +lower alluvial land of the Tigris-Euphrates basin itself has very +little rainfall. Some years ago Professor James Henry Breasted called +the alluvial lands of the Tigris-Euphrates a part of the fertile +crescent. These alluvial lands are very fertile if irrigated. Breasted +was most interested in the oriental civilizations of conventional +ancient history, and irrigation had been discovered before they +appeared. + +The country of hilly flanks above Breasteds crescent receives from +10 to 20 or more inches of winter rainfall each year, which is about +what Kansas has. Above the hilly-flanks zone tower the peaks and ridges +of the Lebanon-Amanus chain bordering the coast-line from Palestine +to Turkey, the Taurus Mountains of southern Turkey, and the Zagros +range of the Iraq-Iran borderland. This rugged mountain frame for our +hilly-flanks zone rises to some magnificent alpine scenery, with peaks +of from ten to fifteen thousand feet in elevation. There are several +gaps in the Mediterranean coastal portion of the frame, through which +the winters rain-bearing winds from the sea may break so as to carry +rain to the foothills of the Taurus and the Zagros. + +The picture I hope you will have from this description is that of an +intermediate hilly-flanks zone lying between two regions of extremes. +The lower Tigris-Euphrates basin land is low and far too dry and hot +for agriculture based on rainfall alone; to the south and southwest, it +merges directly into the great desert of Arabia. The mountains which +lie above the hilly-flanks zone are much too high and rugged to have +encouraged farmers. + + +THE NATURAL ENVIRONMENT OF THE NUCLEAR NEAR EAST + +The more we learn of this hilly-flanks zone that I describe, the +more it seems surely to have been a nuclear area. This is where we +archeologists need, and are beginning to get, the help of natural +scientists. They are coming to the conclusion that the natural +environment of the hilly-flanks zone today is much as it was some eight +to ten thousand years ago. There are still two kinds of wild wheat and +a wild barley, and the wild sheep, goat, and pig. We have discovered +traces of each of these at about nine thousand years ago, also traces +of wild ox, horse, and dog, each of which appears to be the probable +ancestor of the domesticated form. In fact, at about nine thousand +years ago, the two wheats, the barley, and at least the goat, were +already well on the road to domestication. + +The wild wheats give us an interesting clue. They are only available +together with the wild barley within the hilly-flanks zone. While the +wild barley grows in a variety of elevations and beyond the zone, +at least one of the wild wheats does not seem to grow below the hill +country. As things look at the moment, the domestication of both the +wheats together could _only_ have taken place within the hilly-flanks +zone. Barley seems to have first come into cultivation due to its +presence as a weed in already cultivated wheat fields. There is also +a suggestion--there is still much more to learn in the matter--that +the animals which were first domesticated were most at home up in the +hilly-flanks zone in their wild state. + +With a single exception--that of the dog--the earliest positive +evidence of domestication includes the two forms of wheat, the barley, +and the goat. The evidence comes from within the hilly-flanks zone. +However, it comes from a settled village proper, Jarmo (which Ill +describe in the next chapter), and is thus from the era of the primary +village-farming community. We are still without positive evidence of +domesticated grain and animals in the first era of the food-producing +stage, that of incipient cultivation and animal domestication. + + +THE ERA OF INCIPIENT CULTIVATION AND ANIMAL DOMESTICATION + +I said above (p. 105) that my era of incipient cultivation and animal +domestication is mainly set up by playing a hunch. Although we cannot +really demonstrate it--and certainly not in the Near East--it would +be very strange for food-collectors not to have known a great deal +about the plants and animals most useful to them. They do seem to have +domesticated the dog. We can easily imagine them remembering to go +back, season after season, to a particular patch of ground where seeds +or acorns or berries grew particularly well. Most human beings, unless +they are extremely hungry, are attracted to baby animals, and many wild +pups or fawns or piglets must have been brought back alive by hunting +parties. + +In this last sense, man has probably always been an incipient +cultivator and domesticator. But I believe that Adams is right in +suggesting that this would be doubly true with the experimenters of +the terminal era of food-collecting. We noticed that they also seem +to have had a tendency to settle down. Now my hunch goes that _when_ +this experimentation and settling down took place within a potential +nuclear area--where a whole constellation of plants and animals +possible of domestication was available--the change was easily made. +Professor Charles A. Reed, our field colleague in zoology, agrees that +year-round settlement with plant domestication probably came before +there were important animal domestications. + + +INCIPIENT ERAS AND NUCLEAR AREAS + +I have put this scheme into a simple chart (p. 111) with the names +of a few of the sites we are going to talk about. You will see that my +hunch means that there are eras of incipient cultivation _only_ within +nuclear areas. In a nuclear area, the terminal era of food-collecting +would probably have been quite short. I do not know for how long a time +the era of incipient cultivation and domestication would have lasted, +but perhaps for several thousand years. Then it passed on into the era +of the primary village-farming community. + +Outside a nuclear area, the terminal era of food-collecting would last +for a long time; in a few out-of-the-way parts of the world, it still +hangs on. It would end in any particular place through contact with +and the spread of ideas of people who had passed on into one of the +more developed eras. In many cases, the terminal era of food-collecting +was ended by the incoming of the food-producing peoples themselves. +For example, the practices of food-production were carried into Europe +by the actual movement of some numbers of peoples (we dont know how +many) who had reached at least the level of the primary village-farming +community. The Forest folk learned food-production from them. There +was never an era of incipient cultivation and domestication proper in +Europe, if my hunch is right. + + +ARCHEOLOGICAL DIFFICULTIES IN SEEING THE INCIPIENT ERA + +The way I see it, two things were required in order that an era of +incipient cultivation and domestication could begin. First, there had +to be the natural environment of a nuclear area, with its whole group +of plants and animals capable of domestication. This is the aspect of +the matter which weve said is directly given by nature. But it is +quite possible that such an environment with such a group of plants +and animals in it may have existed well before ten thousand years ago +in the Near East. It is also quite possible that the same promising +condition may have existed in regions which never developed into +nuclear areas proper. Here, again, we come back to the cultural factor. +I think it was that atmosphere of experimentation weve talked about +once or twice before. I cant define it for you, other than to say that +by the end of the Ice Age, the general level of many cultures was ready +for change. Ask me how and why this was so, and Ill tell you we dont +know yet, and that if we did understand this kind of question, there +would be no need for me to go on being a prehistorian! + +[Illustration: POSSIBLE RELATIONSHIPS OF STAGES AND ERAS IN WESTERN +ASIA AND NORTHEASTERN AFRICA] + +Now since this was an era of incipience, of the birth of new ideas, +and of experimentation, it is very difficult to see its traces +archeologically. New tools having to do with the new ways of getting +and, in fact, producing food would have taken some time to develop. +It need not surprise us too much if we cannot find hoes for planting +and sickles for reaping grain at the very beginning. We might expect +a time of making-do with some of the older tools, or with make-shift +tools, for some of the new jobs. The present-day wild cousin of the +domesticated sheep still lives in the mountains of western Asia. It has +no wool, only a fine down under hair like that of a deer, so it need +not surprise us to find neither the whorls used for spinning nor traces +of woolen cloth. It must have taken some time for a wool-bearing sheep +to develop and also time for the invention of the new tools which go +with weaving. It would have been the same with other kinds of tools for +the new way of life. + +It is difficult even for an experienced comparative zoologist to tell +which are the bones of domesticated animals and which are those of +their wild cousins. This is especially so because the animal bones the +archeologists find are usually fragmentary. Furthermore, we do not have +a sort of library collection of the skeletons of the animals or an +herbarium of the plants of those times, against which the traces which +the archeologists find may be checked. We are only beginning to get +such collections for the modern wild forms of animals and plants from +some of our nuclear areas. In the nuclear area in the Near East, some +of the wild animals, at least, have already become extinct. There are +no longer wild cattle or wild horses in western Asia. We know they were +there from the finds weve made in caves of late Ice Age times, and +from some slightly later sites. + + +SITES WITH ANTIQUITIES OF THE INCIPIENT ERA + +So far, we know only a very few sites which would suit my notion of the +incipient era of cultivation and animal domestication. I am closing +this chapter with descriptions of two of the best Near Eastern examples +I know of. You may not be satisfied that what I am able to describe +makes a full-bodied era of development at all. Remember, however, that +Ive told you Im largely playing a kind of a hunch, and also that the +archeological materials of this era will always be extremely difficult +to interpret. At the beginning of any new way of life, there will be a +great tendency for people to make-do, at first, with tools and habits +they are already used to. I would suspect that a great deal of this +making-do went on almost to the end of this era. + + +THE NATUFIAN, AN ASSEMBLAGE OF THE INCIPIENT ERA + +The assemblage called the Natufian comes from the upper layers of a +number of caves in Palestine. Traces of its flint industry have also +turned up in Syria and Lebanon. We dont know just how old it is. I +guess that it probably falls within five hundred years either way of +about 5000 B.C. + +Until recently, the people who produced the Natufian assemblage were +thought to have been only cave dwellers, but now at least three open +air Natufian sites have been briefly described. In their best-known +dwelling place, on Mount Carmel, the Natufian folk lived in the open +mouth of a large rock-shelter and on the terrace in front of it. On the +terrace, they had set at least two short curving lines of stones; but +these were hardly architecture; they seem more like benches or perhaps +the low walls of open pens. There were also one or two small clusters +of stones laid like paving, and a ring of stones around a hearth or +fireplace. One very round and regular basin-shaped depression had been +cut into the rocky floor of the terrace, and there were other less +regular basin-like depressions. In the newly reported open air sites, +there seem to have been huts with rounded corners. + +Most of the finds in the Natufian layer of the Mount Carmel cave were +flints. About 80 per cent of these flint tools were microliths made +by the regular working of tiny blades into various tools, some having +geometric forms. The larger flint tools included backed blades, burins, +scrapers, a few arrow points, some larger hacking or picking tools, and +one special type. This last was the sickle blade. + +We know a sickle blade of flint when we see one, because of a strange +polish or sheen which seems to develop on the cutting edge when the +blade has been used to cut grasses or grain, or--perhaps--reeds. In +the Natufian, we have even found the straight bone handles in which a +number of flint sickle blades were set in a line. + +There was a small industry in ground or pecked stone (that is, abraded +not chipped) in the Natufian. This included some pestle and mortar +fragments. The mortars are said to have a deep and narrow hole, +and some of the pestles show traces of red ochre. We are not sure +that these mortars and pestles were also used for grinding food. In +addition, there were one or two bits of carving in stone. + + +NATUFIAN ANTIQUITIES IN OTHER MATERIALS; BURIALS AND PEOPLE + +The Natufian industry in bone was quite rich. It included, beside the +sickle hafts mentioned above, points and harpoons, straight and curved +types of fish-hooks, awls, pins and needles, and a variety of beads and +pendants. There were also beads and pendants of pierced teeth and shell. + +A number of Natufian burials have been found in the caves; some burials +were grouped together in one grave. The people who were buried within +the Mount Carmel cave were laid on their backs in an extended position, +while those on the terrace seem to have been flexed (placed in their +graves in a curled-up position). This may mean no more than that it was +easier to dig a long hole in cave dirt than in the hard-packed dirt of +the terrace. The people often had some kind of object buried with them, +and several of the best collections of beads come from the burials. On +two of the skulls there were traces of elaborate head-dresses of shell +beads. + +[Illustration: SKETCH OF NATUFIAN ASSEMBLAGE + + MICROLITHS + ARCHITECTURE? + BURIAL + CHIPPED STONE + GROUND STONE + BONE] + +The animal bones of the Natufian layers show beasts of a modern type, +but with some differences from those of present-day Palestine. The +bones of the gazelle far outnumber those of the deer; since gazelles +like a much drier climate than deer, Palestine must then have had much +the same climate that it has today. Some of the animal bones were those +of large or dangerous beasts: the hyena, the bear, the wild boar, +and the leopard. But the Natufian people may have had the help of a +large domesticated dog. If our guess at a date for the Natufian is +right (about 7750 B.C.), this is an earlier dog than was that in the +Maglemosian of northern Europe. More recently, it has been reported +that a domesticated goat is also part of the Natufian finds. + +The study of the human bones from the Natufian burials is not yet +complete. Until Professor McCowns study becomes available, we may note +Professor Coons assessment that these people were of a basically +Mediterranean type. + + +THE KARIM SHAHIR ASSEMBLAGE + +Karim Shahir differs from the Natufian sites in that it shows traces +of a temporary open site or encampment. It lies on the top of a bluff +in the Kurdish hill-country of northeastern Iraq. It was dug by Dr. +Bruce Howe of the expedition I directed in 1950-51 for the Oriental +Institute and the American Schools of Oriental Research. In 1954-55, +our expedition located another site, Mlefaat, with general resemblance +to Karim Shahir, but about a hundred miles north of it. In 1956, Dr. +Ralph Solecki located still another Karim Shahir type of site called +Zawi Chemi Shanidar. The Zawi Chemi site has a radiocarbon date of 8900 + 300 B.C. + +Karim Shahir has evidence of only one very shallow level of occupation. +It was probably not lived on very long, although the people who lived +on it spread out over about three acres of area. In spots, the single +layer yielded great numbers of fist-sized cracked pieces of limestone, +which had been carried up from the bed of a stream at the bottom of the +bluff. We think these cracked stones had something to do with a kind of +architecture, but we were unable to find positive traces of hut plans. +At Mlefaat and Zawi Chemi, there were traces of rounded hut plans. + +As in the Natufian, the great bulk of small objects of the Karim Shahir +assemblage was in chipped flint. A large proportion of the flint tools +were microlithic bladelets and geometric forms. The flint sickle blade +was almost non-existent, being far scarcer than in the Natufian. The +people of Karim Shahir did a modest amount of work in the grinding of +stone; there were milling stone fragments of both the mortar and the +quern type, and stone hoes or axes with polished bits. Beads, pendants, +rings, and bracelets were made of finer quality stone. We found a few +simple points and needles of bone, and even two rather formless unbaked +clay figurines which seemed to be of animal form. + +[Illustration: SKETCH OF KARIM SHAHIR ASSEMBLAGE + + CHIPPED STONE + GROUND STONE + UNBAKED CLAY + SHELL + BONE + ARCHITECTURE] + +Karim Shahir did not yield direct evidence of the kind of vegetable +food its people ate. The animal bones showed a considerable +increase in the proportion of the bones of the species capable of +domestication--sheep, goat, cattle, horse, dog--as compared with animal +bones from the earlier cave sites of the area, which have a high +proportion of bones of wild forms like deer and gazelle. But we do not +know that any of the Karim Shahir animals were actually domesticated. +Some of them may have been, in an incipient way, but we have no means +at the moment that will tell us from the bones alone. + + +WERE THE NATUFIAN AND KARIM SHAHIR PEOPLES FOOD-PRODUCERS? + +It is clear that a great part of the food of the Natufian people +must have been hunted or collected. Shells of land, fresh-water, and +sea animals occur in their cave layers. The same is true as regards +Karim Shahir, save for sea shells. But on the other hand, we have +the sickles, the milling stones, the possible Natufian dog, and the +goat, and the general animal situation at Karim Shahir to hint at an +incipient approach to food-production. At Karim Shahir, there was the +tendency to settle down out in the open; this is echoed by the new +reports of open air Natufian sites. The large number of cracked stones +certainly indicates that it was worth the peoples while to have some +kind of structure, even if the site as a whole was short-lived. + +It is a part of my hunch that these things all point toward +food-production--that the hints we seek are there. But in the sense +that the peoples of the era of the primary village-farming community, +which we shall look at next, are fully food-producing, the Natufian +and Karim Shahir folk had not yet arrived. I think they were part of +a general build-up to full scale food-production. They were possibly +controlling a few animals of several kinds and perhaps one or two +plants, without realizing the full possibilities of this control as a +new way of life. + +This is why I think of the Karim Shahir and Natufian folk as being at +a level, or in an era, of incipient cultivation and domestication. But +we shall have to do a great deal more excavation in this range of time +before well get the kind of positive information we need. + + +SUMMARY + +I am sorry that this chapter has had to be so much more about ideas +than about the archeological traces of prehistoric men themselves. +But the antiquities of the incipient era of cultivation and animal +domestication will not be spectacular, even when we do have them +excavated in quantity. Few museums will be interested in these +antiquities for exhibition purposes. The charred bits or impressions +of plants, the fragments of animal bone and shell, and the varied +clues to climate and environment will be as important as the artifacts +themselves. It will be the ideas to which these traces lead us that +will be important. I am sure that this unspectacular material--when we +have much more of it, and learn how to understand what it says--will +lead us to how and why answers about the first great change in human +history. + +We know the earliest village-farming communities appeared in western +Asia, in a nuclear area. We do not yet know why the Near Eastern +experiment came first, or why it didnt happen earlier in some other +nuclear area. Apparently, the level of culture and the promise of the +natural environment were ready first in western Asia. The next sites +we look at will show a simple but effective food-production already +in existence. Without effective food-production and the settled +village-farming communities, civilization never could have followed. +How effective food-production came into being by the end of the +incipient era, is, I believe, one of the most fascinating questions any +archeologist could face. + +It now seems probable--from possibly two of the Palestinian sites with +varieties of the Natufian (Jericho and Nahal Oren)--that there were +one or more local Palestinian developments out of the Natufian into +later times. In the same way, what followed after the Karim Shahir type +of assemblage in northeastern Iraq was in some ways a reflection of +beginnings made at Karim Shahir and Zawi Chemi. + + + + +THE First Revolution + +[Illustration] + + +As the incipient era of cultivation and animal domestication passed +onward into the era of the primary village-farming community, the first +basic change in human economy was fully achieved. In southwestern Asia, +this seems to have taken place about nine thousand years ago. I am +going to restrict my description to this earliest Near Eastern case--I +do not know enough about the later comparable experiments in the Far +East and in the New World. Let us first, once again, think of the +contrast between food-collecting and food-producing as ways of life. + + +THE DIFFERENCE BETWEEN FOOD-COLLECTORS AND FOOD-PRODUCERS + +Childe used the word revolution because of the radical change that +took place in the habits and customs of man. Food-collectors--that is, +hunters, fishers, berry- and nut-gatherers--had to live in small groups +or bands, for they had to be ready to move wherever their food supply +moved. Not many people can be fed in this way in one area, and small +children and old folks are a burden. There is not enough food to store, +and it is not the kind that can be stored for long. + +Do you see how this all fits into a picture? Small groups of people +living now in this cave, now in that--or out in the open--as they moved +after the animals they hunted; no permanent villages, a few half-buried +huts at best; no breakable utensils; no pottery; no signs of anything +for clothing beyond the tools that were probably used to dress the +skins of animals; no time to think of much of anything but food and +protection and disposal of the dead when death did come: an existence +which takes nature as it finds it, which does little or nothing to +modify nature--all in all, a savages existence, and a very tough one. +A man who spends his whole life following animals just to kill them to +eat, or moving from one berry patch to another, is really living just +like an animal himself. + + +THE FOOD-PRODUCING ECONOMY + +Against this picture let me try to draw another--that of mans life +after food-production had begun. His meat was stored on the hoof, +his grain in silos or great pottery jars. He lived in a house: it was +worth his while to build one, because he couldnt move far from his +fields and flocks. In his neighborhood enough food could be grown +and enough animals bred so that many people were kept busy. They all +lived close to their flocks and fields, in a village. The village was +already of a fair size, and it was growing, too. Everybody had more to +eat; they were presumably all stronger, and there were more children. +Children and old men could shepherd the animals by day or help with +the lighter work in the fields. After the crops had been harvested the +younger men might go hunting and some of them would fish, but the food +they brought in was only an addition to the food in the village; the +villagers wouldnt starve, even if the hunters and fishermen came home +empty-handed. + +There was more time to do different things, too. They began to modify +nature. They made pottery out of raw clay, and textiles out of hair +or fiber. People who became good at pottery-making traded their pots +for food and spent all of their time on pottery alone. Other people +were learning to weave cloth or to make new tools. There were already +people in the village who were becoming full-time craftsmen. + +Other things were changing, too. The villagers must have had +to agree on new rules for living together. The head man of the +village had problems different from those of the chief of the small +food-collectors band. If somebodys flock of sheep spoiled a wheat +field, the owner wanted payment for the grain he lost. The chief of +the hunters was never bothered with such questions. Even the gods +had changed. The spirits and the magic that had been used by hunters +werent of any use to the villagers. They needed gods who would watch +over the fields and the flocks, and they eventually began to erect +buildings where their gods might dwell, and where the men who knew most +about the gods might live. + + +WAS FOOD-PRODUCTION A REVOLUTION? + +If you can see the difference between these two pictures--between +life in the food-collecting stage and life after food-production +had begun--youll see why Professor Childe speaks of a revolution. +By revolution, he doesnt mean that it happened over night or that +it happened only once. We dont know exactly how long it took. Some +people think that all these changes may have occurred in less than +500 years, but I doubt that. The incipient era was probably an affair +of some duration. Once the level of the village-farming community had +been established, however, things did begin to move very fast. By +six thousand years ago, the descendants of the first villagers had +developed irrigation and plow agriculture in the relatively rainless +Mesopotamian alluvium and were living in towns with temples. Relative +to the half million years of food-gathering which lay behind, this had +been achieved with truly revolutionary suddenness. + + +GAPS IN OUR KNOWLEDGE OF THE NEAR EAST + +If youll look again at the chart (p. 111) youll see that I have +very few sites and assemblages to name in the incipient era of +cultivation and domestication, and not many in the earlier part of +the primary village-farming level either. Thanks in no small part +to the intelligent co-operation given foreign excavators by the +Iraq Directorate General of Antiquities, our understanding of the +sequence in Iraq is growing more complete. I shall use Iraq as my main +yard-stick here. But I am far from being able to show you a series of +Sears Roebuck catalogues, even century by century, for any part of +the nuclear area. There is still a great deal of earth to move, and a +great mass of material to recover and interpret before we even begin to +understand how and why. + +Perhaps here, because this kind of archeology is really my specialty, +youll excuse it if I become personal for a moment. I very much look +forward to having further part in closing some of the gaps in knowledge +of the Near East. This is not, as Ive told you, the spectacular +range of Near Eastern archeology. There are no royal tombs, no gold, +no great buildings or sculpture, no writing, in fact nothing to +excite the normal museum at all. Nevertheless it is a range which, +idea-wise, gives the archeologist tremendous satisfaction. The country +of the hilly flanks is an exciting combination of green grasslands +and mountainous ridges. The Kurds, who inhabit the part of the area +in which Ive worked most recently, are an extremely interesting and +hospitable people. Archeologists dont become rich, but Ill forego +the Cadillac for any bright spring morning in the Kurdish hills, on a +good site with a happy crew of workmen and an interested and efficient +staff. It is probably impossible to convey the full feeling which life +on such a dig holds--halcyon days for the body and acute pleasurable +stimulation for the mind. Old things coming newly out of the good dirt, +and the pieces of the human puzzle fitting into place! I think I am +an honest man; I cannot tell you that I am sorry the job is not yet +finished and that there are still gaps in this part of the Near Eastern +archeological sequence. + + +EARLIEST SITES OF THE VILLAGE FARMERS + +So far, the Karim Shahir type of assemblage, which we looked at in the +last chapter, is the earliest material available in what I take to +be the nuclear area. We do not believe that Karim Shahir was a village +site proper: it looks more like the traces of a temporary encampment. +Two caves, called Belt and Hotu, which are outside the nuclear area +and down on the foreshore of the Caspian Sea, have been excavated +by Professor Coon. These probably belong in the later extension of +the terminal era of food-gathering; in their upper layers are traits +like the use of pottery borrowed from the more developed era of the +same time in the nuclear area. The same general explanation doubtless +holds true for certain materials in Egypt, along the upper Nile and in +the Kharga oasis: these materials, called Sebilian III, the Khartoum +neolithic, and the Khargan microlithic, are from surface sites, +not from caves. The chart (p. 111) shows where I would place these +materials in era and time. + +[Illustration: THE HILLY FLANKS OF THE CRESCENT AND EARLY SITES OF THE +NEAR EAST] + +Both Mlefaat and Dr. Soleckis Zawi Chemi Shanidar site appear to have +been slightly more settled in than was Karim Shahir itself. But I do +not think they belong to the era of farming-villages proper. The first +site of this era, in the hills of Iraqi Kurdistan, is Jarmo, on which +we have spent three seasons of work. Following Jarmo comes a variety of +sites and assemblages which lie along the hilly flanks of the crescent +and just below it. I am going to describe and illustrate some of these +for you. + +Since not very much archeological excavation has yet been done on sites +of this range of time, I shall have to mention the names of certain +single sites which now alone stand for an assemblage. This does not +mean that I think the individual sites I mention were unique. In the +times when their various cultures flourished, there must have been +many little villages which shared the same general assemblage. We are +only now beginning to locate them again. Thus, if I speak of Jarmo, +or Jericho, or Sialk as single examples of their particular kinds of +assemblages, I dont mean that they were unique at all. I think I could +take you to the sites of at least three more Jarmos, within twenty +miles of the original one. They are there, but they simply havent yet +been excavated. In 1956, a Danish expedition discovered material of +Jarmo type at Shimshara, only two dozen miles northeast of Jarmo, and +below an assemblage of Hassunan type (which I shall describe presently). + + +THE GAP BETWEEN KARIM SHAHIR AND JARMO + +As we see the matter now, there is probably still a gap in the +available archeological record between the Karim Shahir-Mlefaat-Zawi +Chemi group (of the incipient era) and that of Jarmo (of the +village-farming era). Although some items of the Jarmo type materials +do reflect the beginnings of traditions set in the Karim Shahir group +(see p. 120), there is not a clear continuity. Moreover--to the +degree that we may trust a few radiocarbon dates--there would appear +to be around two thousand years of difference in time. The single +available Zawi Chemi date is 8900 300 B.C.; the most reasonable +group of dates from Jarmo average to about 6750 200 B.C. I am +uncertain about this two thousand years--I do not think it can have +been so long. + +This suggests that we still have much work to do in Iraq. You can +imagine how earnestly we await the return of political stability in the +Republic of Iraq. + + +JARMO, IN THE KURDISH HILLS, IRAQ + +The site of Jarmo has a depth of deposit of about twenty-seven feet, +and approximately a dozen layers of architectural renovation and +change. Nevertheless it is a one period site: its assemblage remains +essentially the same throughout, although one or two new items are +added in later levels. It covers about four acres of the top of a +bluff, below which runs a small stream. Jarmo lies in the hill country +east of the modern oil town of Kirkuk. The Iraq Directorate General of +Antiquities suggested that we look at it in 1948, and we have had three +seasons of digging on it since. + +The people of Jarmo grew the barley plant and two different kinds of +wheat. They made flint sickles with which to reap their grain, mortars +or querns on which to crack it, ovens in which it might be parched, and +stone bowls out of which they might eat their porridge. We are sure +that they had the domesticated goat, but Professor Reed (the staff +zoologist) is not convinced that the bones of the other potentially +domesticable animals of Jarmo--sheep, cattle, pig, horse, dog--show +sure signs of domestication. We had first thought that all of these +animals were domesticated ones, but Reed feels he must find out much +more before he can be sure. As well as their grain and the meat from +their animals, the people of Jarmo consumed great quantities of land +snails. Botanically, the Jarmo wheat stands about half way between +fully bred wheat and the wild forms. + + +ARCHITECTURE: HALL-MARK OF THE VILLAGE + +The sure sign of the village proper is in its traces of architectural +permanence. The houses of Jarmo were only the size of a small cottage +by our standards, but each was provided with several rectangular rooms. +The walls of the houses were made of puddled mud, often set on crude +foundations of stone. (The puddled mud wall, which the Arabs call +_touf_, is built by laying a three to six inch course of soft mud, +letting this sun-dry for a day or two, then adding the next course, +etc.) The village probably looked much like the simple Kurdish farming +village of today, with its mud-walled houses and low mud-on-brush +roofs. I doubt that the Jarmo village had more than twenty houses at +any one moment of its existence. Today, an average of about seven +people live in a comparable Kurdish house; probably the population of +Jarmo was about 150 people. + +[Illustration: SKETCH OF JARMO ASSEMBLAGE + + CHIPPED STONE + UNBAKED CLAY + GROUND STONE + POTTERY _UPPER THIRD OF SITE ONLY._ + REED MATTING + BONE + ARCHITECTURE] + +It is interesting that portable pottery does not appear until the +last third of the life of the Jarmo village. Throughout the duration +of the village, however, its people had experimented with the plastic +qualities of clay. They modeled little figurines of animals and of +human beings in clay; one type of human figurine they favored was that +of a markedly pregnant woman, probably the expression of some sort of +fertility spirit. They provided their house floors with baked-in-place +depressions, either as basins or hearths, and later with domed ovens of +clay. As weve noted, the houses themselves were of clay or mud; one +could almost say they were built up like a house-sized pot. Then, +finally, the idea of making portable pottery itself appeared, although +I very much doubt that the people of the Jarmo village discovered the +art. + +On the other hand, the old tradition of making flint blades and +microlithic tools was still very strong at Jarmo. The sickle-blade was +made in quantities, but so also were many of the much older tool types. +Strangely enough, it is within this age-old category of chipped stone +tools that we see one of the clearest pointers to a newer age. Many of +the Jarmo chipped stone tools--microliths--were made of obsidian, a +black volcanic natural glass. The obsidian beds nearest to Jarmo are +over three hundred miles to the north. Already a bulk carrying trade +had been established--the forerunner of commerce--and the routes were +set by which, in later times, the metal trade was to move. + +There are now twelve radioactive carbon dates from Jarmo. The most +reasonable cluster of determinations averages to about 6750 200 +B.C., although there is a completely unreasonable range of dates +running from 3250 to 9250 B.C.! _If_ I am right in what I take to be +reasonable, the first flush of the food-producing revolution had been +achieved almost nine thousand years ago. + + +HASSUNA, IN UPPER MESOPOTAMIAN IRAQ + +We are not sure just how soon after Jarmo the next assemblage of Iraqi +material is to be placed. I do not think the time was long, and there +are a few hints that detailed habits in the making of pottery and +ground stone tools were actually continued from Jarmo times into the +time of the next full assemblage. This is called after a site named +Hassuna, a few miles to the south and west of modern Mosul. We also +have Hassunan type materials from several other sites in the same +general region. It is probably too soon to make generalizations about +it, but the Hassunan sites seem to cluster at slightly lower elevations +than those we have been talking about so far. + +The catalogue of the Hassuna assemblage is of course more full and +elaborate than that of Jarmo. The Iraqi governments archeologists +who dug Hassuna itself, exposed evidence of increasing architectural +know-how. The walls of houses were still formed of puddled mud; +sun-dried bricks appear only in later periods. There were now several +different ways of making and decorating pottery vessels. One style of +pottery painting, called the Samarran style, is an extremely handsome +one and must have required a great deal of concentration and excellence +of draftsmanship. On the other hand, the old habits for the preparation +of good chipped stone tools--still apparent at Jarmo--seem to have +largely disappeared by Hassunan times. The flint work of the Hassunan +catalogue is, by and large, a wretched affair. We might guess that the +kinaesthetic concentration of the Hassuna craftsmen now went into other +categories; that is, they suddenly discovered they might have more fun +working with the newer materials. Its a shame, for example, that none +of their weaving is preserved for us. + +The two available radiocarbon determinations from Hassunan contexts +stand at about 5100 and 5600 B.C. 250 years. + + +OTHER EARLY VILLAGE SITES IN THE NUCLEAR AREA + +Ill now name and very briefly describe a few of the other early +village assemblages either in or adjacent to the hilly flanks of the +crescent. Unfortunately, we do not have radioactive carbon dates for +many of these materials. We may guess that some particular assemblage, +roughly comparable to that of Hassuna, for example, must reflect a +culture which lived at just about the same time as that of Hassuna. We +do this guessing on the basis of the general similarity and degree of +complexity of the Sears Roebuck catalogues of the particular assemblage +and that of Hassuna. We suppose that for sites near at hand and of a +comparable cultural level, as indicated by their generally similar +assemblages, the dating must be about the same. We may also know that +in a general stratigraphic sense, the sites in question may both appear +at the bottom of the ascending village sequence in their respective +areas. Without a number of consistent radioactive carbon dates, we +cannot be precise about priorities. + +[Illustration: SKETCH OF HASSUNA ASSEMBLAGE + + POTTERY + POTTERY OBJECTS + CHIPPED STONE + BONE + GROUND STONE + ARCHITECTURE + REED MATTING + BURIAL] + +The ancient mound at Jericho, in the Dead Sea valley in Palestine, +yields some very interesting material. Its catalogue somewhat resembles +that of Jarmo, especially in the sense that there is a fair depth +of deposit without portable pottery vessels. On the other hand, the +architecture of Jericho is surprisingly complex, with traces of massive +stone fortification walls and the general use of formed sun-dried +mud brick. Jericho lies in a somewhat strange and tropically lush +ecological niche, some seven hundred feet below sea level; it is +geographically within the hilly-flanks zone but environmentally not +part of it. + +Several radiocarbon dates for Jericho fall within the range of those +I find reasonable for Jarmo, and their internal statistical consistency +is far better than that for the Jarmo determinations. It is not yet +clear exactly what this means. + +The mound at Jericho (Tell es-Sultan) contains a remarkably +fine sequence, which perhaps does not have the gap we noted in +Iraqi-Kurdistan between the Karim Shahir group and Jarmo. While I am +not sure that the Jericho sequence will prove valid for those parts +of Palestine outside the special Dead Sea environmental niche, the +sequence does appear to proceed from the local variety of Natufian into +that of a very well settled community. So far, we have little direct +evidence for the food-production basis upon which the Jericho people +subsisted. + +There is an early village assemblage with strong characteristics of its +own in the land bordering the northeast corner of the Mediterranean +Sea, where Syria and the Cilician province of Turkey join. This early +Syro-Cilician assemblage must represent a general cultural pattern +which was at least in part contemporary with that of the Hassuna +assemblage. These materials from the bases of the mounds at Mersin, and +from Judaidah in the Amouq plain, as well as from a few other sites, +represent the remains of true villages. The walls of their houses were +built of puddled mud, but some of the house foundations were of stone. +Several different kinds of pottery were made by the people of these +villages. None of it resembles the pottery from Hassuna or from the +upper levels of Jarmo or Jericho. The Syro-Cilician people had not +lost their touch at working flint. An important southern variation of +the Syro-Cilician assemblage has been cleared recently at Byblos, a +port town famous in later Phoenician times. There are three radiocarbon +determinations which suggest that the time range for these developments +was in the sixth or early fifth millennium B.C. + +It would be fascinating to search for traces of even earlier +village-farming communities and for the remains of the incipient +cultivation era, in the Syro-Cilician region. + + +THE IRANIAN PLATEAU AND THE NILE VALLEY + +The map on page 125 shows some sites which lie either outside or in +an extension of the hilly-flanks zone proper. From the base of the +great mound at Sialk on the Iranian plateau came an assemblage of +early village material, generally similar, in the kinds of things it +contained, to the catalogues of Hassuna and Judaidah. The details of +how things were made are different; the Sialk assemblage represents +still another cultural pattern. I suspect it appeared a bit later +in time than did that of Hassuna. There is an important new item in +the Sialk catalogue. The Sialk people made small drills or pins of +hammered copper. Thus the metallurgists specialized craft had made its +appearance. + +There is at least one very early Iranian site on the inward slopes +of the hilly-flanks zone. It is the earlier of two mounds at a place +called Bakun, in southwestern Iran; the results of the excavations +there are not yet published and we only know of its coarse and +primitive pottery. I only mention Bakun because it helps us to plot the +extent of the hilly-flanks zone villages on the map. + +The Nile Valley lies beyond the peculiar environmental zone of the +hilly flanks of the crescent, and it is probable that the earliest +village-farming communities in Egypt were established by a few people +who wandered into the Nile delta area from the nuclear area. The +assemblage which is most closely comparable to the catalogue of Hassuna +or Judaidah, for example, is that from little settlements along the +shore of the Fayum lake. The Fayum materials come mainly from grain +bins or silos. Another site, Merimde, in the western part of the Nile +delta, shows the remains of a true village, but it may be slightly +later than the settlement of the Fayum. There are radioactive carbon +dates for the Fayum materials at about 4275 B.C. 320 years, which +is almost fifteen hundred years later than the determinations suggested +for the Hassunan or Syro-Cilician assemblages. I suspect that this +is a somewhat over-extended indication of the time it took for the +generalized cultural pattern of village-farming community life to +spread from the nuclear area down into Egypt, but as yet we have no way +of testing these matters. + +In this same vein, we have two radioactive carbon dates for an +assemblage from sites near Khartoum in the Sudan, best represented by +the mound called Shaheinab. The Shaheinab catalogue roughly corresponds +to that of the Fayum; the distance between the two places, as the Nile +flows, is roughly 1,500 miles. Thus it took almost a thousand years for +the new way of life to be carried as far south into Africa as Khartoum; +the two Shaheinab dates average about 3300 B.C. 400 years. + +If the movement was up the Nile (southward), as these dates suggest, +then I suspect that the earliest available village material of middle +Egypt, the so-called Tasian, is also later than that of the Fayum. The +Tasian materials come from a few graves near a village called Deir +Tasa, and I have an uncomfortable feeling that the Tasian assemblage +may be mainly an artificial selection of poor examples of objects which +belong in the following range of time. + + +SPREAD IN TIME AND SPACE + +There are now two things we can do; in fact, we have already begun to +do them. We can watch the spread of the new way of life upward through +time in the nuclear area. We can also see how the new way of life +spread outward in space from the nuclear area, as time went on. There +is good archeological evidence that both these processes took place. +For the hill country of northeastern Iraq, in the nuclear area, we +have already noticed how the succession (still with gaps) from Karim +Shahir, through Mlefaat and Jarmo, to Hassuna can be charted (see +chart, p. 111). In the next chapter, we shall continue this charting +and description of what happened in Iraq upward through time. We also +watched traces of the new way of life move through space up the Nile +into Africa, to reach Khartoum in the Sudan some thirty-five hundred +years later than we had seen it at Jarmo or Jericho. We caught glimpses +of it in the Fayum and perhaps at Tasa along the way. + +For the remainder of this chapter, I shall try to suggest briefly for +you the directions taken by the spread of the new way of life from the +nuclear area in the Near East. First, let me make clear again that +I _do not_ believe that the village-farming community way of life +was invented only once and in the Near East. It seems to me that the +evidence is very clear that a separate experiment arose in the New +World. For China, the question of independence or borrowing--in the +appearance of the village-farming community there--is still an open +one. In the last chapter, we noted the probability of an independent +nuclear area in southeastern Asia. Professor Carl Sauer strongly +champions the great importance of this area as _the_ original center +of agricultural pursuits, as a kind of cradle of all incipient eras +of the Old World at least. While there is certainly not the slightest +archeological evidence to allow us to go that far, we may easily expect +that an early southeast Asian development would have been felt in +China. However, the appearance of the village-farming community in the +northwest of India, at least, seems to have depended on the earlier +development in the Near East. It is also probable that ideas of the new +way of life moved well beyond Khartoum in Africa. + + +THE SPREAD OF THE VILLAGE-FARMING COMMUNITY WAY OF LIFE INTO EUROPE + +How about Europe? I wont give you many details. You can easily imagine +that the late prehistoric prelude to European history is a complicated +affair. We all know very well how complicated an area Europe is now, +with its welter of different languages and cultures. Remember, however, +that a great deal of archeology has been done on the late prehistory of +Europe, and very little on that of further Asia and Africa. If we knew +as much about these areas as we do of Europe, I expect wed find them +just as complicated. + +This much is clear for Europe, as far as the spread of the +village-community way of life is concerned. The general idea and much +of the know-how and the basic tools of food-production moved from the +Near East to Europe. So did the plants and animals which had been +domesticated; they were not naturally at home in Europe, as they were +in western Asia. I do not, of course, mean that there were traveling +salesmen who carried these ideas and things to Europe with a commercial +gleam in their eyes. The process took time, and the ideas and things +must have been passed on from one group of people to the next. There +was also some actual movement of peoples, but we dont know the size of +the groups that moved. + +The story of the colonization of Europe by the first farmers is +thus one of (1) the movement from the eastern Mediterranean lands +of some people who were farmers; (2) the spread of ideas and things +beyond the Near East itself and beyond the paths along which the +colonists moved; and (3) the adaptations of the ideas and things +by the indigenous Forest folk, about whose receptiveness Professor +Mathiassen speaks (p. 97). It is important to note that the resulting +cultures in the new European environment were European, not Near +Eastern. The late Professor Childe remarked that the peoples of the +West were not slavish imitators; they adapted the gifts from the East +... into a new and organic whole capable of developing on its own +original lines. + + +THE WAYS TO EUROPE + +Suppose we want to follow the traces of those earliest village-farmers +who did travel from western Asia into Europe. Let us start from +Syro-Cilicia, that part of the hilly-flanks zone proper which lies in +the very northeastern corner of the Mediterranean. Three ways would be +open to us (of course we could not be worried about permission from the +Soviet authorities!). We would go north, or north and slightly east, +across Anatolian Turkey, and skirt along either shore of the Black Sea +or even to the east of the Caucasus Mountains along the Caspian Sea, +to reach the plains of Ukrainian Russia. From here, we could march +across eastern Europe to the Baltic and Scandinavia, or even hook back +southwestward to Atlantic Europe. + +Our second way from Syro-Cilicia would also lie over Anatolia, to the +northwest, where we would have to swim or raft ourselves over the +Dardanelles or the Bosphorus to the European shore. Then we would bear +left toward Greece, but some of us might turn right again in Macedonia, +going up the valley of the Vardar River to its divide and on down +the valley of the Morava beyond, to reach the Danube near Belgrade +in Jugoslavia. Here we would turn left, following the great river +valley of the Danube up into central Europe. We would have a number of +tributary valleys to explore, or we could cross the divide and go down +the valley of the Rhine to the North Sea. + +Our third way from Syro-Cilicia would be by sea. We would coast along +southern Anatolia and visit Cyprus, Crete, and the Aegean islands on +our way to Greece, where, in the north, we might meet some of those who +had taken the second route. From Greece, we would sail on to Italy and +the western isles, to reach southern France and the coasts of Spain. +Eventually a few of us would sail up the Atlantic coast of Europe, to +reach western Britain and even Ireland. + +[Illustration: PROBABLE ROUTES AND TIMING IN THE SPREAD OF THE +VILLAGE-FARMING COMMUNITY WAY OF LIFE FROM THE NEAR EAST TO EUROPE] + +Of course none of us could ever take these journeys as the first +farmers took them, since the whole course of each journey must have +lasted many lifetimes. The date given to the assemblage called Windmill +Hill, the earliest known trace of village-farming communities in +England, is about 2500 B.C. I would expect about 5500 B.C. to be a +safe date to give for the well-developed early village communities of +Syro-Cilicia. We suspect that the spread throughout Europe did not +proceed at an even rate. Professor Piggott writes that at a date +probably about 2600 B.C., simple agricultural communities were being +established in Spain and southern France, and from the latter region a +spread northwards can be traced ... from points on the French seaboard +of the [English] Channel ... there were emigrations of a certain number +of these tribes by boat, across to the chalk lands of Wessex and Sussex +[in England], probably not more than three or four generations later +than the formation of the south French colonies. + +New radiocarbon determinations are becoming available all the +time--already several suggest that the food-producing way of life +had reached the lower Rhine and Holland by 4000 B.C. But not all +prehistorians accept these dates, so I do not show them on my map +(p. 139). + + +THE EARLIEST FARMERS OF ENGLAND + +To describe the later prehistory of all Europe for you would take +another book and a much larger one than this is. Therefore, I have +decided to give you only a few impressions of the later prehistory of +Britain. Of course the British Isles lie at the other end of Europe +from our base-line in western Asia. Also, they received influences +along at least two of the three ways in which the new way of life +moved into Europe. We will look at more of their late prehistory in a +following chapter: here, I shall speak only of the first farmers. + +The assemblage called Windmill Hill, which appears in the south of +England, exhibits three different kinds of structures, evidence of +grain-growing and of stock-breeding, and some distinctive types of +pottery and stone implements. The most remarkable type of structure +is the earthwork enclosures which seem to have served as seasonal +cattle corrals. These enclosures were roughly circular, reached over +a thousand feet in diameter, and sometimes included two or three +concentric sets of banks and ditches. Traces of oblong timber houses +have been found, but not within the enclosures. The second type of +structure is mine-shafts, dug down into the chalk beds where good +flint for the making of axes or hoes could be found. The third type +of structure is long simple mounds or unchambered barrows, in one +end of which burials were made. It has been commonly believed that the +Windmill Hill assemblage belonged entirely to the cultural tradition +which moved up through France to the Channel. Professor Piggott is now +convinced, however, that important elements of Windmill Hill stem from +northern Germany and Denmark--products of the first way into Europe +from the east. + +The archeological traces of a second early culture are to be found +in the west of England, western and northern Scotland, and most of +Ireland. The bearers of this culture had come up the Atlantic coast +by sea from southern France and Spain. The evidence they have left us +consists mainly of tombs and the contents of tombs, with only very +rare settlement sites. The tombs were of some size and received the +bodies of many people. The tombs themselves were built of stone, heaped +over with earth; the stones enclosed a passage to a central chamber +(passage graves), or to a simple long gallery, along the sides of +which the bodies were laid (gallery graves). The general type of +construction is called megalithic (= great stone), and the whole +earth-mounded structure is often called a _barrow_. Since many have +proper chambers, in one sense or another, we used the term unchambered +barrow above to distinguish those of the Windmill Hill type from these +megalithic structures. There is some evidence for sacrifice, libations, +and ceremonial fires, and it is clear that some form of community +ritual was focused on the megalithic tombs. + +The cultures of the people who produced the Windmill Hill assemblage +and of those who made the megalithic tombs flourished, at least in +part, at the same time. Although the distributions of the two different +types of archeological traces are in quite different parts of the +country, there is Windmill Hill pottery in some of the megalithic +tombs. But the tombs also contain pottery which seems to have arrived +with the tomb builders themselves. + +The third early British group of antiquities of this general time +(following 2500 B.C.) comes from sites in southern and eastern England. +It is not so certain that the people who made this assemblage, called +Peterborough, were actually farmers. While they may on occasion have +practiced a simple agriculture, many items of their assemblage link +them closely with that of the Forest folk of earlier times in +England and in the Baltic countries. Their pottery is decorated with +impressions of cords and is quite different from that of Windmill Hill +and the megalithic builders. In addition, the distribution of their +finds extends into eastern Britain, where the other cultures have left +no trace. The Peterborough people had villages with semi-subterranean +huts, and the bones of oxen, pigs, and sheep have been found in a few +of these. On the whole, however, hunting and fishing seem to have been +their vital occupations. They also established trade routes especially +to acquire the raw material for stone axes. + +A probably slightly later culture, whose traces are best known from +Skara Brae on Orkney, also had its roots in those cultures of the +Baltic area which fused out of the meeting of the Forest folk and +the peoples who took the eastern way into Europe. Skara Brae is very +well preserved, having been built of thin stone slabs about which +dune-sand drifted after the village died. The individual houses, the +bedsteads, the shelves, the chests for clothes and oddments--all built +of thin stone-slabs--may still be seen in place. But the Skara Brae +people lived entirely by sheep- and cattle-breeding, and by catching +shellfish. Neither grain nor the instruments of agriculture appeared at +Skara Brae. + + +THE EUROPEAN ACHIEVEMENT + +The above is only a very brief description of what went on in Britain +with the arrival of the first farmers. There are many interesting +details which I have omitted in order to shorten the story. + +I believe some of the difficulty we have in understanding the +establishment of the first farming communities in Europe is with +the word colonization. We have a natural tendency to think of +colonization as it has happened within the last few centuries. In the +case of the colonization of the Americas, for example, the colonists +came relatively quickly, and in increasingly vast numbers. They had +vastly superior technical, political, and war-making skills, compared +with those of the Indians. There was not much mixing with the Indians. +The case in Europe five or six thousand years ago must have been very +different. I wonder if it is even proper to call people colonists +who move some miles to a new region, settle down and farm it for some +years, then move on again, generation after generation? The ideas and +the things which these new people carried were only _potentially_ +superior. The ideas and things and the people had to prove themselves +in their adaptation to each new environment. Once this was done another +link to the chain would be added, and then the forest-dwellers and +other indigenous folk of Europe along the way might accept the new +ideas and things. It is quite reasonable to expect that there must have +been much mixture of the migrants and the indigenes along the way; the +Peterborough and Skara Brae assemblages we mentioned above would seem +to be clear traces of such fused cultures. Sometimes, especially if the +migrants were moving by boat, long distances may have been covered in +a short time. Remember, however, we seem to have about three thousand +years between the early Syro-Cilician villages and Windmill Hill. + +Let me repeat Professor Childe again. The peoples of the West were +not slavish imitators: they adapted the gifts from the East ... into +a new and organic whole capable of developing on its own original +lines. Childe is of course completely conscious of the fact that his +peoples of the West were in part the descendants of migrants who came +originally from the East, bringing their gifts with them. This +was the late prehistoric achievement of Europe--to take new ideas and +things and some migrant peoples and, by mixing them with the old in its +own environments, to forge a new and unique series of cultures. + +What we know of the ways of men suggests to us that when the details +of the later prehistory of further Asia and Africa are learned, their +stories will be just as exciting. + + + + +THE Conquest of Civilization + +[Illustration] + + +Now we must return to the Near East again. We are coming to the point +where history is about to begin. I am going to stick pretty close +to Iraq and Egypt in this chapter. These countries will perhaps be +the most interesting to most of us, for the foundations of western +civilization were laid in the river lands of the Tigris and Euphrates +and of the Nile. I shall probably stick closest of all to Iraq, because +things first happened there and also because I know it best. + +There is another interesting thing, too. We have seen that the first +experiment in village-farming took place in the Near East. So did +the first experiment in civilization. Both experiments took. The +traditions we live by today are based, ultimately, on those ancient +beginnings in food-production and civilization in the Near East. + + +WHAT CIVILIZATION MEANS + +I shall not try to define civilization for you; rather, I shall +tell you what the word brings to my mind. To me civilization means +urbanization: the fact that there are cities. It means a formal +political set-up--that there are kings or governing bodies that the +people have set up. It means formal laws--rules of conduct--which the +government (if not the people) believes are necessary. It probably +means that there are formalized projects--roads, harbors, irrigation +canals, and the like--and also some sort of army or police force +to protect them. It means quite new and different art forms. It +also usually means there is writing. (The people of the Andes--the +Incas--had everything which goes to make up a civilization but formal +writing. I can see no reason to say they were not civilized.) Finally, +as the late Professor Redfield reminded us, civilization seems to bring +with it the dawn of a new kind of moral order. + +In different civilizations, there may be important differences in the +way such things as the above are managed. In early civilizations, it is +usual to find religion very closely tied in with government, law, and +so forth. The king may also be a high priest, or he may even be thought +of as a god. The laws are usually thought to have been given to the +people by the gods. The temples are protected just as carefully as the +other projects. + + +CIVILIZATION IMPOSSIBLE WITHOUT FOOD-PRODUCTION + +Civilizations have to be made up of many people. Some of the people +live in the country; some live in very large towns or cities. Classes +of society have begun. There are officials and government people; there +are priests or religious officials; there are merchants and traders; +there are craftsmen, metal-workers, potters, builders, and so on; there +are also farmers, and these are the people who produce the food for the +whole population. It must be obvious that civilization cannot exist +without food-production and that food-production must also be at a +pretty efficient level of village-farming before civilization can even +begin. + +But people can be food-producing without being civilized. In many +parts of the world this is still the case. When the white men first +came to America, the Indians in most parts of this hemisphere were +food-producers. They grew corn, potatoes, tomatoes, squash, and many +other things the white men had never eaten before. But only the Aztecs +of Mexico, the Mayas of Yucatan and Guatemala, and the Incas of the +Andes were civilized. + + +WHY DIDNT CIVILIZATION COME TO ALL FOOD-PRODUCERS? + +Once you have food-production, even at the well-advanced level of +the village-farming community, what else has to happen before you +get civilization? Many men have asked this question and have failed +to give a full and satisfactory answer. There is probably no _one_ +answer. I shall give you my own idea about how civilization _may_ have +come about in the Near East alone. Remember, it is only a guess--a +putting together of hunches from incomplete evidence. It is _not_ meant +to explain how civilization began in any of the other areas--China, +southeast Asia, the Americas--where other early experiments in +civilization went on. The details in those areas are quite different. +Whether certain general principles hold, for the appearance of any +early civilization, is still an open and very interesting question. + + +WHERE CIVILIZATION FIRST APPEARED IN THE NEAR EAST + +You remember that our earliest village-farming communities lay along +the hilly flanks of a great crescent. (See map on p. 125.) +Professor Breasteds fertile crescent emphasized the rich river +valleys of the Nile and the Tigris-Euphrates Rivers. Our hilly-flanks +area of the crescent zone arches up from Egypt through Palestine and +Syria, along southern Turkey into northern Iraq, and down along the +southwestern fringe of Iran. The earliest food-producing villages we +know already existed in this area by about 6750 B.C. ( 200 years). + +Now notice that this hilly-flanks zone does not include southern +Mesopotamia, the alluvial land of the lower Tigris and Euphrates in +Iraq, or the Nile Valley proper. The earliest known villages of classic +Mesopotamia and Egypt seem to appear fifteen hundred or more years +after those of the hilly-flanks zone. For example, the early Fayum +village which lies near a lake west of the Nile Valley proper (see p. +135) has a radiocarbon date of 4275 B.C. 320 years. It was in the +river lands, however, that the immediate beginnings of civilization +were made. + +We know that by about 3200 B.C. the Early Dynastic period had begun +in southern Mesopotamia. The beginnings of writing go back several +hundred years earlier, but we can safely say that civilization had +begun in Mesopotamia by 3200 B.C. In Egypt, the beginning of the First +Dynasty is slightly later, at about 3100 B.C., and writing probably +did not appear much earlier. There is no question but that history and +civilization were well under way in both Mesopotamia and Egypt by 3000 +B.C.--about five thousand years ago. + + +THE HILLY-FLANKS ZONE VERSUS THE RIVER LANDS + +Why did these two civilizations spring up in these two river +lands which apparently were not even part of the area where the +village-farming community began? Why didnt we have the first +civilizations in Palestine, Syria, north Iraq, or Iran, where were +sure food-production had had a long time to develop? I think the +probable answer gives a clue to the ways in which civilization began in +Egypt and Mesopotamia. + +The land in the hilly flanks is of a sort which people can farm without +too much trouble. There is a fairly fertile coastal strip in Palestine +and Syria. There are pleasant mountain slopes, streams running out to +the sea, and rain, at least in the winter months. The rain belt and the +foothills of the Turkish mountains also extend to northern Iraq and on +to the Iranian plateau. The Iranian plateau has its mountain valleys, +streams, and some rain. These hilly flanks of the crescent, through +most of its arc, are almost made-to-order for beginning farmers. The +grassy slopes of the higher hills would be pasture for their herds +and flocks. As soon as the earliest experiments with agriculture and +domestic animals had been successful, a pleasant living could be +made--and without too much trouble. + +I should add here again, that our evidence points increasingly to a +climate for those times which is very little different from that for +the area today. Now look at Egypt and southern Mesopotamia. Both are +lands without rain, for all intents and purposes. Both are lands with +rivers that have laid down very fertile soil--soil perhaps superior to +that in the hilly flanks. But in both lands, the rivers are of no great +aid without some control. + +The Nile floods its banks once a year, in late September or early +October. It not only soaks the narrow fertile strip of land on either +side; it lays down a fresh layer of new soil each year. Beyond the +fertile strip on either side rise great cliffs, and behind them is the +desert. In its natural, uncontrolled state, the yearly flood of the +Nile must have caused short-lived swamps that were full of crocodiles. +After a short time, the flood level would have dropped, the water and +the crocodiles would have run back into the river, and the swamp plants +would have become parched and dry. + +The Tigris and the Euphrates of Mesopotamia are less likely to flood +regularly than the Nile. The Tigris has a shorter and straighter course +than the Euphrates; it is also the more violent river. Its banks are +high, and when the snows melt and flow into all of its tributary rivers +it is swift and dangerous. The Euphrates has a much longer and more +curving course and few important tributaries. Its banks are lower and +it is less likely to flood dangerously. The land on either side and +between the two rivers is very fertile, south of the modern city of +Baghdad. Unlike the Nile Valley, neither the Tigris nor the Euphrates +is flanked by cliffs. The land on either side of the rivers stretches +out for miles and is not much rougher than a poor tennis court. + + +THE RIVERS MUST BE CONTROLLED + +The real trick in both Egypt and Mesopotamia is to make the rivers work +for you. In Egypt, this is a matter of building dikes and reservoirs +that will catch and hold the Nile flood. In this way, the water is held +and allowed to run off over the fields as it is needed. In Mesopotamia, +it is a matter of taking advantage of natural river channels and branch +channels, and of leading ditches from these onto the fields. + +Obviously, we can no longer find the first dikes or reservoirs of +the Nile Valley, or the first canals or ditches of Mesopotamia. The +same land has been lived on far too long for any traces of the first +attempts to be left; or, especially in Egypt, it has been covered by +the yearly deposits of silt, dropped by the river floods. But were +pretty sure the first food-producers of Egypt and southern Mesopotamia +must have made such dikes, canals, and ditches. In the first place, +there cant have been enough rain for them to grow things otherwise. +In the second place, the patterns for such projects seem to have been +pretty well set by historic times. + + +CONTROL OF THE RIVERS THE BUSINESS OF EVERYONE + +Here, then, is a _part_ of the reason why civilization grew in Egypt +and Mesopotamia first--not in Palestine, Syria, or Iran. In the latter +areas, people could manage to produce their food as individuals. It +wasnt too hard; there were rain and some streams, and good pasturage +for the animals even if a crop or two went wrong. In Egypt and +Mesopotamia, people had to put in a much greater amount of work, and +this work couldnt be individual work. Whole villages or groups of +people had to turn out to fix dikes or dig ditches. The dikes had to be +repaired and the ditches carefully cleared of silt each year, or they +would become useless. + +There also had to be hard and fast rules. The person who lived nearest +the ditch or the reservoir must not be allowed to take all the water +and leave none for his neighbors. It was not only a business of +learning to control the rivers and of making their waters do the +farmers work. It also meant controlling men. But once these men had +managed both kinds of controls, what a wonderful yield they had! The +soil was already fertile, and the silt which came in the floods and +ditches kept adding fertile soil. + + +THE GERM OF CIVILIZATION IN EGYPT AND MESOPOTAMIA + +This learning to work together for the common good was the real germ of +the Egyptian and the Mesopotamian civilizations. The bare elements of +civilization were already there: the need for a governing hand and for +laws to see that the communities work was done and that the water was +justly shared. You may object that there is a sort of chicken and egg +paradox in this idea. How could the people set up the rules until they +had managed to get a way to live, and how could they manage to get a +way to live until they had set up the rules? I think that small groups +must have moved down along the mud-flats of the river banks quite +early, making use of naturally favorable spots, and that the rules grew +out of such cases. It would have been like the hand-in-hand growth of +automobiles and paved highways in the United States. + +Once the rules and the know-how did get going, there must have been a +constant interplay of the two. Thus, the more the crops yielded, the +richer and better-fed the people would have been, and the more the +population would have grown. As the population grew, more land would +have needed to be flooded or irrigated, and more complex systems of +dikes, reservoirs, canals, and ditches would have been built. The more +complex the system, the more necessity for work on new projects and for +the control of their use.... And so on.... + +What I have just put down for you is a guess at the manner of growth of +some of the formalized systems that go to make up a civilized society. +My explanation has been pointed particularly at Egypt and Mesopotamia. +I have already told you that the irrigation and water-control part of +it does not apply to the development of the Aztecs or the Mayas, or +perhaps anybody else. But I think that a fair part of the story of +Egypt and Mesopotamia must be as Ive just told you. + +I am particularly anxious that you do _not_ understand me to mean that +irrigation _caused_ civilization. I am sure it was not that simple at +all. For, in fact, a complex and highly engineered irrigation system +proper did not come until later times. Lets say rather that the simple +beginnings of irrigation allowed and in fact encouraged a great number +of things in the technological, political, social, and moral realms of +culture. We do not yet understand what all these things were or how +they worked. But without these other aspects of culture, I do not +think that urbanization and civilization itself could have come into +being. + + +THE ARCHEOLOGICAL SEQUENCE TO CIVILIZATION IN IRAQ + +We last spoke of the archeological materials of Iraq on page 130, +where I described the village-farming community of Hassunan type. The +Hassunan type villages appear in the hilly-flanks zone and in the +rolling land adjacent to the Tigris in northern Iraq. It is probable +that even before the Hassuna pattern of culture lived its course, a +new assemblage had been established in northern Iraq and Syria. This +assemblage is called Halaf, after a site high on a tributary of the +Euphrates, on the Syro-Turkish border. + +[Illustration: SKETCH OF SELECTED ITEMS OF HALAFIAN ASSEMBLAGE + + BEADS AND PENDANTS + POTTERY MOTIFS + POTTERY] + +The Halafian assemblage is incompletely known. The culture it +represents included a remarkably handsome painted pottery. +Archeologists have tended to be so fascinated with this pottery that +they have bothered little with the rest of the Halafian assemblage. We +do know that strange stone-founded houses, with plans like those of the +popular notion of an Eskimo igloo, were built. Like the pottery of the +Samarran style, which appears as part of the Hassunan assemblage (see +p. 131), the Halafian painted pottery implies great concentration and +excellence of draftsmanship on the part of the people who painted it. + +We must mention two very interesting sites adjacent to the mud-flats of +the rivers, half way down from northern Iraq to the classic alluvial +Mesopotamian area. One is Baghouz on the Euphrates; the other is +Samarra on the Tigris (see map, p. 125). Both these sites yield the +handsome painted pottery of the style called Samarran: in fact it +is Samarra which gives its name to the pottery. Neither Baghouz nor +Samarra have completely Hassunan types of assemblages, and at Samarra +there are a few pots of proper Halafian style. I suppose that Samarra +and Baghouz give us glimpses of those early farmers who had begun to +finger their way down the mud-flats of the river banks toward the +fertile but yet untilled southland. + + +CLASSIC SOUTHERN MESOPOTAMIA FIRST OCCUPIED + +Our next step is into the southland proper. Here, deep in the core of +the mound which later became the holy Sumerian city of Eridu, Iraqi +archeologists uncovered a handsome painted pottery. Pottery of the same +type had been noticed earlier by German archeologists on the surface +of a small mound, awash in the spring floods, near the remains of the +Biblical city of Erich (Sumerian = Uruk; Arabic = Warka). This Eridu +pottery, which is about all we have of the assemblage of the people who +once produced it, may be seen as a blend of the Samarran and Halafian +painted pottery styles. This may over-simplify the case, but as yet we +do not have much evidence to go on. The idea does at least fit with my +interpretation of the meaning of Baghouz and Samarra as way-points on +the mud-flats of the rivers half way down from the north. + +My colleague, Robert Adams, believes that there were certainly +riverine-adapted food-collectors living in lower Mesopotamia. The +presence of such would explain why the Eridu assemblage is not simply +the sum of the Halafian and Samarran assemblages. But the domesticated +plants and animals and the basic ways of food-production must have +come from the hilly-flanks country in the north. + +Above the basal Eridu levels, and at a number of other sites in the +south, comes a full-fledged assemblage called Ubaid. Incidentally, +there is an aspect of the Ubaidian assemblage in the north as well. It +seems to move into place before the Halaf manifestation is finished, +and to blend with it. The Ubaidian assemblage in the south is by far +the more spectacular. The development of the temple has been traced +at Eridu from a simple little structure to a monumental building some +62 feet long, with a pilaster-decorated faade and an altar in its +central chamber. There is painted Ubaidian pottery, but the style is +hurried and somewhat careless and gives the _impression_ of having been +a cheap mass-production means of decoration when compared with the +carefully drafted styles of Samarra and Halaf. The Ubaidian people made +other items of baked clay: sickles and axes of very hard-baked clay +are found. The northern Ubaidian sites have yielded tools of copper, +but metal tools of unquestionable Ubaidian find-spots are not yet +available from the south. Clay figurines of human beings with monstrous +turtle-like faces are another item in the southern Ubaidian assemblage. + +[Illustration: SKETCH OF SELECTED ITEMS OF UBAIDIAN ASSEMBLAGE] + +There is a large Ubaid cemetery at Eridu, much of it still awaiting +excavation. The few skeletons so far tentatively studied reveal a +completely modern type of Mediterraneanoid; the individuals whom the +skeletons represent would undoubtedly blend perfectly into the modern +population of southern Iraq. What the Ubaidian assemblage says to us is +that these people had already adapted themselves and their culture to +the peculiar riverine environment of classic southern Mesopotamia. For +example, hard-baked clay axes will chop bundles of reeds very well, or +help a mason dress his unbaked mud bricks, and there were only a few +soft and pithy species of trees available. The Ubaidian levels of Eridu +yield quantities of date pits; that excellent and characteristically +Iraqi fruit was already in use. The excavators also found the clay +model of a ship, with the stepping-point for a mast, so that Sinbad the +Sailor must have had his antecedents as early as the time of Ubaid. +The bones of fish, which must have flourished in the larger canals as +well as in the rivers, are common in the Ubaidian levels and thereafter. + + +THE UBAIDIAN ACHIEVEMENT + +On present evidence, my tendency is to see the Ubaidian assemblage +in southern Iraq as the trace of a new era. I wish there were more +evidence, but what we have suggests this to me. The culture of southern +Ubaid soon became a culture of towns--of centrally located towns with +some rural villages about them. The town had a temple and there must +have been priests. These priests probably had political and economic +functions as well as religious ones, if the somewhat later history of +Mesopotamia may suggest a pattern for us. Presently the temple and its +priesthood were possibly the focus of the market; the temple received +its due, and may already have had its own lands and herds and flocks. +The people of the town, undoubtedly at least in consultation with the +temple administration, planned and maintained the simple irrigation +ditches. As the system flourished, the community of rural farmers would +have produced more than sufficient food. The tendency for specialized +crafts to develop--tentative at best at the cultural level of the +earlier village-farming community era--would now have been achieved, +and probably many other specialists in temple administration, water +control, architecture, and trade would also have appeared, as the +surplus food-supply was assured. + +Southern Mesopotamia is not a land rich in natural resources other +than its fertile soil. Stone, good wood for construction, metal, and +innumerable other things would have had to be imported. Grain and +dates--although both are bulky and difficult to transport--and wool and +woven stuffs must have been the mediums of exchange. Over what area did +the trading net-work of Ubaid extend? We start with the idea that the +Ubaidian assemblage is most richly developed in the south. We assume, I +think, correctly, that it represents a cultural flowering of the south. +On the basis of the pottery of the still elusive Eridu immigrants +who had first followed the rivers into alluvial Mesopotamia, we get +the notion that the characteristic painted pottery style of Ubaid +was developed in the southland. If this reconstruction is correct +then we may watch with interest where the Ubaid pottery-painting +tradition spread. We have already mentioned that there is a substantial +assemblage of (and from the southern point of view, _fairly_ pure) +Ubaidian material in northern Iraq. The pottery appears all along the +Iranian flanks, even well east of the head of the Persian Gulf, and +ends in a later and spectacular flourish in an extremely handsome +painted style called the Susa style. Ubaidian pottery has been noted +up the valleys of both of the great rivers, well north of the Iraqi +and Syrian borders on the southern flanks of the Anatolian plateau. +It reaches the Mediterranean Sea and the valley of the Orontes in +Syria, and it may be faintly reflected in the painted style of a +site called Ghassul, on the east bank of the Jordan in the Dead Sea +Valley. Over this vast area--certainly in all of the great basin of +the Tigris-Euphrates drainage system and its natural extensions--I +believe we may lay our fingers on the traces of a peculiar way of +decorating pottery, which we call Ubaidian. This cursive and even +slap-dash decoration, it appears to me, was part of a new cultural +tradition which arose from the adjustments which immigrant northern +farmers first made to the new and challenging environment of southern +Mesopotamia. But exciting as the idea of the spread of influences of +the Ubaid tradition in space may be, I believe you will agree that the +consequences of the growth of that tradition in southern Mesopotamia +itself, as time passed, are even more important. + + +THE WARKA PHASE IN THE SOUTH + +So far, there are only two radiocarbon determinations for the Ubaidian +assemblage, one from Tepe Gawra in the north and one from Warka in the +south. My hunch would be to use the dates 4500 to 3750 B.C., with a +plus or more probably a minus factor of about two hundred years for +each, as the time duration of the Ubaidian assemblage in southern +Mesopotamia. + +Next, much to our annoyance, we have what is almost a temporary +black-out. According to the system of terminology I favor, our next +assemblage after that of Ubaid is called the _Warka_ phase, from +the Arabic name for the site of Uruk or Erich. We know it only from +six or seven levels in a narrow test-pit at Warka, and from an even +smaller hole at another site. This assemblage, so far, is known only +by its pottery, some of which still bears Ubaidian style painting. The +characteristic Warkan pottery is unpainted, with smoothed red or gray +surfaces and peculiar shapes. Unquestionably, there must be a great +deal more to say about the Warkan assemblage, but someone will first +have to excavate it! + + +THE DAWN OF CIVILIZATION + +After our exasperation with the almost unknown Warka interlude, +following the brilliant false dawn of Ubaid, we move next to an +assemblage which yields traces of a preponderance of those elements +which we noted (p. 144) as meaning civilization. This assemblage +is that called _Proto-Literate_; it already contains writing. On +the somewhat shaky principle that writing, however early, means +history--and no longer prehistory--the assemblage is named for the +historical implications of its content, and no longer after the name of +the site where it was first found. Since some of the older books used +site-names for this assemblage, I will tell you that the Proto-Literate +includes the latter half of what used to be called the Uruk period +_plus_ all of what used to be called the Jemdet Nasr period. It shows +a consistent development from beginning to end. + +I shall, in fact, leave much of the description and the historic +implications of the Proto-Literate assemblage to the conventional +historians. Professor T. J. Jacobsen, reaching backward from the +legends he finds in the cuneiform writings of slightly later times, can +in fact tell you a more complete story of Proto-Literate culture than +I can. It should be enough here if I sum up briefly what the excavated +archeological evidence shows. + +We have yet to dig a Proto-Literate site in its entirety, but the +indications are that the sites cover areas the size of small cities. +In architecture, we know of large and monumental temple structures, +which were built on elaborate high terraces. The plans and decoration +of these temples follow the pattern set in the Ubaid phase: the chief +difference is one of size. The German excavators at the site of Warka +reckoned that the construction of only one of the Proto-Literate temple +complexes there must have taken 1,500 men, each working a ten-hour day, +five years to build. + + +ART AND WRITING + +If the architecture, even in its monumental forms, can be seen to +stem from Ubaidian developments, this is not so with our other +evidence of Proto-Literate artistic expression. In relief and applied +sculpture, in sculpture in the round, and on the engraved cylinder +seals--all of which now make their appearance--several completely +new artistic principles are apparent. These include the composition +of subject-matter in groups, commemorative scenes, and especially +the ability and apparent desire to render the human form and face. +Excellent as the animals of the Franco-Cantabrian art may have been +(see p. 85), and however handsome were the carefully drafted +geometric designs and conventionalized figures on the pottery of the +early farmers, there seems to have been, up to this time, a mental +block about the drawing of the human figure and especially the human +face. We do not yet know what caused this self-consciousness about +picturing themselves which seems characteristic of men before the +appearance of civilization. We do know that with civilization, the +mental block seems to have been removed. + +Clay tablets bearing pictographic signs are the Proto-Literate +forerunners of cuneiform writing. The earliest examples are not well +understood but they seem to be devices for making accounts and +for remembering accounts. Different from the later case in Egypt, +where writing appears fully formed in the earliest examples, the +development from simple pictographic signs to proper cuneiform writing +may be traced, step by step, in Mesopotamia. It is most probable +that the development of writing was connected with the temple and +the need for keeping account of the temples possessions. Professor +Jacobsen sees writing as a means for overcoming space, time, and the +increasing complications of human affairs: Literacy, which began +with ... civilization, enhanced mightily those very tendencies in its +development which characterize it as a civilization and mark it off as +such from other types of culture. + +[Illustration: RELIEF ON A PROTO-LITERATE STONE VASE, WARKA + +Unrolled drawing, with restoration suggested by figures from +contemporary cylinder seals] + +While the new principles in art and the idea of writing are not +foreshadowed in the Ubaid phase, or in what little we know of the +Warkan, I do not think we need to look outside southern Mesopotamia +for their beginnings. We do know something of the adjacent areas, +too, and these beginnings are not there. I think we must accept them +as completely new discoveries, made by the people who were developing +the whole new culture pattern of classic southern Mesopotamia. Full +description of the art, architecture, and writing of the Proto-Literate +phase would call for many details. Men like Professor Jacobsen and Dr. +Adams can give you these details much better than I can. Nor shall I do +more than tell you that the common pottery of the Proto-Literate phase +was so well standardized that it looks factory made. There was also +some handsome painted pottery, and there were stone bowls with inlaid +decoration. Well-made tools in metal had by now become fairly common, +and the metallurgist was experimenting with the casting process. Signs +for plows have been identified in the early pictographs, and a wheeled +chariot is shown on a cylinder seal engraving. But if I were forced to +a guess in the matter, I would say that the development of plows and +draft-animals probably began in the Ubaid period and was another of the +great innovations of that time. + +The Proto-Literate assemblage clearly suggests a highly developed and +sophisticated culture. While perhaps not yet fully urban, it is on +the threshold of urbanization. There seems to have been a very dense +settlement of Proto-Literate sites in classic southern Mesopotamia, +many of them newly founded on virgin soil where no earlier settlements +had been. When we think for a moment of what all this implies, of the +growth of an irrigation system which must have existed to allow the +flourish of this culture, and of the social and political organization +necessary to maintain the irrigation system, I think we will agree that +at last we are dealing with civilization proper. + + +FROM PREHISTORY TO HISTORY + +Now it is time for the conventional ancient historians to take over +the story from me. Remember this when you read what they write. Their +real base-line is with cultures ruled over by later kings and emperors, +whose writings describe military campaigns and the administration of +laws and fully organized trading ventures. To these historians, the +Proto-Literate phase is still a simple beginning for what is to follow. +If they mention the Ubaid assemblage at all--the one I was so lyrical +about--it will be as some dim and fumbling step on the path to the +civilized way of life. + +I suppose you could say that the difference in the approach is that as +a prehistorian I have been looking forward or upward in time, while the +historians look backward to glimpse what Ive been describing here. My +base-line was half a million years ago with a being who had little more +than the capacity to make tools and fire to distinguish him from the +animals about him. Thus my point of view and that of the conventional +historian are bound to be different. You will need both if you want to +understand all of the story of men, as they lived through time to the +present. + + + + +End of PREHISTORY + +[Illustration] + + +Youll doubtless easily recall your general course in ancient history: +how the Sumerian dynasties of Mesopotamia were supplanted by those of +Babylonia, how the Hittite kingdom appeared in Anatolian Turkey, and +about the three great phases of Egyptian history. The literate kingdom +of Crete arose, and by 1500 B.C. there were splendid fortified Mycenean +towns on the mainland of Greece. This was the time--about the whole +eastern end of the Mediterranean--of what Professor Breasted called the +first great internationalism, with flourishing trade, international +treaties, and royal marriages between Egyptians, Babylonians, and +Hittites. By 1200 B.C., the whole thing had fragmented: the peoples of +the sea were restless in their isles, and the great ancient centers in +Egypt, Mesopotamia, and Anatolia were eclipsed. Numerous smaller states +arose--Assyria, Phoenicia, Israel--and the Trojan war was fought. +Finally Assyria became the paramount power of all the Near East, +presently to be replaced by Persia. + +A new culture, partaking of older west Asiatic and Egyptian elements, +but casting them with its own tradition into a new mould, arose in +mainland Greece. + +I once shocked my Classical colleagues to the core by referring to +Greece as a second degree derived civilization, but there is much +truth in this. The principles of bronze- and then of iron-working, of +the alphabet, and of many other elements in Greek culture were borrowed +from western Asia. Our debt to the Greeks is too well known for me even +to mention it, beyond recalling to you that it is to Greece we owe the +beginnings of rational or empirical science and thought in general. But +Greece fell in its turn to Rome, and in 55 B.C. Caesar invaded Britain. + +I last spoke of Britain on page 142; I had chosen it as my single +example for telling you something of how the earliest farming +communities were established in Europe. Now I will continue with +Britains later prehistory, so you may sense something of the end of +prehistory itself. Remember that Britain is simply a single example +we select; the same thing could be done for all the other countries +of Europe, and will be possible also, some day, for further Asia and +Africa. Remember, too, that prehistory in most of Europe runs on for +three thousand or more years _after_ conventional ancient history +begins in the Near East. Britain is a good example to use in showing +how prehistory ended in Europe. As we said earlier, it lies at the +opposite end of Europe from the area of highest cultural achievement in +those times, and should you care to read more of the story in detail, +you may do so in the English language. + + +METAL USERS REACH ENGLAND + +We left the story of Britain with the peoples who made three different +assemblages--the Windmill Hill, the megalith-builders, and the +Peterborough--making adjustments to their environments, to the original +inhabitants of the island, and to each other. They had first arrived +about 2500 B.C., and were simple pastoralists and hoe cultivators who +lived in little village communities. Some of them planted little if any +grain. By 2000 B.C., they were well settled in. Then, somewhere in the +range from about 1900 to 1800 B.C., the traces of the invasion of a new +series of peoples began to appear. + +The first newcomers are called the Beaker folk, after the name of a +peculiar form of pottery they made. The beaker type of pottery seems +oldest in Spain, where it occurs with great collective tombs of +megalithic construction and with copper tools. But the Beaker folk who +reached England seem already to have moved first from Spain(?) to the +Rhineland and Holland. While in the Rhineland, and before leaving for +England, the Beaker folk seem to have mixed with the local population +and also with incomers from northeastern Europe whose culture included +elements brought originally from the Near East by the eastern way +through the steppes. This last group has also been named for a peculiar +article in its assemblage; the group is called the Battle-axe folk. A +few Battle-axe folk elements, including, in fact, stone battle-axes, +reached England with the earliest Beaker folk,[6] coming from the +Rhineland. + + [6] The British authors use the term Beaker folk to mean both + archeological assemblage and human physical type. They speak + of a ... tall, heavy-boned, rugged, and round-headed strain + which they take to have developed, apparently in the Rhineland, + by a mixture of the original (Spanish?) beaker-makers and + the northeast European battle-axe makers. However, since the + science of physical anthropology is very much in flux at the + moment, and since I am not able to assess the evidence for these + physical types, I _do not_ use the term folk in this book with + its usual meaning of standardized physical type. When I use + folk here, I mean simply _the makers of a given archeological + assemblage_. The difficulty only comes when assemblages are + named for some item in them; it is too clumsy to make an + adjective of the item and refer to a beakerian assemblage. + +The Beaker folk settled earliest in the agriculturally fertile south +and east. There seem to have been several phases of Beaker folk +invasions, and it is not clear whether these all came strictly from the +Rhineland or Holland. We do know that their copper daggers and awls +and armlets are more of Irish or Atlantic European than of Rhineland +origin. A few simple habitation sites and many burials of the Beaker +folk are known. They buried their dead singly, sometimes in conspicuous +individual barrows with the dead warrior in his full trappings. The +spectacular element in the assemblage of the Beaker folk is a group +of large circular monuments with ditches and with uprights of wood or +stone. These henges became truly monumental several hundred years +later; while they were occasionally dedicated with a burial, they were +not primarily tombs. The effect of the invasion of the Beaker folk +seems to cut across the whole fabric of life in Britain. + +[Illustration: BEAKER] + +There was, however, a second major element in British life at this +time. It shows itself in the less well understood traces of a group +again called after one of the items in their catalogue, the Food-vessel +folk. There are many burials in these food-vessel pots in northern +England, Scotland, and Ireland, and the pottery itself seems to +link back to that of the Peterborough assemblage. Like the earlier +Peterborough people in the highland zone before them, the makers of +the food-vessels seem to have been heavily involved in trade. It is +quite proper to wonder whether the food-vessel pottery itself was made +by local women who were married to traders who were middlemen in the +transmission of Irish metal objects to north Germany and Scandinavia. +The belt of high, relatively woodless country, from southwest to +northeast, was already established as a natural route for inland trade. + + +MORE INVASIONS + +About 1500 B.C., the situation became further complicated by the +arrival of new people in the region of southern England anciently +called Wessex. The traces suggest the Brittany coast of France as a +source, and the people seem at first to have been a small but heroic +group of aristocrats. Their heroes are buried with wealth and +ceremony, surrounded by their axes and daggers of bronze, their gold +ornaments, and amber and jet beads. These rich finds show that the +trade-linkage these warriors patronized spread from the Baltic sources +of amber to Mycenean Greece or even Egypt, as evidenced by glazed blue +beads. + +The great visual trace of Wessex achievement is the final form of +the spectacular sanctuary at Stonehenge. A wooden henge or circular +monument was first made several hundred years earlier, but the site +now received its great circles of stone uprights and lintels. The +diameter of the surrounding ditch at Stonehenge is about 350 feet, the +diameter of the inner circle of large stones is about 100 feet, and +the tallest stone of the innermost horseshoe-shaped enclosure is 29 +feet 8 inches high. One circle is made of blue stones which must have +been transported from Pembrokeshire, 145 miles away as the crow flies. +Recently, many carvings representing the profile of a standard type of +bronze axe of the time, and several profiles of bronze daggers--one of +which has been called Mycenean in type--have been found carved in the +stones. We cannot, of course, describe the details of the religious +ceremonies which must have been staged in Stonehenge, but we can +certainly imagine the well-integrated and smoothly working culture +which must have been necessary before such a great monument could have +been built. + + +THIS ENGLAND + +The range from 1900 to about 1400 B.C. includes the time of development +of the archeological features usually called the Early Bronze Age +in Britain. In fact, traces of the Wessex warriors persisted down to +about 1200 B.C. The main regions of the island were populated, and the +adjustments to the highland and lowland zones were distinct and well +marked. The different aspects of the assemblages of the Beaker folk and +the clearly expressed activities of the Food-vessel folk and the Wessex +warriors show that Britain was already taking on her characteristic +trading role, separated from the European continent but conveniently +adjacent to it. The tin of Cornwall--so important in the production +of good bronze--as well as the copper of the west and of Ireland, +taken with the gold of Ireland and the general excellence of Irish +metal work, assured Britain a traders place in the then known world. +Contacts with the eastern Mediterranean may have been by sea, with +Cornish tin as the attraction, or may have been made by the Food-vessel +middlemen on their trips to the Baltic coast. There they would have +encountered traders who traveled the great north-south European road, +by which Baltic amber moved southward to Greece and the Levant, and +ideas and things moved northward again. + +There was, however, the Channel between England and Europe, and this +relative isolation gave some peace and also gave time for a leveling +and further fusion of culture. The separate cultural traditions began +to have more in common. The growing of barley, the herding of sheep and +cattle, and the production of woolen garments were already features +common to all Britains inhabitants save a few in the remote highlands, +the far north, and the distant islands not yet fully touched by +food-production. The personality of Britain was being formed. + + +CREMATION BURIALS BEGIN + +Along with people of certain religious faiths, archeologists are +against cremation (for other people!). Individuals to be cremated seem +in past times to have been dressed in their trappings and put upon a +large pyre: it takes a lot of wood and a very hot fire for a thorough +cremation. When the burning had been completed, the few fragile scraps +of bone and such odd beads of stone or other rare items as had resisted +the great heat seem to have been whisked into a pot and the pot buried. +The archeologist is left with the pot and the unsatisfactory scraps in +it. + +Tentatively, after about 1400 B.C. and almost completely over the whole +island by 1200 B.C., Britain became the scene of cremation burials +in urns. We know very little of the people themselves. None of their +settlements have been identified, although there is evidence that they +grew barley and made enclosures for cattle. The urns used for the +burials seem to have antecedents in the pottery of the Food-vessel +folk, and there are some other links with earlier British traditions. +In Lancashire, a wooden circle seems to have been built about a grave +with cremated burials in urns. Even occasional instances of cremation +may be noticed earlier in Britain, and it is not clear what, if any, +connection the British cremation burials in urns have with the classic +_Urnfields_ which were now beginning in the east Mediterranean and +which we shall mention below. + +The British cremation-burial-in-urns folk survived a long time in the +highland zone. In the general British scheme, they make up what is +called the Middle Bronze Age, but in the highland zone they last +until after 900 B.C. and are considered to be a specialized highland +Late Bronze Age. In the highland zone, these later cremation-burial +folk seem to have continued the older Food-vessel tradition of being +middlemen in the metal market. + +Granting that our knowledge of this phase of British prehistory is +very restricted because the cremations have left so little for the +archeologist, it does not appear that the cremation-burial-urn folk can +be sharply set off from their immediate predecessors. But change on a +grander scale was on the way. + + +REVERBERATIONS FROM CENTRAL EUROPE + +In the centuries immediately following 1000 B.C., we see with fair +clarity two phases of a cultural process which must have been going +on for some time. Certainly several of the invasions we have already +described in this chapter were due to earlier phases of the same +cultural process, but we could not see the details. + +[Illustration: SLASHING SWORD] + +Around 1200 B.C. central Europe was upset by the spread of the +so-called Urnfield folk, who practiced cremation burial in urns and +whom we also know to have been possessors of long, slashing swords and +the horse. I told you above that we have no idea that the Urnfield +folk proper were in any way connected with the people who made +cremation-burial-urn cemeteries a century or so earlier in Britain. It +has been supposed that the Urnfield folk themselves may have shared +ideas with the people who sacked Troy. We know that the Urnfield +pressure from central Europe displaced other people in northern France, +and perhaps in northwestern Germany, and that this reverberated into +Britain about 1000 B.C. + +Soon after 750 B.C., the same thing happened again. This time, the +pressure from central Europe came from the Hallstatt folk who were iron +tool makers: the reverberation brought people from the western Alpine +region across the Channel into Britain. + +At first it is possible to see the separate results of these folk +movements, but the developing cultures soon fused with each other and +with earlier British elements. Presently there were also strains of +other northern and western European pottery and traces of Urnfield +practices themselves which appeared in the finished British product. I +hope you will sense that I am vastly over-simplifying the details. + +The result seems to have been--among other things--a new kind of +agricultural system. The land was marked off by ditched divisions. +Rectangular fields imply the plow rather than hoe cultivation. We seem +to get a picture of estate or tribal boundaries which included village +communities; we find a variety of tools in bronze, and even whetstones +which show that iron has been honed on them (although the scarce iron +has not been found). Let me give you the picture in Professor S. +Piggotts words: The ... Late Bronze Age of southern England was but +the forerunner of the earliest Iron Age in the same region, not only in +the techniques of agriculture, but almost certainly in terms of ethnic +kinship ... we can with some assurance talk of the Celts ... the great +early Celtic expansion of the Continent is recognized to be that of the +Urnfield people. + +Thus, certainly by 500 B.C., there were people in Britain, some of +whose descendants we may recognize today in name or language in remote +parts of Wales, Scotland, and the Hebrides. + + +THE COMING OF IRON + +Iron--once the know-how of reducing it from its ore in a very hot, +closed fire has been achieved--produces a far cheaper and much more +efficient set of tools than does bronze. Iron tools seem first to +have been made in quantity in Hittite Anatolia about 1500 B.C. In +continental Europe, the earliest, so-called Hallstatt, iron-using +cultures appeared in Germany soon after 750 B.C. Somewhat later, +Greek and especially Etruscan exports of _objets dart_--which moved +with a flourishing trans-Alpine wine trade--influenced the Hallstatt +iron-working tradition. Still later new classical motifs, together with +older Hallstatt, oriental, and northern nomad motifs, gave rise to a +new style in metal decoration which characterizes the so-called La Tne +phase. + +A few iron users reached Britain a little before 400 B.C. Not long +after that, a number of allied groups appeared in southern and +southeastern England. They came over the Channel from France and must +have been Celts with dialects related to those already in England. A +second wave of Celts arrived from the Marne district in France about +250 B.C. Finally, in the second quarter of the first century B.C., +there were several groups of newcomers, some of whom were Belgae of +a mixed Teutonic-Celtic confederacy of tribes in northern France and +Belgium. The Belgae preceded the Romans by only a few years. + + +HILL-FORTS AND FARMS + +The earliest iron-users seem to have entrenched themselves temporarily +within hill-top forts, mainly in the south. Gradually, they moved +inland, establishing _individual_ farm sites with extensive systems +of rectangular fields. We recognize these fields by the lynchets or +lines of soil-creep which plowing left on the slopes of hills. New +crops appeared; there were now bread wheat, oats, and rye, as well as +barley. + +At Little Woodbury, near the town of Salisbury, a farmstead has been +rather completely excavated. The rustic buildings were within a +palisade, the round house itself was built of wood, and there were +various outbuildings and pits for the storage of grain. Weaving was +done on the farm, but not blacksmithing, which must have been a +specialized trade. Save for the lack of firearms, the place might +almost be taken for a farmstead on the American frontier in the early +1800s. + +Toward 250 B.C. there seems to have been a hasty attempt to repair the +hill-forts and to build new ones, evidently in response to signs of +restlessness being shown by remote relatives in France. + + +THE SECOND PHASE + +Perhaps the hill-forts were not entirely effective or perhaps a +compromise was reached. In any case, the newcomers from the Marne +district did establish themselves, first in the southeast and then to +the north and west. They brought iron with decoration of the La Tne +type and also the two-wheeled chariot. Like the Wessex warriors of +over a thousand years earlier, they made heroes graves, with their +warriors buried in the war-chariots and dressed in full trappings. + +[Illustration: CELTIC BUCKLE] + +The metal work of these Marnian newcomers is excellent. The peculiar +Celtic art style, based originally on the classic tendril motif, +is colorful and virile, and fits with Greek and Roman descriptions +of Celtic love of color in dress. There is a strong trace of these +newcomers northward in Yorkshire, linked by Ptolemys description to +the Parisii, doubtless part of the Celtic tribe which originally gave +its name to Paris on the Seine. Near Glastonbury, in Somerset, two +villages in swamps have been excavated. They seem to date toward the +middle of the first century B.C., which was a troubled time in Britain. +The circular houses were built on timber platforms surrounded with +palisades. The preservation of antiquities by the water-logged peat of +the swamp has yielded us a long catalogue of the materials of these +villagers. + +In Scotland, which yields its first iron tools at a date of about 100 +B.C., and in northern Ireland even slightly earlier, the effects of the +two phases of newcomers tend especially to blend. Hill-forts, brochs +(stone-built round towers) and a variety of other strange structures +seem to appear as the new ideas develop in the comparative isolation of +northern Britain. + + +THE THIRD PHASE + +For the time of about the middle of the first century B.C., we again +see traces of frantic hill-fort construction. This simple military +architecture now took some new forms. Its multiple ramparts must +reflect the use of slings as missiles, rather than spears. We probably +know the reason. In 56 B.C., Julius Caesar chastised the Veneti of +Brittany for outraging the dignity of Roman ambassadors. The Veneti +were famous slingers, and doubtless the reverberations of escaping +Veneti were felt across the Channel. The military architecture suggests +that some Veneti did escape to Britain. + +Also, through Caesar, we learn the names of newcomers who arrived in +two waves, about 75 B.C. and about 50 B.C. These were the Belgae. Now, +at last, we can even begin to speak of dynasties and individuals. +Some time before 55 B.C., the Catuvellauni, originally from the Marne +district in France, had possessed themselves of a large part of +southeastern England. They evidently sailed up the Thames and built a +town of over a hundred acres in area. Here ruled Cassivellaunus, the +first man in England whose name we know, and whose town Caesar sacked. +The town sprang up elsewhere again, however. + + +THE END OF PREHISTORY + +Prehistory, strictly speaking, is now over in southern Britain. +Claudius effective invasion took place in 43 A.D.; by 83 A.D., a raid +had been made as far north as Aberdeen in Scotland. But by 127 A.D., +Hadrian had completed his wall from the Solway to the Tyne, and the +Romans settled behind it. In Scotland, Romanization can have affected +the countryside very little. Professor Piggott adds that ... it is +when the pressure of Romanization is relaxed by the break-up of the +Dark Ages that we see again the Celtic metal-smiths handling their +material with the same consummate skill as they had before the Roman +Conquest, and with traditional styles that had not even then forgotten +their Marnian and Belgic heritage. + +In fact, many centuries go by, in Britain as well as in the rest of +Europe, before the archeologists task is complete and the historian on +his own is able to describe the ways of men in the past. + + +BRITAIN AS A SAMPLE OF THE GENERAL COURSE OF PREHISTORY IN EUROPE + +In giving this very brief outline of the later prehistory of Britain, +you will have noticed how often I had to refer to the European +continent itself. Britain, beyond the English Channel for all of her +later prehistory, had a much simpler course of events than did most of +the rest of Europe in later prehistoric times. This holds, in spite +of all the invasions and reverberations from the continent. Most +of Europe was the scene of an even more complicated ebb and flow of +cultural change, save in some of its more remote mountain valleys and +peninsulas. + +The whole course of later prehistory in Europe is, in fact, so very +complicated that there is no single good book to cover it all; +certainly there is none in English. There are some good regional +accounts and some good general accounts of part of the range from about +3000 B.C. to A.D. 1. I suspect that the difficulty of making a good +book that covers all of its later prehistory is another aspect of what +makes Europe so very complicated a continent today. The prehistoric +foundations for Europes very complicated set of civilizations, +cultures, and sub-cultures--which begin to appear as history +proceeds--were in themselves very complicated. + +Hence, I selected the case of Britain as a single example of how +prehistory ends in Europe. It could have been more complicated than we +found it to be. Even in the subject matter on Britain in the chapter +before the last, we did not see direct traces of the effect on Britain +of the very important developments which took place in the Danubian +way from the Near East. Apparently Britain was not affected. Britain +received the impulses which brought copper, bronze, and iron tools from +an original east Mediterranean homeland into Europe, almost at the ends +of their journeys. But by the same token, they had had time en route to +take on their characteristic European aspects. + +Some time ago, Sir Cyril Fox wrote a famous book called _The +Personality of Britain_, sub-titled Its Influence on Inhabitant and +Invader in Prehistoric and Early Historic Times. We have not gone +into the post-Roman early historic period here; there are still the +Anglo-Saxons and Normans to account for as well as the effects of +the Romans. But what I have tried to do was to begin the story of +how the personality of Britain was formed. The principles that Fox +used, in trying to balance cultural and environmental factors and +interrelationships would not be greatly different for other lands. + + + + +Summary + +[Illustration] + + +In the pages you have read so far, you have been brought through the +earliest 99 per cent of the story of mans life on this planet. I have +left only 1 per cent of the story for the historians to tell. + + +THE DRAMA OF THE PAST + +Men first became men when evolution had carried them to a certain +point. This was the point where the eye-hand-brain co-ordination was +good enough so that tools could be made. When tools began to be made +according to sets of lasting habits, we know that men had appeared. +This happened over a half million years ago. The stage for the play +may have been as broad as all of Europe, Africa, and Asia. At least, +it seems unlikely that it was only one little region that saw the +beginning of the drama. + +Glaciers and different climates came and went, to change the settings. +But the play went on in the same first act for a very long time. The +men who were the players had simple roles. They had to feed themselves +and protect themselves as best they could. They did this by hunting, +catching, and finding food wherever they could, and by taking such +protection as caves, fire, and their simple tools would give them. +Before the first act was over, the last of the glaciers was melting +away, and the players had added the New World to their stage. If +we want a special name for the first act, we could call it _The +Food-Gatherers_. + +There were not many climaxes in the first act, so far as we can see. +But I think there may have been a few. Certainly the pace of the +first act accelerated with the swing from simple gathering to more +intensified collecting. The great cave art of France and Spain was +probably an expression of a climax. Even the ideas of burying the dead +and of the Venus figurines must also point to levels of human thought +and activity that were over and above pure food-getting. + + +THE SECOND ACT + +The second act began only about ten thousand years ago. A few of the +players started it by themselves near the center of the Old World part +of the stage, in the Near East. It began as a plant and animal act, but +it soon became much more complicated. + +But the players in this one part of the stage--in the Near East--were +not the only ones to start off on the second act by themselves. Other +players, possibly in several places in the Far East, and certainly in +the New World, also started second acts that began as plant and animal +acts, and then became complicated. We can call the whole second act +_The Food-Producers_. + + +THE FIRST GREAT CLIMAX OF THE SECOND ACT + +In the Near East, the first marked climax of the second act happened +in Mesopotamia and Egypt. The play and the players reached that great +climax that we call civilization. This seems to have come less than +five thousand years after the second act began. But it could never have +happened in the first act at all. + +There is another curious thing about the first act. Many of the players +didnt know it was over and they kept on with their roles long after +the second act had begun. On the edges of the stage there are today +some players who are still going on with the first act. The Eskimos, +and the native Australians, and certain tribes in the Amazon jungle are +some of these players. They seem perfectly happy to keep on with the +first act. + +The second act moved from climax to climax. The civilizations of +Mesopotamia and Egypt were only the earliest of these climaxes. The +players to the west caught the spirit of the thing, and climaxes +followed there. So also did climaxes come in the Far Eastern and New +World portions of the stage. + +The greater part of the second act should really be described to you +by a historian. Although it was a very short act when compared to the +first one, the climaxes complicate it a great deal. I, a prehistorian, +have told you about only the first act, and the very beginning of the +second. + + +THE THIRD ACT + +Also, as a prehistorian I probably should not even mention the third +act--it began so recently. The third act is _The Industrialization_. +It is the one in which we ourselves are players. If the pace of the +second act was so much faster than that of the first, the pace of the +third act is terrific. The danger is that it may wear down the players +completely. + +What sort of climaxes will the third act have, and are we already in +one? You have seen by now that the acts of my play are given in terms +of modes or basic patterns of human economy--ways in which people +get food and protection and safety. The climaxes involve more than +human economy. Economics and technological factors may be part of the +climaxes, but they are not all. The climaxes may be revolutions in +their own way, intellectual and social revolutions if you like. + +If the third act follows the pattern of the second act, a climax should +come soon after the act begins. We may be due for one soon if we are +not already in it. Remember the terrific pace of this third act. + + +WHY BOTHER WITH PREHISTORY? + +Why do we bother about prehistory? The main reason is that we think it +may point to useful ideas for the present. We are in the troublesome +beginnings of the third act of the play. The beginnings of the second +act may have lessons for us and give depth to our thinking. I know +there are at least _some_ lessons, even in the present incomplete +state of our knowledge. The players who began the second act--that of +food-production--separately, in different parts of the world, were not +all of one pure race nor did they have pure cultural traditions. +Some apparently quite mixed Mediterraneans got off to the first start +on the second act and brought it to its first two climaxes as well. +Peoples of quite different physical type achieved the first climaxes in +China and in the New World. + +In our British example of how the late prehistory of Europe worked, we +listed a continuous series of invasions and reverberations. After +each of these came fusion. Even though the Channel protected Britain +from some of the extreme complications of the mixture and fusion of +continental Europe, you can see how silly it would be to refer to a +pure British race or a pure British culture. We speak of the United +States as a melting pot. But this is nothing new. Actually, Britain +and all the rest of the world have been melting pots at one time or +another. + +By the time the written records of Mesopotamia and Egypt begin to turn +up in number, the climaxes there are well under way. To understand the +beginnings of the climaxes, and the real beginnings of the second act +itself, we are thrown back on prehistoric archeology. And this is as +true for China, India, Middle America, and the Andes, as it is for the +Near East. + +There are lessons to be learned from all of mans past, not simply +lessons of how to fight battles or win peace conferences, but of how +human society evolves from one stage to another. Many of these lessons +can only be looked for in the prehistoric past. So far, we have only +made a beginning. There is much still to do, and many gaps in the story +are yet to be filled. The prehistorians job is to find the evidence, +to fill the gaps, and to discover the lessons men have learned in the +past. As I see it, this is not only an exciting but a very practical +goal for which to strive. + + + + +List of Books + + +BOOKS OF GENERAL INTEREST + +(Chosen from a variety of the increasingly useful list of cheap +paperbound books.) + + Childe, V. Gordon + _What Happened in History._ 1954. Penguin. + _Man Makes Himself._ 1955. Mentor. + _The Prehistory of European Society._ 1958. Penguin. + + Dunn, L. C., and Dobzhansky, Th. + _Heredity, Race, and Society._ 1952. Mentor. + + Frankfort, Henri, Frankfort, H. A., Jacobsen, Thorkild, and Wilson, + John A. + _Before Philosophy._ 1954. Penguin. + + Simpson, George G. + _The Meaning of Evolution._ 1955. Mentor. + + Wheeler, Sir Mortimer + _Archaeology from the Earth._ 1956. Penguin. + + +GEOCHRONOLOGY AND THE ICE AGE + +(Two general books. Some Pleistocene geologists disagree with Zeuners +interpretation of the dating evidence, but their points of view appear +in professional journals, in articles too cumbersome to list here.) + + Flint, R. F. + _Glacial Geology and the Pleistocene Epoch._ 1947. John Wiley + and Sons. + + Zeuner, F. E. + _Dating the Past._ 1952 (3rd ed.). Methuen and Co. + + +FOSSIL MEN AND RACE + +(The points of view of physical anthropologists and human +paleontologists are changing very quickly. Two of the different points +of view are listed here.) + + Clark, W. E. Le Gros + _History of the Primates._ 1956 (5th ed.). British Museum + (Natural History). (Also in Phoenix edition, 1957.) + + Howells, W. W. + _Mankind So Far._ 1944. Doubleday, Doran. + + +GENERAL ANTHROPOLOGY + +(These are standard texts not absolutely up to date in every detail, or +interpretative essays concerned with cultural change through time as +well as in space.) + + Kroeber, A. L. + _Anthropology._ 1948. Harcourt, Brace. + + Linton, Ralph + _The Tree of Culture._ 1955. Alfred A. Knopf, Inc. + + Redfield, Robert + _The Primitive World and Its Transformations._ 1953. Cornell + University Press. + + Steward, Julian H. + _Theory of Culture Change._ 1955. University of Illinois Press. + + White, Leslie + _The Science of Culture._ 1949. Farrar, Strauss. + + +GENERAL PREHISTORY + +(A sampling of the more useful and current standard works in English.) + + Childe, V. Gordon + _The Dawn of European Civilization._ 1957. Kegan Paul, Trench, + Trubner. + _Prehistoric Migrations in Europe._ 1950. Instituttet for + Sammenlignende Kulturforskning. + + Clark, Grahame + _Archaeology and Society._ 1957. Harvard University Press. + + Clark, J. G. D. + _Prehistoric Europe: The Economic Basis._ 1952. Methuen and Co. + + Garrod, D. A. E. + _Environment, Tools, and Man._ 1946. Cambridge University + Press. + + Movius, Hallam L., Jr. + Old World Prehistory: Paleolithic in _Anthropology Today_. + Kroeber, A. L., ed. 1953. University of Chicago Press. + + Oakley, Kenneth P. + _Man the Tool-Maker._ 1956. British Museum (Natural History). + (Also in Phoenix edition, 1957.) + + Piggott, Stuart + _British Prehistory._ 1949. Oxford University Press. + + Pittioni, Richard + _Die Urgeschichtlichen Grundlagen der Europischen Kultur._ + 1949. Deuticke. (A single book which does attempt to cover the + whole range of European prehistory to ca. 1 A.D.) + + +THE NEAR EAST + + Adams, Robert M. + Developmental Stages in Ancient Mesopotamia, _in_ Steward, + Julian, _et al_, _Irrigation Civilizations: A Comparative + Study_. 1955. Pan American Union. + + Braidwood, Robert J. + _The Near East and the Foundations for Civilization._ 1952. + University of Oregon. + + Childe, V. Gordon + _New Light on the Most Ancient East._ 1952. Oriental Dept., + Routledge and Kegan Paul. + + Frankfort, Henri + _The Birth of Civilization in the Near East._ 1951. University + of Indiana Press. (Also in Anchor edition, 1956.) + + Pallis, Svend A. + _The Antiquity of Iraq._ 1956. Munksgaard. + + Wilson, John A. + _The Burden of Egypt._ 1951. University of Chicago Press. (Also + in Phoenix edition, called _The Culture of Ancient Egypt_, + 1956.) + + +HOW DIGGING IS DONE + + Braidwood, Linda + _Digging beyond the Tigris._ 1953. Schuman, New York. + + Wheeler, Sir Mortimer + _Archaeology from the Earth._ 1954. Oxford, London. + + + + +Index + + + Abbevillian, 48; + core-biface tool, 44, 48 + + Acheulean, 48, 60 + + Acheuleo-Levalloisian, 63 + + Acheuleo-Mousterian, 63 + + Adams, R. M., 106 + + Adzes, 45 + + Africa, east, 67, 89; + north, 70, 89; + south, 22, 25, 34, 40, 67 + + Agriculture, incipient, in England, 140; + in Near East, 123 + + Ain Hanech, 48 + + Amber, taken from Baltic to Greece, 167 + + American Indians, 90, 142 + + Anatolia, used as route to Europe, 138 + + Animals, in caves, 54, 64; + in cave art, 85 + + Antevs, Ernst, 19 + + Anyathian, 47 + + Archeological interpretation, 8 + + Archeology, defined, 8 + + Architecture, at Jarmo, 128; + at Jericho, 133 + + Arrow, points, 94; + shaft straightener, 83 + + Art, in caves, 84; + East Spanish, 85; + figurines, 84; + Franco-Cantabrian, 84, 85; + movable (engravings, modeling, scratchings), 83; + painting, 83; + sculpture, 83 + + Asia, western, 67 + + Assemblage, defined, 13, 14; + European, 94; + Jarmo, 129; + Maglemosian, 94; + Natufian, 113 + + Aterian, industry, 67; + point, 89 + + Australopithecinae, 24 + + Australopithecine, 25, 26 + + Awls, 77 + + Axes, 62, 94 + + Ax-heads, 15 + + Azilian, 97 + + Aztecs, 145 + + + Baghouz, 152 + + Bakun, 134 + + Baltic sea, 93 + + Banana, 107 + + Barley, wild, 108 + + Barrow, 141 + + Battle-axe folk, 164; + assemblage, 164 + + Beads, 80; + bone, 114 + + Beaker folk, 164; + assemblage, 164-165 + + Bear, in cave art, 85; + cult, 68 + + Belgium, 94 + + Belt cave, 126 + + Bering Strait, used as route to New World, 98 + + Bison, in cave art, 85 + + Blade, awl, 77; + backed, 75; + blade-core, 71; + end-scraper, 77; + stone, defined, 71; + strangulated (notched), 76; + tanged point, 76; + tools, 71, 75-80, 90; + tool tradition, 70 + + Boar, wild, in cave art, 85 + + Bogs, source of archeological materials, 94 + + Bolas, 54 + + Bordes, Franois, 62 + + Borer, 77 + + Boskop skull, 34 + + Boyd, William C., 35 + + Bracelets, 118 + + Brain, development of, 24 + + Breadfruit, 107 + + Breasted, James H., 107 + + Brick, at Jericho, 133 + + Britain, 94; + late prehistory, 163-175; + invaders, 173 + + Broch, 172 + + Buffalo, in China, 54; + killed by stampede, 86 + + Burials, 66, 86; + in henges, 164; + in urns, 168 + + Burins, 75 + + Burma, 90 + + Byblos, 134 + + + Camel, 54 + + Cannibalism, 55 + + Cattle, wild, 85, 112; + in cave art, 85; + domesticated, 15; + at Skara Brae, 142 + + Caucasoids, 34 + + Cave men, 29 + + Caves, 62; + art in, 84 + + Celts, 170 + + Chariot, 160 + + Chicken, domestication of, 107 + + Chiefs, in food-gathering groups, 68 + + Childe, V. Gordon, 8 + + China, 136 + + Choukoutien, 28, 35 + + Choukoutienian, 47 + + Civilization, beginnings, 144, 149, 157; + meaning of, 144 + + Clactonian, 45, 47 + + Clay, used in modeling, 128; + baked, used for tools, 153 + + Club-heads, 82, 94 + + Colonization, in America, 142; + in Europe, 142 + + Combe Capelle, 30 + + Combe Capelle-Brnn group, 34 + + Commont, Victor, 51 + + Coon, Carlton S., 73 + + Copper, 134 + + Corn, in America, 145 + + Corrals for cattle, 140 + + Cradle of mankind, 136 + + Cremation, 167 + + Crete, 162 + + Cro-Magnon, 30, 34 + + Cultivation, incipient, 105, 109, 111 + + Culture, change, 99; + characteristics, defined, 38, 49; + prehistoric, 39 + + + Danube Valley, used as route from Asia, 138 + + Dates, 153 + + Deer, 54, 96 + + Dog, domesticated, 96 + + Domestication, of animals, 100, 105, 107; + of plants, 100 + + Dragon teeth fossils in China, 28 + + Drill, 77 + + Dubois, Eugene, 26 + + + Early Dynastic Period, Mesopotamia, 147 + + East Spanish art, 72, 85 + + Egypt, 70, 126 + + Ehringsdorf, 31 + + Elephant, 54 + + Emiliani, Cesare, 18 + + Emiran flake point, 73 + + England, 163-168; + prehistoric, 19, 40; + farmers in, 140 + + Eoanthropus dawsoni, 29 + + Eoliths, 41 + + Erich, 152 + + Eridu, 152 + + Euphrates River, floods in, 148 + + Europe, cave dwellings, 58; + at end of Ice Age, 93; + early farmers, 140; + glaciers in, 40; + huts in, 86; + routes into, 137-140; + spread of food-production to, 136 + + + Far East, 69, 90 + + Farmers, 103 + + Fauresmith industry, 67 + + Fayum, 135; + radiocarbon date, 146 + + Fertile Crescent, 107, 146 + + Figurines, Venus, 84; + at Jarmo, 128; + at Ubaid, 153 + + Fire, used by Peking man, 54 + + First Dynasty, Egypt, 147 + + Fish-hooks, 80, 94 + + Fishing, 80; + by food-producers, 122 + + Fish-lines, 80 + + Fish spears, 94 + + Flint industry, 127 + + Fontchevade, 32, 56, 58 + + Food-collecting, 104, 121; + end of, 104 + + Food-gatherers, 53, 176 + + Food-gathering, 99, 104; + in Old World, 104; + stages of, 104 + + Food-producers, 176 + + Food-producing economy, 122; + in America, 145; + in Asia, 105 + + Food-producing revolution, 99, 105; + causes of, 101; + preconditions for, 100 + + Food-production, beginnings of, 99; + carried to Europe, 110 + + Food-vessel folk, 164 + + Forest folk, 97, 98, 104, 110 + + Fox, Sir Cyril, 174 + + France, caves in, 56 + + + Galley Hill (fossil type), 29 + + Garrod, D. A., 73 + + Gazelle, 114 + + Germany, 94 + + Ghassul, 156 + + Glaciers, 18, 30; + destruction by, 40 + + Goat, wild, 108; + domesticated, 128 + + Grain, first planted, 20 + + Graves, passage, 141; + gallery, 141 + + Greece, civilization in, 163; + as route to western Europe, 138; + towns in, 162 + + Grimaldi skeletons, 34 + + + Hackberry seeds used as food, 55 + + Halaf, 151; + assemblage, 151 + + Hallstatt, tradition, 169 + + Hand, development of, 24, 25 + + Hand adzes, 46 + + Hand axes, 44 + + Harpoons, antler, 83, 94; + bone, 82, 94 + + Hassuna, 131; + assemblage, 131, 132 + + Heidelberg, fossil type, 28 + + Hill-forts, in England, 171; + in Scotland, 172 + + Hilly flanks of Near East, 107, 108, 125, 131, 146, 147 + + History, beginning of, 7, 17 + + Hoes, 112 + + Holland, 164 + + Homo sapiens, 32 + + Hooton, E. A., 34 + + Horse, 112; + wild, in cave art, 85; + in China, 54 + + Hotu cave, 126 + + Houses, 122; + at Jarmo, 128; + at Halaf, 151 + + Howe, Bruce, 116 + + Howell, F. Clark, 30 + + Hunting, 93 + + + Ice Age, in Asia, 99; + beginning of, 18; + glaciers in, 41; + last glaciation, 93 + + Incas, 145 + + India, 90, 136 + + Industrialization, 178 + + Industry, blade-tool, 88; + defined, 58; + ground stone, 94 + + Internationalism, 162 + + Iran, 107, 147 + + Iraq, 107, 124, 127, 136, 147 + + Iron, introduction of, 170 + + Irrigation, 123, 149, 155 + + Italy, 138 + + + Jacobsen, T. J., 157 + + Jarmo, 109, 126, 128, 130; + assemblage, 129 + + Java, 23, 29 + + Java man, 26, 27, 29 + + Jefferson, Thomas, 11 + + Jericho, 119, 133 + + Judaidah, 134 + + + Kafuan, 48 + + Kanam, 23, 36 + + Karim Shahir, 116-119, 124; + assemblage, 116, 117 + + Keith, Sir Arthur, 33 + + Kelley, Harper, 51 + + Kharga, 126 + + Khartoum, 136 + + Knives, 80 + + Krogman, W. M., 3, 25 + + + Lamps, 85 + + Land bridges in Mediterranean, 19 + + La Tne phase, 170 + + Laurel leaf point, 78, 89 + + Leakey, L. S. B., 40 + + Le Moustier, 57 + + Levalloisian, 47, 61, 62 + + Levalloiso-Mousterian, 47, 63 + + Little Woodbury, 170 + + + Magic, used by hunters, 123 + + Maglemosian, assemblage, 94, 95; + folk, 98 + + Makapan, 40 + + Mammoth, 93; + in cave art, 85 + + Man-apes, 26 + + Mango, 107 + + Mankind, age, 17 + + Maringer, J., 45 + + Markets, 155 + + Marston, A. T., 11 + + Mathiassen, T., 97 + + McCown, T. D., 33 + + Meganthropus, 26, 27, 36 + + Men, defined, 25; + modern, 32 + + Merimde, 135 + + Mersin, 133 + + Metal-workers, 160, 163, 167, 172 + + Micoquian, 48, 60 + + Microliths, 87; + at Jarmo, 130; + lunates, 87; + trapezoids, 87; + triangles, 87 + + Minerals used as coloring matter, 66 + + Mine-shafts, 140 + + Mlefaat, 126, 127 + + Mongoloids, 29, 90 + + Mortars, 114, 118, 127 + + Mounds, how formed, 12 + + Mount Carmel, 11, 33, 52, 59, 64, 69, 113, 114 + + Mousterian man, 64 + + Mousterian tools, 61, 62; + of Acheulean tradition, 62 + + Movius, H. L., 47 + + + Natufian, animals in, 114; + assemblage, 113, 114, 115; + burials, 114; + date of, 113 + + Neanderthal man, 29, 30, 31, 56 + + Near East, beginnings of civilization in, 20, 144; + cave sites, 58; + climate in Ice Age, 99; + Fertile Crescent, 107, 146; + food-production in, 99; + Natufian assemblage in, 113-115; + stone tools, 114 + + Needles, 80 + + Negroid, 34 + + New World, 90 + + Nile River valley, 102, 134; + floods in, 148 + + Nuclear area, 106, 110; + in Near East, 107 + + + Obsidian, used for blade tools, 71; + at Jarmo, 130 + + Ochre, red, with burials, 86 + + Oldowan, 48 + + Old World, 67, 70, 90; + continental phases in, 18 + + Olorgesailie, 40, 51 + + Ostrich, in China, 54 + + Ovens, 128 + + Oxygen isotopes, 18 + + + Paintings in caves, 83 + + Paleoanthropic man, 50 + + Palestine, burials, 56; + cave sites, 52; + types of man, 69 + + Parpallo, 89 + + Patjitanian, 45, 47 + + Pebble tools, 42 + + Peking cave, 54; + animals in, 54 + + Peking man, 27, 28, 29, 54, 58 + + Pendants, 80; + bone, 114 + + Pestle, 114 + + Peterborough, 141; + assemblage, 141 + + Pictographic signs, 158 + + Pig, wild, 108 + + Piltdown man, 29 + + Pins, 80 + + Pithecanthropus, 26, 27, 30, 36 + + Pleistocene, 18, 25 + + Plows developed, 123 + + Points, arrow, 76; + laurel leaf, 78; + shouldered, 78, 79; + split-based bone, 80, 82; + tanged, 76; + willow leaf, 78 + + Potatoes, in America, 145 + + Pottery, 122, 130, 156; + decorated, 142; + painted, 131, 151, 152; + Susa style, 156; + in tombs, 141 + + Prehistory, defined, 7; + range of, 18 + + Pre-neanderthaloids, 30, 31, 37 + + Pre-Solutrean point, 89 + + Pre-Stellenbosch, 48 + + Proto-Literate assemblage, 157-160 + + + Race, 35; + biological, 36; + pure, 16 + + Radioactivity, 9, 10 + + Radioactive carbon dates, 18, 92, 120, 130, 135, 156 + + Redfield, Robert, 38, 49 + + Reed, C. A., 128 + + Reindeer, 94 + + Rhinoceros, 93; + in cave art, 85 + + Rhodesian man, 32 + + Riss glaciation, 58 + + Rock-shelters, 58; + art in, 85 + + + Saccopastore, 31 + + Sahara Desert, 34, 102 + + Samarra, 152; + pottery, 131, 152 + + Sangoan industry, 67 + + Sauer, Carl, 136 + + Sbaikian point, 89 + + Schliemann, H., 11, 12 + + Scotland, 171 + + Scraper, flake, 79; + end-scraper on blade, 77, 78; + keel-shaped, 79, 80, 81 + + Sculpture in caves, 83 + + Sebilian III, 126 + + Shaheinab, 135 + + Sheep, wild, 108; + at Skara Brae, 142; + in China, 54 + + Shellfish, 142 + + Ship, Ubaidian, 153 + + Sialk, 126, 134; + assemblage, 134 + + Siberia, 88; + pathway to New World, 98 + + Sickle, 112, 153; + blade, 113, 130 + + Silo, 122 + + Sinanthropus, 27, 30, 35 + + Skara Brae, 142 + + Snails used as food, 128 + + Soan, 47 + + Solecki, R., 116 + + Solo (fossil type), 29, 32 + + Solutrean industry, 77 + + Spear, shaft, 78; + thrower, 82, 83 + + Speech, development of organs of, 25 + + Squash, in America, 145 + + Steinheim fossil skull, 28 + + Stillbay industry, 67 + + Stonehenge, 166 + + Stratification, in caves, 12, 57; + in sites, 12 + + Swanscombe (fossil type), 11, 28 + + Syria, 107 + + + Tabun, 60, 71 + + Tardenoisian, 97 + + Taro, 107 + + Tasa, 135 + + Tayacian, 47, 59 + + Teeth, pierced, in beads and pendants, 114 + + Temples, 123, 155 + + Tepe Gawra, 156 + + Ternafine, 29 + + Teshik Tash, 69 + + Textiles, 122 + + Thong-stropper, 80 + + Tigris River, floods in, 148 + + Toggle, 80 + + Tomatoes, in America, 145 + + Tombs, megalithic, 141 + + Tool-making, 42, 49 + + Tool-preparation traditions, 65 + + Tools, 62; + antler, 80; + blade, 70, 71, 75; + bone, 66; + chopper, 47; + core-biface, 43, 48, 60, 61; + flake, 44, 47, 51, 60, 64; + flint, 80, 127; + ground stone, 68, 127; + handles, 94; + pebble, 42, 43, 48, 53; + use of, 24 + + Touf (mud wall), 128 + + Toynbee, A. J., 101 + + Trade, 130, 155, 162 + + Traders, 167 + + Traditions, 15; + blade tool, 70; + definition of, 51; + interpretation of, 49; + tool-making, 42, 48; + chopper-tool, 47; + chopper-chopping tool, 45; + core-biface, 43, 48; + flake, 44, 47; + pebble tool, 42, 48 + + Tool-making, prehistory of, 42 + + Turkey, 107, 108 + + + Ubaid, 153; + assemblage, 153-155 + + Urnfields, 168, 169 + + + Village-farming community era, 105, 119 + + + Wad B, 72 + + Wadjak, 34 + + Warka phase, 156; + assemblage, 156 + + Washburn, Sherwood L., 36 + + Water buffalo, domestication of, 107 + + Weidenreich, F., 29, 34 + + Wessex, 166, 167 + + Wheat, wild, 108; + partially domesticated, 127 + + Willow leaf point, 78 + + Windmill Hill, 138; + assemblage, 138, 140 + + Witch doctors, 68 + + Wool, 112; + in garments, 167 + + Writing, 158; + cuneiform, 158 + + Wrm I glaciation, 58 + + + Zebu cattle, domestication of, 107 + + Zeuner, F. 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Thus, we do not +necessarily keep eBooks in compliance with any particular paper +edition. + +Most people start at our Web site which has the main PG search +facility: www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. diff --git a/ciphers/affine_cipher.py b/ciphers/affine_cipher.py new file mode 100644 index 000000000..b74ec6f4e --- /dev/null +++ b/ciphers/affine_cipher.py @@ -0,0 +1,76 @@ +import sys, random, cryptomath_module as cryptoMath + +SYMBOLS = """ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~""" + +def main(): + message = input('Enter message: ') + key = int(input('Enter key [2000 - 9000]: ')) + mode = input('Encrypt/Decrypt [E/D]: ') + + if mode.lower().startswith('e'): + mode = 'encrypt' + translated = encryptMessage(key, message) + elif mode.lower().startswith('d'): + mode = 'decrypt' + translated = decryptMessage(key, message) + print('\n%sed text: \n%s' % (mode.title(), translated)) + +def getKeyParts(key): + keyA = key // len(SYMBOLS) + keyB = key % len(SYMBOLS) + return (keyA, keyB) + +def checkKeys(keyA, keyB, mode): + if keyA == 1 and mode == 'encrypt': + sys.exit('The affine cipher becomes weak when key A is set to 1. Choose different key') + if keyB == 0 and mode == 'encrypt': + sys.exit('The affine cipher becomes weak when key A is set to 1. Choose different key') + if keyA < 0 or keyB < 0 or keyB > len(SYMBOLS) - 1: + sys.exit('Key A must be greater than 0 and key B must be between 0 and %s.' % (len(SYMBOLS) - 1)) + if cryptoMath.gcd(keyA, len(SYMBOLS)) != 1: + sys.exit('Key A %s and the symbol set size %s are not relatively prime. Choose a different key.' % (keyA, len(SYMBOLS))) + +def encryptMessage(key, message): + ''' + >>> encryptMessage(4545, 'The affine cipher is a type of monoalphabetic substitution cipher.') + 'VL}p MM{I}p~{HL}Gp{vp pFsH}pxMpyxIx JHL O}F{~pvuOvF{FuF{xIp~{HL}Gi' + ''' + keyA, keyB = getKeyParts(key) + checkKeys(keyA, keyB, 'encrypt') + cipherText = '' + for symbol in message: + if symbol in SYMBOLS: + symIndex = SYMBOLS.find(symbol) + cipherText += SYMBOLS[(symIndex * keyA + keyB) % len(SYMBOLS)] + else: + cipherText += symbol + return cipherText + +def decryptMessage(key, message): + ''' + >>> decryptMessage(4545, 'VL}p MM{I}p~{HL}Gp{vp pFsH}pxMpyxIx JHL O}F{~pvuOvF{FuF{xIp~{HL}Gi') + 'The affine cipher is a type of monoalphabetic substitution cipher.' + ''' + keyA, keyB = getKeyParts(key) + checkKeys(keyA, keyB, 'decrypt') + plainText = '' + modInverseOfkeyA = cryptoMath.findModInverse(keyA, len(SYMBOLS)) + for symbol in message: + if symbol in SYMBOLS: + symIndex = SYMBOLS.find(symbol) + plainText += SYMBOLS[(symIndex - keyB) * modInverseOfkeyA % len(SYMBOLS)] + else: + plainText += symbol + return plainText + +def getRandomKey(): + while True: + keyA = random.randint(2, len(SYMBOLS)) + keyB = random.randint(2, len(SYMBOLS)) + if cryptoMath.gcd(keyA, len(SYMBOLS)) == 1: + return keyA * len(SYMBOLS) + keyB + +if __name__ == '__main__': + import doctest + doctest.testmod() + main() diff --git a/ciphers/brute-force_caesar_cipher.py b/ciphers/brute-force_caesar_cipher.py new file mode 100644 index 000000000..3e6e975c8 --- /dev/null +++ b/ciphers/brute-force_caesar_cipher.py @@ -0,0 +1,53 @@ +def decrypt(message): + """ + >>> decrypt('TMDETUX PMDVU') + Decryption using Key #0: TMDETUX PMDVU + Decryption using Key #1: SLCDSTW OLCUT + Decryption using Key #2: RKBCRSV NKBTS + Decryption using Key #3: QJABQRU MJASR + Decryption using Key #4: PIZAPQT LIZRQ + Decryption using Key #5: OHYZOPS KHYQP + Decryption using Key #6: NGXYNOR JGXPO + Decryption using Key #7: MFWXMNQ IFWON + Decryption using Key #8: LEVWLMP HEVNM + Decryption using Key #9: KDUVKLO GDUML + Decryption using Key #10: JCTUJKN FCTLK + Decryption using Key #11: IBSTIJM EBSKJ + Decryption using Key #12: HARSHIL DARJI + Decryption using Key #13: GZQRGHK CZQIH + Decryption using Key #14: FYPQFGJ BYPHG + Decryption using Key #15: EXOPEFI AXOGF + Decryption using Key #16: DWNODEH ZWNFE + Decryption using Key #17: CVMNCDG YVMED + Decryption using Key #18: BULMBCF XULDC + Decryption using Key #19: ATKLABE WTKCB + Decryption using Key #20: ZSJKZAD VSJBA + Decryption using Key #21: YRIJYZC URIAZ + Decryption using Key #22: XQHIXYB TQHZY + Decryption using Key #23: WPGHWXA SPGYX + Decryption using Key #24: VOFGVWZ ROFXW + Decryption using Key #25: UNEFUVY QNEWV + """ + LETTERS = "ABCDEFGHIJKLMNOPQRSTUVWXYZ" + for key in range(len(LETTERS)): + translated = "" + for symbol in message: + if symbol in LETTERS: + num = LETTERS.find(symbol) + num = num - key + if num < 0: + num = num + len(LETTERS) + translated = translated + LETTERS[num] + else: + translated = translated + symbol + print("Decryption using Key #%s: %s" % (key, translated)) + +def main(): + message = input("Encrypted message: ") + message = message.upper() + decrypt(message) + +if __name__ == '__main__': + import doctest + doctest.testmod() + main() diff --git a/ciphers/caesar_cipher.py b/ciphers/caesar_cipher.py new file mode 100644 index 000000000..b590f81f9 --- /dev/null +++ b/ciphers/caesar_cipher.py @@ -0,0 +1,44 @@ +# The Caesar Cipher Algorithm + +def main(): + message = input("Enter message: ") + key = int(input("Key [1-26]: ")) + mode = input("Encrypt or Decrypt [e/d]: ") + + if mode.lower().startswith('e'): + mode = "encrypt" + elif mode.lower().startswith('d'): + mode = "decrypt" + + translated = encdec(message, key, mode) + if mode == "encrypt": + print("Encryption:", translated) + elif mode == "decrypt": + print("Decryption:", translated) + +def encdec(message, key, mode): + message = message.upper() + translated = "" + LETTERS = "ABCDEFGHIJKLMNOPQRSTUVWXYZ" + for symbol in message: + if symbol in LETTERS: + num = LETTERS.find(symbol) + if mode == "encrypt": + num = num + key + elif mode == "decrypt": + num = num - key + + if num >= len(LETTERS): + num -= len(LETTERS) + elif num < 0: + num += len(LETTERS) + + translated += LETTERS[num] + else: + translated += symbol + return translated + +if __name__ == '__main__': + import doctest + doctest.testmod() + main() diff --git a/ciphers/cryptomath_module.py b/ciphers/cryptomath_module.py new file mode 100644 index 000000000..3e8e71b11 --- /dev/null +++ b/ciphers/cryptomath_module.py @@ -0,0 +1,14 @@ +def gcd(a, b): + while a != 0: + a, b = b % a, a + return b + +def findModInverse(a, m): + if gcd(a, m) != 1: + return None + u1, u2, u3 = 1, 0, a + v1, v2, v3 = 0, 1, m + while v3 != 0: + q = u3 // v3 + v1, v2, v3, u1, u2, u3 = (u1 - q * v1), (u2 - q * v2), (u3 - q *v3), v1, v2, v3 + return u1 % m diff --git a/ciphers/playfair_cipher.py b/ciphers/playfair_cipher.py new file mode 100644 index 000000000..da547a337 --- /dev/null +++ b/ciphers/playfair_cipher.py @@ -0,0 +1,102 @@ +import string +import itertools + +def chunker(seq, size): + it = iter(seq) + while True: + chunk = tuple(itertools.islice(it, size)) + if not chunk: + return + yield chunk + + + +def prepare_input(dirty): + """ + Prepare the plaintext by uppcasing it + and seperating repeated letters with X's + """ + + dirty = ''.join([c.upper() for c in dirty if c in string.ascii_letters]) + clean = "" + + if len(dirty) < 2: + return dirty + + for i in range(len(dirty)-1): + clean += dirty[i] + + if dirty[i] == dirty[i+1]: + clean += 'X' + + clean += dirty[-1] + + if len(clean) & 1: + clean += 'X' + + return clean + +def generate_table(key): + + # I and J are used interchangably to allow + # us to use a 5x5 table (25 letters) + alphabet = "ABCDEFGHIKLMNOPQRSTUVWXYZ" + # we're using a list instead of a '2d' array because it makes the math + # for setting up the table and doing the actual encoding/decoding simpler + table = [] + + # copy key chars into the table if they are in `alphabet` ignoring duplicates + for char in key.upper(): + if char not in table and char in alphabet: + table.append(char) + + # fill the rest of the table in with the remaining alphabet chars + for char in alphabet: + if char not in table: + table.append(char) + + return table + +def encode(plaintext, key): + table = generate_table(key) + plaintext = prepare_input(plaintext) + ciphertext = "" + + # https://en.wikipedia.org/wiki/Playfair_cipher#Description + for char1, char2 in chunker(plaintext, 2): + row1, col1 = divmod(table.index(char1), 5) + row2, col2 = divmod(table.index(char2), 5) + + if row1 == row2: + ciphertext += table[row1*5+(col1+1)%5] + ciphertext += table[row2*5+(col2+1)%5] + elif col1 == col2: + ciphertext += table[((row1+1)%5)*5+col1] + ciphertext += table[((row2+1)%5)*5+col2] + else: # rectangle + ciphertext += table[row1*5+col2] + ciphertext += table[row2*5+col1] + + return ciphertext + + +def decode(ciphertext, key): + table = generate_table(key) + plaintext = "" + + # https://en.wikipedia.org/wiki/Playfair_cipher#Description + for char1, char2 in chunk(ciphertext, 2): + row1, col1 = divmod(table.index(char1), 5) + row2, col2 = divmod(table.index(char2), 5) + + if row1 == row2: + plaintext += table[row1*5+(col1-1)%5] + plaintext += table[row2*5+(col2-1)%5] + elif col1 == col2: + plaintext += table[((row1-1)%5)*5+col1] + plaintext += table[((row2-1)%5)*5+col2] + else: # rectangle + plaintext += table[row1*5+col2] + plaintext += table[row2*5+col1] + + return plaintext diff --git a/ciphers/rabin_miller.py b/ciphers/rabin_miller.py new file mode 100644 index 000000000..d6e5cbe8f --- /dev/null +++ b/ciphers/rabin_miller.py @@ -0,0 +1,63 @@ +# Primality Testing with the Rabin-Miller Algorithm + +import random + +def rabinMiller(num): + s = num - 1 + t = 0 + + while s % 2 == 0: + s = s // 2 + t += 1 + + for trials in range(5): + a = random.randrange(2, num - 1) + v = pow(a, s, num) + if v != 1: + i = 0 + while v != (num - 1): + if i == t - 1: + return False + else: + i = i + 1 + v = (v ** 2) % num + return True + +def isPrime(num): + if (num < 2): + return False + + lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, + 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, + 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, + 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, + 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, + 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, + 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, + 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, + 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, + 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, + 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, + 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, + 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, + 971, 977, 983, 991, 997] + + if num in lowPrimes: + return True + + for prime in lowPrimes: + if (num % prime) == 0: + return False + + return rabinMiller(num) + +def generateLargePrime(keysize = 1024): + while True: + num = random.randrange(2 ** (keysize - 1), 2 ** (keysize)) + if isPrime(num): + return num + +if __name__ == '__main__': + num = generateLargePrime() + print('Prime number:', num) + print('isPrime:', isPrime(num)) diff --git a/ciphers/rsa_cipher.py b/ciphers/rsa_cipher.py new file mode 100644 index 000000000..7e2dc5fd1 --- /dev/null +++ b/ciphers/rsa_cipher.py @@ -0,0 +1,124 @@ +import sys, rsa_key_generator as rkg, os + +DEFAULT_BLOCK_SIZE = 128 +BYTE_SIZE = 256 + +def main(): + filename = 'encrypted_file.txt' + response = input('Encrypte\Decrypt [e\d]: ') + + if response.lower().startswith('e'): + mode = 'encrypt' + elif response.lower().startswith('d'): + mode = 'decrypt' + + if mode == 'encrypt': + if not os.path.exists('rsa_pubkey.txt'): + rkg.makeKeyFiles('rsa', 1024) + + message = input('\nEnter message: ') + pubKeyFilename = 'rsa_pubkey.txt' + print('Encrypting and writing to %s...' % (filename)) + encryptedText = encryptAndWriteToFile(filename, pubKeyFilename, message) + + print('\nEncrypted text:') + print(encryptedText) + + elif mode == 'decrypt': + privKeyFilename = 'rsa_privkey.txt' + print('Reading from %s and decrypting...' % (filename)) + decryptedText = readFromFileAndDecrypt(filename, privKeyFilename) + print('writing decryption to rsa_decryption.txt...') + with open('rsa_decryption.txt', 'w') as dec: + dec.write(decryptedText) + + print('\nDecryption:') + print(decryptedText) + + +def getBlocksFromText(message, blockSize=DEFAULT_BLOCK_SIZE): + messageBytes = message.encode('ascii') + + blockInts = [] + for blockStart in range(0, len(messageBytes), blockSize): + blockInt = 0 + for i in range(blockStart, min(blockStart + blockSize, len(messageBytes))): + blockInt += messageBytes[i] * (BYTE_SIZE ** (i % blockSize)) + blockInts.append(blockInt) + return blockInts + + +def getTextFromBlocks(blockInts, messageLength, blockSize=DEFAULT_BLOCK_SIZE): + message = [] + for blockInt in blockInts: + blockMessage = [] + for i in range(blockSize - 1, -1, -1): + if len(message) + i < messageLength: + asciiNumber = blockInt // (BYTE_SIZE ** i) + blockInt = blockInt % (BYTE_SIZE ** i) + blockMessage.insert(0, chr(asciiNumber)) + message.extend(blockMessage) + return ''.join(message) + + +def encryptMessage(message, key, blockSize=DEFAULT_BLOCK_SIZE): + encryptedBlocks = [] + n, e = key + + for block in getBlocksFromText(message, blockSize): + encryptedBlocks.append(pow(block, e, n)) + return encryptedBlocks + + +def decryptMessage(encryptedBlocks, messageLength, key, blockSize=DEFAULT_BLOCK_SIZE): + decryptedBlocks = [] + n, d = key + for block in encryptedBlocks: + decryptedBlocks.append(pow(block, d, n)) + return getTextFromBlocks(decryptedBlocks, messageLength, blockSize) + + +def readKeyFile(keyFilename): + fo = open(keyFilename) + content = fo.read() + fo.close() + keySize, n, EorD = content.split(',') + return (int(keySize), int(n), int(EorD)) + + +def encryptAndWriteToFile(messageFilename, keyFilename, message, blockSize=DEFAULT_BLOCK_SIZE): + keySize, n, e = readKeyFile(keyFilename) + if keySize < blockSize * 8: + sys.exit('ERROR: Block size is %s bits and key size is %s bits. The RSA cipher requires the block size to be equal to or greater than the key size. Either decrease the block size or use different keys.' % (blockSize * 8, keySize)) + + encryptedBlocks = encryptMessage(message, (n, e), blockSize) + + for i in range(len(encryptedBlocks)): + encryptedBlocks[i] = str(encryptedBlocks[i]) + encryptedContent = ','.join(encryptedBlocks) + encryptedContent = '%s_%s_%s' % (len(message), blockSize, encryptedContent) + fo = open(messageFilename, 'w') + fo.write(encryptedContent) + fo.close() + return encryptedContent + + +def readFromFileAndDecrypt(messageFilename, keyFilename): + keySize, n, d = readKeyFile(keyFilename) + fo = open(messageFilename) + content = fo.read() + messageLength, blockSize, encryptedMessage = content.split('_') + messageLength = int(messageLength) + blockSize = int(blockSize) + + if keySize < blockSize * 8: + sys.exit('ERROR: Block size is %s bits and key size is %s bits. The RSA cipher requires the block size to be equal to or greater than the key size. Did you specify the correct key file and encrypted file?' % (blockSize * 8, keySize)) + + encryptedBlocks = [] + for block in encryptedMessage.split(','): + encryptedBlocks.append(int(block)) + + return decryptMessage(encryptedBlocks, messageLength, (n, d), blockSize) + +if __name__ == '__main__': + main() diff --git a/ciphers/rsa_key_generator.py b/ciphers/rsa_key_generator.py new file mode 100644 index 000000000..7cd7163b6 --- /dev/null +++ b/ciphers/rsa_key_generator.py @@ -0,0 +1,45 @@ +import random, sys, os +import rabin_miller as rabinMiller, cryptomath_module as cryptoMath + +def main(): + print('Making key files...') + makeKeyFiles('rsa', 1024) + print('Key files generation successful.') + +def generateKey(keySize): + print('Generating prime p...') + p = rabinMiller.generateLargePrime(keySize) + print('Generating prime q...') + q = rabinMiller.generateLargePrime(keySize) + n = p * q + + print('Generating e that is relatively prime to (p - 1) * (q - 1)...') + while True: + e = random.randrange(2 ** (keySize - 1), 2 ** (keySize)) + if cryptoMath.gcd(e, (p - 1) * (q - 1)) == 1: + break + + print('Calculating d that is mod inverse of e...') + d = cryptoMath.findModInverse(e, (p - 1) * (q - 1)) + + publicKey = (n, e) + privateKey = (n, d) + return (publicKey, privateKey) + +def makeKeyFiles(name, keySize): + if os.path.exists('%s_pubkey.txt' % (name)) or os.path.exists('%s_privkey.txt' % (name)): + print('\nWARNING:') + print('"%s_pubkey.txt" or "%s_privkey.txt" already exists. \nUse a different name or delete these files and re-run this program.' % (name, name)) + sys.exit() + + publicKey, privateKey = generateKey(keySize) + print('\nWriting public key to file %s_pubkey.txt...' % name) + with open('%s_pubkey.txt' % name, 'w') as fo: + fo.write('%s,%s,%s' % (keySize, publicKey[0], publicKey[1])) + + print('Writing private key to file %s_privkey.txt...' % name) + with open('%s_privkey.txt' % name, 'w') as fo: + fo.write('%s,%s,%s' % (keySize, privateKey[0], privateKey[1])) + +if __name__ == '__main__': + main() diff --git a/ciphers/simple_substitution_cipher.py b/ciphers/simple_substitution_cipher.py new file mode 100644 index 000000000..41ac4a6a7 --- /dev/null +++ b/ciphers/simple_substitution_cipher.py @@ -0,0 +1,70 @@ +import sys, random + +LETTERS = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' + +def main(): + message = input('Enter message: ') + key = 'LFWOAYUISVKMNXPBDCRJTQEGHZ' + resp = input('Encrypt/Decrypt [e/d]: ') + + checkValidKey(key) + + if resp.lower().startswith('e'): + mode = 'encrypt' + translated = encryptMessage(key, message) + elif resp.lower().startswith('d'): + mode = 'decrypt' + translated = decryptMessage(key, message) + + print('\n%sion: \n%s' % (mode.title(), translated)) + +def checkValidKey(key): + keyList = list(key) + lettersList = list(LETTERS) + keyList.sort() + lettersList.sort() + + if keyList != lettersList: + sys.exit('Error in the key or symbol set.') + +def encryptMessage(key, message): + """ + >>> encryptMessage('LFWOAYUISVKMNXPBDCRJTQEGHZ', 'Harshil Darji') + 'Ilcrism Olcvs' + """ + return translateMessage(key, message, 'encrypt') + +def decryptMessage(key, message): + """ + >>> decryptMessage('LFWOAYUISVKMNXPBDCRJTQEGHZ', 'Ilcrism Olcvs') + 'Harshil Darji' + """ + return translateMessage(key, message, 'decrypt') + +def translateMessage(key, message, mode): + translated = '' + charsA = LETTERS + charsB = key + + if mode == 'decrypt': + charsA, charsB = charsB, charsA + + for symbol in message: + if symbol.upper() in charsA: + symIndex = charsA.find(symbol.upper()) + if symbol.isupper(): + translated += charsB[symIndex].upper() + else: + translated += charsB[symIndex].lower() + else: + translated += symbol + + return translated + +def getRandomKey(): + key = list(LETTERS) + random.shuffle(key) + return ''.join(key) + +if __name__ == '__main__': + main() diff --git a/ciphers/transposition_cipher.py b/ciphers/transposition_cipher.py new file mode 100644 index 000000000..1c2ed0aa0 --- /dev/null +++ b/ciphers/transposition_cipher.py @@ -0,0 +1,53 @@ +import math + +def main(): + message = input('Enter message: ') + key = int(input('Enter key [2-%s]: ' % (len(message) - 1))) + mode = input('Encryption/Decryption [e/d]: ') + + if mode.lower().startswith('e'): + text = encryptMessage(key, message) + elif mode.lower().startswith('d'): + text = decryptMessage(key, message) + + # Append pipe symbol (vertical bar) to identify spaces at the end. + print('Output:\n%s' %(text + '|')) + +def encryptMessage(key, message): + """ + >>> encryptMessage(6, 'Harshil Darji') + 'Hlia rDsahrij' + """ + cipherText = [''] * key + for col in range(key): + pointer = col + while pointer < len(message): + cipherText[col] += message[pointer] + pointer += key + return ''.join(cipherText) + +def decryptMessage(key, message): + """ + >>> decryptMessage(6, 'Hlia rDsahrij') + 'Harshil Darji' + """ + numCols = math.ceil(len(message) / key) + numRows = key + numShadedBoxes = (numCols * numRows) - len(message) + plainText = [""] * numCols + col = 0; row = 0; + + for symbol in message: + plainText[col] += symbol + col += 1 + + if (col == numCols) or (col == numCols - 1) and (row >= numRows - numShadedBoxes): + col = 0 + row += 1 + + return "".join(plainText) + +if __name__ == '__main__': + import doctest + doctest.testmod() + main() diff --git a/ciphers/transposition_cipher_encrypt-decrypt_file.py b/ciphers/transposition_cipher_encrypt-decrypt_file.py new file mode 100644 index 000000000..f2252de8a --- /dev/null +++ b/ciphers/transposition_cipher_encrypt-decrypt_file.py @@ -0,0 +1,35 @@ +import time, os, sys +import transposition_cipher as transCipher + +def main(): + inputFile = 'Prehistoric Men.txt' + outputFile = 'Output.txt' + key = int(input('Enter key: ')) + mode = input('Encrypt/Decrypt [e/d]: ') + + if not os.path.exists(inputFile): + print('File %s does not exist. Quitting...' % inputFile) + sys.exit() + if os.path.exists(outputFile): + print('Overwrite %s? [y/n]' % outputFile) + response = input('> ') + if not response.lower().startswith('y'): + sys.exit() + + startTime = time.time() + if mode.lower().startswith('e'): + content = open(inputFile).read() + translated = transCipher.encryptMessage(key, content) + elif mode.lower().startswith('d'): + content = open(outputFile).read() + translated =transCipher .decryptMessage(key, content) + + outputObj = open(outputFile, 'w') + outputObj.write(translated) + outputObj.close() + + totalTime = round(time.time() - startTime, 2) + print('Done (', totalTime, 'seconds )') + +if __name__ == '__main__': + main() diff --git a/ciphers/vigenere_cipher.py b/ciphers/vigenere_cipher.py new file mode 100644 index 000000000..95eeb4311 --- /dev/null +++ b/ciphers/vigenere_cipher.py @@ -0,0 +1,60 @@ +LETTERS = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' + +def main(): + message = input('Enter message: ') + key = input('Enter key [alphanumeric]: ') + mode = input('Encrypt/Decrypt [e/d]: ') + + if mode.lower().startswith('e'): + mode = 'encrypt' + translated = encryptMessage(key, message) + elif mode.lower().startswith('d'): + mode = 'decrypt' + translated = decryptMessage(key, message) + + print('\n%sed message:' % mode.title()) + print(translated) + +def encryptMessage(key, message): + ''' + >>> encryptMessage('HDarji', 'This is Harshil Darji from Dharmaj.') + 'Akij ra Odrjqqs Gaisq muod Mphumrs.' + ''' + return translateMessage(key, message, 'encrypt') + +def decryptMessage(key, message): + ''' + >>> decryptMessage('HDarji', 'Akij ra Odrjqqs Gaisq muod Mphumrs.') + 'This is Harshil Darji from Dharmaj.' + ''' + return translateMessage(key, message, 'decrypt') + +def translateMessage(key, message, mode): + translated = [] + keyIndex = 0 + key = key.upper() + + for symbol in message: + num = LETTERS.find(symbol.upper()) + if num != -1: + if mode == 'encrypt': + num += LETTERS.find(key[keyIndex]) + elif mode == 'decrypt': + num -= LETTERS.find(key[keyIndex]) + + num %= len(LETTERS) + + if symbol.isupper(): + translated.append(LETTERS[num]) + elif symbol.islower(): + translated.append(LETTERS[num].lower()) + + keyIndex += 1 + if keyIndex == len(key): + keyIndex = 0 + else: + translated.append(symbol) + return ''.join(translated) + +if __name__ == '__main__': + main() diff --git a/data_structures/AVL/AVL.py b/data_structures/AVL/AVL.py new file mode 100644 index 000000000..9717f1b6e --- /dev/null +++ b/data_structures/AVL/AVL.py @@ -0,0 +1,180 @@ +''' +A AVL tree +''' + + +class Node: + + def __init__(self, label): + self.label = label + self._parent = None + self._left = None + self._right = None + self.height = 0 + + @property + def right(self): + return self._right + + @right.setter + def right(self, node): + if node is not None: + node._parent = self + self._right = node + + @property + def left(self): + return self._left + + @left.setter + def left(self, node): + if node is not None: + node._parent = self + self._left = node + + @property + def parent(self): + return self._parent + + @parent.setter + def parent(self, node): + if node is not None: + self._parent = node + self.height = self.parent.height + 1 + else: + self.height = 0 + + +class AVL: + + def __init__(self): + self.root = None + self.size = 0 + + def insert(self, value): + node = Node(value) + + if self.root is None: + self.root = node + self.root.height = 0 + self.size = 1 + else: + # Same as Binary Tree + dad_node = None + curr_node = self.root + + while True: + if curr_node is not None: + + dad_node = curr_node + + if node.label < curr_node.label: + curr_node = curr_node.left + else: + curr_node = curr_node.right + else: + node.height = dad_node.height + dad_node.height += 1 + if node.label < dad_node.label: + dad_node.left = node + else: + dad_node.right = node + self.rebalance(node) + self.size += 1 + break + + def rebalance(self, node): + n = node + + while n is not None: + height_right = n.height + height_left = n.height + + if n.right is not None: + height_right = n.right.height + + if n.left is not None: + height_left = n.left.height + + if abs(height_left - height_right) > 1: + if height_left > height_right: + left_child = n.left + if left_child is not None: + h_right = (right_child.right.height + if (right_child.right is not None) else 0) + h_left = (right_child.left.height + if (right_child.left is not None) else 0) + if (h_left > h_right): + self.rotate_left(n) + break + else: + self.double_rotate_right(n) + break + else: + right_child = n.right + if right_child is not None: + h_right = (right_child.right.height + if (right_child.right is not None) else 0) + h_left = (right_child.left.height + if (right_child.left is not None) else 0) + if (h_left > h_right): + self.double_rotate_left(n) + break + else: + self.rotate_right(n) + break + n = n.parent + + def rotate_left(self, node): + aux = node.parent.label + node.parent.label = node.label + node.parent.right = Node(aux) + node.parent.right.height = node.parent.height + 1 + node.parent.left = node.right + + + def rotate_right(self, node): + aux = node.parent.label + node.parent.label = node.label + node.parent.left = Node(aux) + node.parent.left.height = node.parent.height + 1 + node.parent.right = node.right + + def double_rotate_left(self, node): + self.rotate_right(node.getRight().getRight()) + self.rotate_left(node) + + def double_rotate_right(self, node): + self.rotate_left(node.getLeft().getLeft()) + self.rotate_right(node) + + def empty(self): + if self.root is None: + return True + return False + + def preShow(self, curr_node): + if curr_node is not None: + self.preShow(curr_node.left) + print(curr_node.label, end=" ") + self.preShow(curr_node.right) + + def preorder(self, curr_node): + if curr_node is not None: + self.preShow(curr_node.left) + self.preShow(curr_node.right) + print(curr_node.label, end=" ") + + def getRoot(self): + return self.root + +t = AVL() +t.insert(1) +t.insert(2) +t.insert(3) +# t.preShow(t.root) +# print("\n") +# t.insert(4) +# t.insert(5) +# t.preShow(t.root) +# t.preorden(t.root) diff --git a/data_structures/Arrays b/data_structures/Arrays new file mode 100644 index 000000000..03eaefac1 --- /dev/null +++ b/data_structures/Arrays @@ -0,0 +1 @@ +Arrays implimentation using python programming. diff --git a/data_structures/Binary Tree/FenwickTree.py b/data_structures/Binary Tree/FenwickTree.py new file mode 100644 index 000000000..02e2d6151 --- /dev/null +++ b/data_structures/Binary Tree/FenwickTree.py @@ -0,0 +1,28 @@ +class FenwickTree: + + def __init__(self, SIZE): # create fenwick tree with size SIZE + self.Size = SIZE + self.ft = [0 for i in range (0,SIZE)] + + def update(self, i, val): # update data (adding) in index i in O(lg N) + while (i < self.Size): + self.ft[i] += val + i += i & (-i) + + def query(self, i): # query cumulative data from index 0 to i in O(lg N) + ret = 0 + while (i > 0): + ret += self.ft[i] + i -= i & (-i) + return ret + +if __name__ == '__main__': + f = FenwickTree(100) + f.update(1,20) + f.update(4,4) + print (f.query(1)) + print (f.query(3)) + print (f.query(4)) + f.update(2,-5) + print (f.query(1)) + print (f.query(3)) diff --git a/data_structures/Binary Tree/LazySegmentTree.py b/data_structures/Binary Tree/LazySegmentTree.py new file mode 100644 index 000000000..bbd880a06 --- /dev/null +++ b/data_structures/Binary Tree/LazySegmentTree.py @@ -0,0 +1,90 @@ +import math + +class SegmentTree: + + def __init__(self, N): + self.N = N + self.st = [0 for i in range(0,4*N)] # approximate the overall size of segment tree with array N + self.lazy = [0 for i in range(0,4*N)] # create array to store lazy update + self.flag = [0 for i in range(0,4*N)] # flag for lazy update + + def left(self, idx): + return idx*2 + + def right(self, idx): + return idx*2 + 1 + + def build(self, idx, l, r, A): + if l==r: + self.st[idx] = A[l-1] + else : + mid = (l+r)//2 + self.build(self.left(idx),l,mid, A) + self.build(self.right(idx),mid+1,r, A) + self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)]) + + # update with O(lg N) (Normal segment tree without lazy update will take O(Nlg N) for each update) + def update(self, idx, l, r, a, b, val): # update(1, 1, N, a, b, v) for update val v to [a,b] + if self.flag[idx] == True: + self.st[idx] = self.lazy[idx] + self.flag[idx] = False + if l!=r: + self.lazy[self.left(idx)] = self.lazy[idx] + self.lazy[self.right(idx)] = self.lazy[idx] + self.flag[self.left(idx)] = True + self.flag[self.right(idx)] = True + + if r < a or l > b: + return True + if l >= a and r <= b : + self.st[idx] = val + if l!=r: + self.lazy[self.left(idx)] = val + self.lazy[self.right(idx)] = val + self.flag[self.left(idx)] = True + self.flag[self.right(idx)] = True + return True + mid = (l+r)//2 + self.update(self.left(idx),l,mid,a,b,val) + self.update(self.right(idx),mid+1,r,a,b,val) + self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)]) + return True + + # query with O(lg N) + def query(self, idx, l, r, a, b): #query(1, 1, N, a, b) for query max of [a,b] + if self.flag[idx] == True: + self.st[idx] = self.lazy[idx] + self.flag[idx] = False + if l != r: + self.lazy[self.left(idx)] = self.lazy[idx] + self.lazy[self.right(idx)] = self.lazy[idx] + self.flag[self.left(idx)] = True + self.flag[self.right(idx)] = True + if r < a or l > b: + return -math.inf + if l >= a and r <= b: + return self.st[idx] + mid = (l+r)//2 + q1 = self.query(self.left(idx),l,mid,a,b) + q2 = self.query(self.right(idx),mid+1,r,a,b) + return max(q1,q2) + + def showData(self): + showList = [] + for i in range(1,N+1): + showList += [self.query(1, 1, self.N, i, i)] + print (showList) + + +if __name__ == '__main__': + A = [1,2,-4,7,3,-5,6,11,-20,9,14,15,5,2,-8] + N = 15 + segt = SegmentTree(N) + segt.build(1,1,N,A) + print (segt.query(1,1,N,4,6)) + print (segt.query(1,1,N,7,11)) + print (segt.query(1,1,N,7,12)) + segt.update(1,1,N,1,3,111) + print (segt.query(1,1,N,1,15)) + segt.update(1,1,N,7,8,235) + segt.showData() diff --git a/data_structures/Binary Tree/SegmentTree.py b/data_structures/Binary Tree/SegmentTree.py new file mode 100644 index 000000000..cf47ca7d7 --- /dev/null +++ b/data_structures/Binary Tree/SegmentTree.py @@ -0,0 +1,64 @@ +import math + +class SegmentTree: + + def __init__(self, N): + self.N = N + self.st = [0 for i in range(0,4*N)] # approximate the overall size of segment tree with array N + + def left(self, idx): + return idx*2 + + def right(self, idx): + return idx*2 + 1 + + def build(self, idx, l, r, A): + if l==r: + self.st[idx] = A[l-1] + else : + mid = (l+r)//2 + self.build(self.left(idx),l,mid, A) + self.build(self.right(idx),mid+1,r, A) + self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)]) + + def update(self, idx, l, r, a, b, val): # update(1, 1, N, a, b, v) for update val v to [a,b] + if r < a or l > b: + return True + if l == r : + self.st[idx] = val + return True + mid = (l+r)//2 + self.update(self.left(idx),l,mid,a,b,val) + self.update(self.right(idx),mid+1,r,a,b,val) + self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)]) + return True + + def query(self, idx, l, r, a, b): #query(1, 1, N, a, b) for query max of [a,b] + if r < a or l > b: + return -math.inf + if l >= a and r <= b: + return self.st[idx] + mid = (l+r)//2 + q1 = self.query(self.left(idx),l,mid,a,b) + q2 = self.query(self.right(idx),mid+1,r,a,b) + return max(q1,q2) + + def showData(self): + showList = [] + for i in range(1,N+1): + showList += [self.query(1, 1, self.N, i, i)] + print (showList) + + +if __name__ == '__main__': + A = [1,2,-4,7,3,-5,6,11,-20,9,14,15,5,2,-8] + N = 15 + segt = SegmentTree(N) + segt.build(1,1,N,A) + print (segt.query(1,1,N,4,6)) + print (segt.query(1,1,N,7,11)) + print (segt.query(1,1,N,7,12)) + segt.update(1,1,N,1,3,111) + print (segt.query(1,1,N,1,15)) + segt.update(1,1,N,7,8,235) + segt.showData() diff --git a/data_structures/Binary Tree/binary_seach_tree.py b/data_structures/Binary Tree/binary_seach_tree.py new file mode 100644 index 000000000..9e468f775 --- /dev/null +++ b/data_structures/Binary Tree/binary_seach_tree.py @@ -0,0 +1,103 @@ +''' +A binary search Tree +''' + + +class Node: + + def __init__(self, label): + self.label = label + self.left = None + self.right = None + + def getLabel(self): + return self.label + + def setLabel(self, label): + self.label = label + + def getLeft(self): + return self.left + + def setLeft(self, left): + self.left = left + + def getRight(self): + return self.right + + def setRight(self, right): + self.right = right + + +class BinarySearchTree: + + def __init__(self): + self.root = None + + def insert(self, label): + + # Create a new Node + + node = Node(label) + + if self.empty(): + self.root = node + else: + dad_node = None + curr_node = self.root + + while True: + if curr_node is not None: + + dad_node = curr_node + + if node.getLabel() < curr_node.getLabel(): + curr_node = curr_node.getLeft() + else: + curr_node = curr_node.getRight() + else: + if node.getLabel() < dad_node.getLabel(): + dad_node.setLeft(node) + else: + dad_node.setRight(node) + break + + def empty(self): + if self.root is None: + return True + return False + + def preShow(self, curr_node): + if curr_node is not None: + print(curr_node.getLabel(), end=" ") + + self.preShow(curr_node.getLeft()) + self.preShow(curr_node.getRight()) + + def getRoot(self): + return self.root + + +''' +Example + 8 + / \ + 3 10 + / \ \ + 1 6 14 + / \ / + 4 7 13 +''' + +t = BinarySearchTree() +t.insert(8) +t.insert(3) +t.insert(1) +t.insert(6) +t.insert(4) +t.insert(7) +t.insert(10) +t.insert(14) +t.insert(13) + +t.preShow(t.getRoot()) diff --git a/data_structures/Graph/BreadthFirstSearch.py b/data_structures/Graph/BreadthFirstSearch.py new file mode 100644 index 000000000..16b1b2007 --- /dev/null +++ b/data_structures/Graph/BreadthFirstSearch.py @@ -0,0 +1,61 @@ +# Author: OMKAR PATHAK + +class Graph(): + def __init__(self): + self.vertex = {} + + # for printing the Graph vertexes + def printGraph(self): + for i in self.vertex.keys(): + print(i,' -> ', ' -> '.join([str(j) for j in self.vertex[i]])) + + # for adding the edge beween two vertexes + def addEdge(self, fromVertex, toVertex): + # check if vertex is already present, + if fromVertex in self.vertex.keys(): + self.vertex[fromVertex].append(toVertex) + else: + # else make a new vertex + self.vertex[fromVertex] = [toVertex] + + def BFS(self, startVertex): + # Take a list for stoting already visited vertexes + visited = [False] * len(self.vertex) + + # create a list to store all the vertexes for BFS + queue = [] + + # mark the source node as visited and enqueue it + visited[startVertex] = True + queue.append(startVertex) + + while queue: + startVertex = queue.pop(0) + print(startVertex, end = ' ') + + # mark all adjacent nodes as visited and print them + for i in self.vertex[startVertex]: + if visited[i] == False: + queue.append(i) + visited[i] = True + +if __name__ == '__main__': + g = Graph() + g.addEdge(0, 1) + g.addEdge(0, 2) + g.addEdge(1, 2) + g.addEdge(2, 0) + g.addEdge(2, 3) + g.addEdge(3, 3) + + g.printGraph() + print('BFS:') + g.BFS(2) + + # OUTPUT: + # 0  ->  1 -> 2 + # 1  ->  2 + # 2  ->  0 -> 3 + # 3  ->  3 + # BFS: + # 2 0 3 1 diff --git a/data_structures/Graph/DepthFirstSearch.py b/data_structures/Graph/DepthFirstSearch.py new file mode 100644 index 000000000..94ef3cb86 --- /dev/null +++ b/data_structures/Graph/DepthFirstSearch.py @@ -0,0 +1,61 @@ +# Author: OMKAR PATHAK + +class Graph(): + def __init__(self): + self.vertex = {} + + # for printing the Graph vertexes + def printGraph(self): + print(self.vertex) + for i in self.vertex.keys(): + print(i,' -> ', ' -> '.join([str(j) for j in self.vertex[i]])) + + # for adding the edge beween two vertexes + def addEdge(self, fromVertex, toVertex): + # check if vertex is already present, + if fromVertex in self.vertex.keys(): + self.vertex[fromVertex].append(toVertex) + else: + # else make a new vertex + self.vertex[fromVertex] = [toVertex] + + def DFS(self): + # visited array for storing already visited nodes + visited = [False] * len(self.vertex) + + # call the recursive helper function + for i in range(len(self.vertex)): + if visited[i] == False: + self.DFSRec(i, visited) + + def DFSRec(self, startVertex, visited): + # mark start vertex as visited + visited[startVertex] = True + + print(startVertex, end = ' ') + + # Recur for all the vertexes that are adjacent to this node + for i in self.vertex.keys(): + if visited[i] == False: + self.DFSRec(i, visited) + +if __name__ == '__main__': + g = Graph() + g.addEdge(0, 1) + g.addEdge(0, 2) + g.addEdge(1, 2) + g.addEdge(2, 0) + g.addEdge(2, 3) + g.addEdge(3, 3) + + g.printGraph() + print('DFS:') + g.DFS() + + # OUTPUT: + # 0  ->  1 -> 2 + # 1  ->  2 + # 2  ->  0 -> 3 + # 3  ->  3 + # DFS: + # 0 1 2 3 diff --git a/data_structures/Graph/Graph.py b/data_structures/Graph/Graph.py new file mode 100644 index 000000000..0fa3f5593 --- /dev/null +++ b/data_structures/Graph/Graph.py @@ -0,0 +1,40 @@ +# Author: OMKAR PATHAK + +# We can use Python's dictionary for constructing the graph + +class AdjacencyList(object): + def __init__(self): + self.List = {} + + def addEdge(self, fromVertex, toVertex): + # check if vertex is already present + if fromVertex in self.List.keys(): + self.List[fromVertex].append(toVertex) + else: + self.List[fromVertex] = [toVertex] + + def printList(self): + for i in self.List: + print(i,'->',' -> '.join([str(j) for j in self.List[i]])) + +if __name__ == '__main__': + al = AdjacencyList() + al.addEdge(0, 1) + al.addEdge(0, 4) + al.addEdge(4, 1) + al.addEdge(4, 3) + al.addEdge(1, 0) + al.addEdge(1, 4) + al.addEdge(1, 3) + al.addEdge(1, 2) + al.addEdge(2, 3) + al.addEdge(3, 4) + + al.printList() + + # OUTPUT: + # 0 -> 1 -> 4 + # 1 -> 0 -> 4 -> 3 -> 2 + # 2 -> 3 + # 3 -> 4 + # 4 -> 1 -> 3 diff --git a/data_structures/Graph/Graph_list.py b/data_structures/Graph/Graph_list.py new file mode 100644 index 000000000..8e33cf55c --- /dev/null +++ b/data_structures/Graph/Graph_list.py @@ -0,0 +1,28 @@ +class Graph: + def __init__(self, vertex): + self.vertex = vertex + self.graph = [[0] for i in range(vertex)] + + def add_edge(self, u, v): + self.graph[u - 1].append(v - 1) + + def show(self): + for i in range(self.vertex): + print('%d: '% (i + 1), end=' ') + for j in self.graph[i]: + print('%d-> '% (j + 1), end=' ') + print(' ') + + + +g = Graph(100) + +g.add_edge(1,3) +g.add_edge(2,3) +g.add_edge(3,4) +g.add_edge(3,5) +g.add_edge(4,5) + + +g.show() + diff --git a/data_structures/Graph/Graph_matrix.py b/data_structures/Graph/Graph_matrix.py new file mode 100644 index 000000000..1998fec8d --- /dev/null +++ b/data_structures/Graph/Graph_matrix.py @@ -0,0 +1,29 @@ +class Graph: + + def __init__(self, vertex): + self.vertex = vertex + self.graph = [[0] * vertex for i in range(vertex) ] + + def add_edge(self, u, v): + self.graph[u - 1][v - 1] = 1 + self.graph[v - 1][u - 1] = 1 + + def show(self): + + for i in self.graph: + for j in i: + print(j, end=' ') + print(' ') + + + + +g = Graph(100) + +g.add_edge(1,4) +g.add_edge(4,2) +g.add_edge(4,5) +g.add_edge(2,5) +g.add_edge(5,3) +g.show() + diff --git a/data_structures/Graph/dijkstra_algorithm.py b/data_structures/Graph/dijkstra_algorithm.py new file mode 100644 index 000000000..c43ff37f5 --- /dev/null +++ b/data_structures/Graph/dijkstra_algorithm.py @@ -0,0 +1,211 @@ +# Title: Dijkstra's Algorithm for finding single source shortest path from scratch +# Author: Shubham Malik +# References: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm + +import math +import sys +# For storing the vertex set to retreive node with the lowest distance + + +class PriorityQueue: + # Based on Min Heap + def __init__(self): + self.cur_size = 0 + self.array = [] + self.pos = {} # To store the pos of node in array + + def isEmpty(self): + return self.cur_size == 0 + + def min_heapify(self, idx): + lc = self.left(idx) + rc = self.right(idx) + if lc < self.cur_size and self.array(lc)[0] < self.array(idx)[0]: + smallest = lc + else: + smallest = idx + if rc < self.cur_size and self.array(rc)[0] < self.array(smallest)[0]: + smallest = rc + if smallest != idx: + self.swap(idx, smallest) + self.min_heapify(smallest) + + def insert(self, tup): + # Inserts a node into the Priority Queue + self.pos[tup[1]] = self.cur_size + self.cur_size += 1 + self.array.append((sys.maxsize, tup[1])) + self.decrease_key((sys.maxsize, tup[1]), tup[0]) + + def extract_min(self): + # Removes and returns the min element at top of priority queue + min_node = self.array[0][1] + self.array[0] = self.array[self.cur_size - 1] + self.cur_size -= 1 + self.min_heapify(1) + del self.pos[min_node] + return min_node + + def left(self, i): + # returns the index of left child + return 2 * i + 1 + + def right(self, i): + # returns the index of right child + return 2 * i + 2 + + def par(self, i): + # returns the index of parent + return math.floor(i / 2) + + def swap(self, i, j): + # swaps array elements at indices i and j + # update the pos{} + self.pos[self.array[i][1]] = j + self.pos[self.array[j][1]] = i + temp = self.array[i] + self.array[i] = self.array[j] + self.array[j] = temp + + def decrease_key(self, tup, new_d): + idx = self.pos[tup[1]] + # assuming the new_d is atmost old_d + self.array[idx] = (new_d, tup[1]) + while idx > 0 and self.array[self.par(idx)][0] > self.array[idx][0]: + self.swap(idx, self.par(idx)) + idx = self.par(idx) + + +class Graph: + def __init__(self, num): + self.adjList = {} # To store graph: u -> (v,w) + self.num_nodes = num # Number of nodes in graph + # To store the distance from source vertex + self.dist = [0] * self.num_nodes + self.par = [-1] * self.num_nodes # To store the path + + def add_edge(self, u, v, w): + # Edge going from node u to v and v to u with weight w + # u (w)-> v, v (w) -> u + # Check if u already in graph + if u in self.adjList.keys(): + self.adjList[u].append((v, w)) + else: + self.adjList[u] = [(v, w)] + + # Assuming undirected graph + if v in self.adjList.keys(): + self.adjList[v].append((u, w)) + else: + self.adjList[v] = [(u, w)] + + def show_graph(self): + # u -> v(w) + for u in self.adjList: + print(u, '->', ' -> '.join(str("{}({})".format(v, w)) + for v, w in self.adjList[u])) + + def dijkstra(self, src): + # Flush old junk values in par[] + self.par = [-1] * self.num_nodes + # src is the source node + self.dist[src] = 0 + Q = PriorityQueue() + Q.insert((0, src)) # (dist from src, node) + for u in self.adjList.keys(): + if u != src: + self.dist[u] = sys.maxsize # Infinity + self.par[u] = -1 + + while not Q.isEmpty(): + u = Q.extract_min() # Returns node with the min dist from source + # Update the distance of all the neighbours of u and + # if their prev dist was INFINITY then push them in Q + for v, w in self.adjList[u]: + new_dist = self.dist[u] + w + if self.dist[v] > new_dist: + if self.dist[v] == sys.maxsize: + Q.insert((new_dist, v)) + else: + Q.decrease_key((self.dist[v], v), new_dist) + self.dist[v] = new_dist + self.par[v] = u + + # Show the shortest distances from src + self.show_distances(src) + + def show_distances(self, src): + print("Distance from node: {}".format(src)) + for u in range(self.num_nodes): + print('Node {} has distance: {}'.format(u, self.dist[u])) + + def show_path(self, src, dest): + # To show the shortest path from src to dest + # WARNING: Use it *after* calling dijkstra + path = [] + cost = 0 + temp = dest + # Backtracking from dest to src + while self.par[temp] != -1: + path.append(temp) + if temp != src: + for v, w in self.adjList[temp]: + if v == self.par[temp]: + cost += w + break + temp = self.par[temp] + path.append(src) + path.reverse() + + print('----Path to reach {} from {}----'.format(dest, src)) + for u in path: + print('{}'.format(u), end=' ') + if u != dest: + print('-> ', end='') + + print('\nTotal cost of path: ', cost) + + +if __name__ == '__main__': + graph = Graph(9) + graph.add_edge(0, 1, 4) + graph.add_edge(0, 7, 8) + graph.add_edge(1, 2, 8) + graph.add_edge(1, 7, 11) + graph.add_edge(2, 3, 7) + graph.add_edge(2, 8, 2) + graph.add_edge(2, 5, 4) + graph.add_edge(3, 4, 9) + graph.add_edge(3, 5, 14) + graph.add_edge(4, 5, 10) + graph.add_edge(5, 6, 2) + graph.add_edge(6, 7, 1) + graph.add_edge(6, 8, 6) + graph.add_edge(7, 8, 7) + graph.show_graph() + graph.dijkstra(0) + graph.show_path(0, 4) + +# OUTPUT +# 0 -> 1(4) -> 7(8) +# 1 -> 0(4) -> 2(8) -> 7(11) +# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7) +# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4) +# 3 -> 2(7) -> 4(9) -> 5(14) +# 8 -> 2(2) -> 6(6) -> 7(7) +# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2) +# 4 -> 3(9) -> 5(10) +# 6 -> 5(2) -> 7(1) -> 8(6) +# Distance from node: 0 +# Node 0 has distance: 0 +# Node 1 has distance: 4 +# Node 2 has distance: 12 +# Node 3 has distance: 19 +# Node 4 has distance: 21 +# Node 5 has distance: 11 +# Node 6 has distance: 9 +# Node 7 has distance: 8 +# Node 8 has distance: 14 +# ----Path to reach 4 from 0---- +# 0 -> 7 -> 6 -> 5 -> 4 +# Total cost of path: 21 diff --git a/data_structures/Heap/heap.py b/data_structures/Heap/heap.py new file mode 100644 index 000000000..d43cc4baa --- /dev/null +++ b/data_structures/Heap/heap.py @@ -0,0 +1,83 @@ +#!/usr/bin/python + +class Heap: + def __init__(self): + self.h = [] + self.currsize = 0 + + def leftChild(self,i): + if 2*i+1 < self.currsize: + return 2*i+1 + return None + + def rightChild(self,i): + if 2*i+2 < self.currsize: + return 2*i+2 + return None + + def maxHeapify(self,node): + if node < self.currsize: + m = node + lc = self.leftChild(node) + rc = self.rightChild(node) + if lc is not None and self.h[lc] > self.h[m]: + m = lc + if rc is not None and self.h[rc] > self.h[m]: + m = rc + if m!=node: + temp = self.h[node] + self.h[node] = self.h[m] + self.h[m] = temp + self.maxHeapify(m) + + def buildHeap(self,a): + self.currsize = len(a) + self.h = list(a) + for i in range(self.currsize/2,-1,-1): + self.maxHeapify(i) + + def getMax(self): + if self.currsize >= 1: + me = self.h[0] + temp = self.h[0] + self.h[0] = self.h[self.currsize-1] + self.h[self.currsize-1] = temp + self.currsize -= 1 + self.maxHeapify(0) + return me + return None + + def heapSort(self): + size = self.currsize + while self.currsize-1 >= 0: + temp = self.h[0] + self.h[0] = self.h[self.currsize-1] + self.h[self.currsize-1] = temp + self.currsize -= 1 + self.maxHeapify(0) + self.currsize = size + + def insert(self,data): + self.h.append(data) + curr = self.currsize + self.currsize+=1 + while self.h[curr] > self.h[curr/2]: + temp = self.h[curr/2] + self.h[curr/2] = self.h[curr] + self.h[curr] = temp + curr = curr/2 + + def display(self): + print (self.h) + +def main(): + l = list(map(int,raw_input().split())) + h = Heap() + h.buildHeap(l) + h.heapSort() + h.display() + +if __name__=='__main__': + main() + + diff --git a/data_structures/LinkedList/DoublyLinkedList.py b/data_structures/LinkedList/DoublyLinkedList.py new file mode 100644 index 000000000..d152e465b --- /dev/null +++ b/data_structures/LinkedList/DoublyLinkedList.py @@ -0,0 +1,73 @@ +''' +- A linked list is similar to an array, it holds values. However, links in a linked list do not have indexes. +- This is an example of a double ended, doubly linked list. +- Each link references the next link and the previous one. +''' +class LinkedList: + def __init__(self): + self.head = None + self.tail = None + + def insertHead(self, x): + newLink = Link(x) #Create a new link with a value attached to it + if(self.isEmpty() == True): #Set the first element added to be the tail + self.tail = newLink + else: + self.head.previous = newLink # newLink <-- currenthead(head) + newLink.next = self.head # newLink <--> currenthead(head) + self.head = newLink # newLink(head) <--> oldhead + + def deleteHead(self): + temp = self.head + self.head = self.head.next # oldHead <--> 2ndElement(head) + self.head.previous = None # oldHead --> 2ndElement(head) nothing pointing at it so the old head will be removed + if(self.head == None): + self.tail = None + return temp + + def insertTail(self, x): + newLink = Link(x) + newLink.next = None # currentTail(tail) newLink --> + self.tail.next = newLink # currentTail(tail) --> newLink --> + newLink.previous = self.tail #currentTail(tail) <--> newLink --> + self.tail = newLink # oldTail <--> newLink(tail) --> + + def deleteTail(self): + temp = self.tail + self.tail = self.tail.previous # 2ndLast(tail) <--> oldTail --> None + self.tail.next = None # 2ndlast(tail) --> None + return temp + + def delete(self, x): + current = self.head + + while(current.value != x): # Find the position to delete + current = current.next + + if(current == self.head): + self.deleteHead() + + elif(current == self.tail): + self.deleteTail() + + else: #Before: 1 <--> 2(current) <--> 3 + current.previous.next = current.next # 1 --> 3 + current.next.previous = current.previous # 1 <--> 3 + + def isEmpty(self): #Will return True if the list is empty + return(self.head == None) + + def display(self): #Prints contents of the list + current = self.head + while(current != None): + current.displayLink() + current = current.next + print() + +class Link: + next = None #This points to the link in front of the new link + previous = None #This points to the link behind the new link + def __init__(self, x): + self.value = x + def displayLink(self): + print("{}".format(self.value), end=" ") \ No newline at end of file diff --git a/data_structures/LinkedList/__init__.py b/data_structures/LinkedList/__init__.py new file mode 100644 index 000000000..1d220599f --- /dev/null +++ b/data_structures/LinkedList/__init__.py @@ -0,0 +1,22 @@ +class Node: + def __init__(self, item, next): + self.item = item + self.next = next + +class LinkedList: + def __init__(self): + self.head = None + + def add(self, item): + self.head = Node(item, self.head) + + def remove(self): + if self.is_empty(): + return None + else: + item = self.head.item + self.head = self.head.next + return item + + def is_empty(self): + return self.head == None diff --git a/data_structures/LinkedList/singly_LinkedList.py b/data_structures/LinkedList/singly_LinkedList.py new file mode 100644 index 000000000..c9a3cec27 --- /dev/null +++ b/data_structures/LinkedList/singly_LinkedList.py @@ -0,0 +1,50 @@ +class Node:#create a Node + def __int__(self,data): + self.data=data#given data + self.next=None#given next to None +class Linked_List: + + pass + + def insert_tail(Head,data): + if(Head.next is None): + Head.next = Node(data) + else: + insert_tail(Head.next, data) + + def insert_head(Head,data): + tamp = Head + if (tamp == None): + newNod = Node()#create a new Node + newNod.data = data + newNod.next = None + Head = newNod#make new node to Head + else: + newNod = Node() + newNod.data = data + newNod.next = Head#put the Head at NewNode Next + Head=newNod#make a NewNode to Head + return Head + + def printList(Head):#print every node data + tamp=Head + while tamp!=None: + print(tamp.data) + tamp=tamp.next + + def delete_head(Head):#delete from head + if Head!=None: + Head=Head.next + return Head#return new Head + + def delete_tail(Head):#delete from tail + if Head!=None: + tamp = Node() + tamp = Head + while (tamp.next).next!= None:#find the 2nd last element + tamp = tamp.next + tamp.next=None#delete the last element by give next None to 2nd last Element + return Head + + def isEmpty(Head): + return Head is None #Return if Head is none \ No newline at end of file diff --git a/data_structures/Queue/DeQueue.py b/data_structures/Queue/DeQueue.py new file mode 100644 index 000000000..175c88163 --- /dev/null +++ b/data_structures/Queue/DeQueue.py @@ -0,0 +1,39 @@ +# Python code to demonstrate working of +# extend(), extendleft(), rotate(), reverse() + +# importing "collections" for deque operations +import collections + +# initializing deque +de = collections.deque([1, 2, 3,]) + +# using extend() to add numbers to right end +# adds 4,5,6 to right end +de.extend([4,5,6]) + +# printing modified deque +print ("The deque after extending deque at end is : ") +print (de) + +# using extendleft() to add numbers to left end +# adds 7,8,9 to right end +de.extendleft([7,8,9]) + +# printing modified deque +print ("The deque after extending deque at beginning is : ") +print (de) + +# using rotate() to rotate the deque +# rotates by 3 to left +de.rotate(-3) + +# printing modified deque +print ("The deque after rotating deque is : ") +print (de) + +# using reverse() to reverse the deque +de.reverse() + +# printing modified deque +print ("The deque after reversing deque is : ") +print (de) diff --git a/data_structures/Queue/QueueOnList.py b/data_structures/Queue/QueueOnList.py new file mode 100644 index 000000000..c8d0b41de --- /dev/null +++ b/data_structures/Queue/QueueOnList.py @@ -0,0 +1,45 @@ +"""Queue represented by a python list""" +class Queue(): + def __init__(self): + self.entries = [] + self.length = 0 + self.front=0 + + def __str__(self): + printed = '<' + str(self.entries)[1:-1] + '>' + return printed + + """Enqueues {@code item} + @param item + item to enqueue""" + def put(self, item): + self.entries.append(item) + self.length = self.length + 1 + + + """Dequeues {@code item} + @requirement: |self.length| > 0 + @return dequeued + item that was dequeued""" + def get(self): + self.length = self.length - 1 + dequeued = self.entries[self.front] + self.front-=1 + self.entries = self.entries[self.front:] + return dequeued + + """Rotates the queue {@code rotation} times + @param rotation + number of times to rotate queue""" + def rotate(self, rotation): + for i in range(rotation): + self.put(self.get()) + + """Enqueues {@code item} + @return item at front of self.entries""" + def front(self): + return self.entries[0] + + """Returns the length of this.entries""" + def size(self): + return self.length diff --git a/data_structures/Queue/QueueOnPseudoStack.py b/data_structures/Queue/QueueOnPseudoStack.py new file mode 100644 index 000000000..b69fbcc98 --- /dev/null +++ b/data_structures/Queue/QueueOnPseudoStack.py @@ -0,0 +1,50 @@ +"""Queue represented by a pseudo stack (represented by a list with pop and append)""" +class Queue(): + def __init__(self): + self.stack = [] + self.length = 0 + + def __str__(self): + printed = '<' + str(self.stack)[1:-1] + '>' + return printed + + """Enqueues {@code item} + @param item + item to enqueue""" + def put(self, item): + self.stack.append(item) + self.length = self.length + 1 + + """Dequeues {@code item} + @requirement: |self.length| > 0 + @return dequeued + item that was dequeued""" + def get(self): + self.rotate(1) + dequeued = self.stack[self.length-1] + self.stack = self.stack[:-1] + self.rotate(self.length-1) + self.length = self.length -1 + return dequeued + + """Rotates the queue {@code rotation} times + @param rotation + number of times to rotate queue""" + def rotate(self, rotation): + for i in range(rotation): + temp = self.stack[0] + self.stack = self.stack[1:] + self.put(temp) + self.length = self.length - 1 + + """Reports item at the front of self + @return item at front of self.stack""" + def front(self): + front = self.get() + self.put(front) + self.rotate(self.length-1) + return front + + """Returns the length of this.stack""" + def size(self): + return self.length diff --git a/data_structures/Queue/__init__.py b/data_structures/Queue/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/data_structures/Stacks/__init__.py b/data_structures/Stacks/__init__.py new file mode 100644 index 000000000..f7e92ae2d --- /dev/null +++ b/data_structures/Stacks/__init__.py @@ -0,0 +1,23 @@ +class Stack: + + def __init__(self): + self.stack = [] + self.top = 0 + + def is_empty(self): + return (self.top == 0) + + def push(self, item): + if self.top < len(self.stack): + self.stack[self.top] = item + else: + self.stack.append(item) + + self.top += 1 + + def pop(self): + if self.is_empty(): + return None + else: + self.top -= 1 + return self.stack[self.top] diff --git a/data_structures/Stacks/balanced_parentheses.py b/data_structures/Stacks/balanced_parentheses.py new file mode 100644 index 000000000..1c9a84843 --- /dev/null +++ b/data_structures/Stacks/balanced_parentheses.py @@ -0,0 +1,21 @@ +from Stack import Stack + +__author__ = 'Omkar Pathak' + + +def balanced_parentheses(parentheses): + """ Use a stack to check if a string of parentheses are balanced.""" + stack = Stack(len(parentheses)) + for parenthesis in parentheses: + if parenthesis == '(': + stack.push(parenthesis) + elif parenthesis == ')': + stack.pop() + return not stack.is_empty() + + +if __name__ == '__main__': + examples = ['((()))', '((())'] + print('Balanced parentheses demonstration:\n') + for example in examples: + print(example + ': ' + str(balanced_parentheses(example))) diff --git a/data_structures/Stacks/infix_to_postfix_conversion.py b/data_structures/Stacks/infix_to_postfix_conversion.py new file mode 100644 index 000000000..f0a8fd072 --- /dev/null +++ b/data_structures/Stacks/infix_to_postfix_conversion.py @@ -0,0 +1,62 @@ +import string + +from Stack import Stack + +__author__ = 'Omkar Pathak' + + +def is_operand(char): + return char in string.ascii_letters or char in string.digits + + +def precedence(char): + """ Return integer value representing an operator's precedence, or + order of operation. + + https://en.wikipedia.org/wiki/Order_of_operations + """ + dictionary = {'+': 1, '-': 1, + '*': 2, '/': 2, + '^': 3} + return dictionary.get(char, -1) + + +def infix_to_postfix(expression): + """ Convert infix notation to postfix notation using the Shunting-yard + algorithm. + + https://en.wikipedia.org/wiki/Shunting-yard_algorithm + https://en.wikipedia.org/wiki/Infix_notation + https://en.wikipedia.org/wiki/Reverse_Polish_notation + """ + stack = Stack(len(expression)) + postfix = [] + for char in expression: + if is_operand(char): + postfix.append(char) + elif char not in {'(', ')'}: + while (not stack.is_empty() + and precedence(char) <= precedence(stack.peek())): + postfix.append(stack.pop()) + stack.push(char) + elif char == '(': + stack.push(char) + elif char == ')': + while not stack.is_empty() and stack.peek() != '(': + postfix.append(stack.pop()) + # Pop '(' from stack. If there is no '(', there is a mismatched + # parentheses. + if stack.peek() != '(': + raise ValueError('Mismatched parentheses') + stack.pop() + while not stack.is_empty(): + postfix.append(stack.pop()) + return ' '.join(postfix) + + +if __name__ == '__main__': + expression = 'a+b*(c^d-e)^(f+g*h)-i' + + print('Infix to Postfix Notation demonstration:\n') + print('Infix notation: ' + expression) + print('Postfix notation: ' + infix_to_postfix(expression)) diff --git a/data_structures/Stacks/next.py b/data_structures/Stacks/next.py new file mode 100644 index 000000000..9765900c0 --- /dev/null +++ b/data_structures/Stacks/next.py @@ -0,0 +1,16 @@ +# Function to print element and NGE pair for all elements of list +def printNGE(arr): + + for i in range(0, len(arr), 1): + + next = -1 + for j in range(i+1, len(arr), 1): + if arr[i] < arr[j]: + next = arr[j] + break + + print(str(arr[i]) + " -- " + str(next)) + +# Driver program to test above function +arr = [11,13,21,3] +printNGE(arr) diff --git a/data_structures/Stacks/stack.py b/data_structures/Stacks/stack.py new file mode 100644 index 000000000..0b100abf3 --- /dev/null +++ b/data_structures/Stacks/stack.py @@ -0,0 +1,68 @@ +__author__ = 'Omkar Pathak' + + +class Stack(object): + """ A stack is an abstract data type that serves as a collection of + elements with two principal operations: push() and pop(). push() adds an + element to the top of the stack, and pop() removes an element from the top + of a stack. The order in which elements come off of a stack are + Last In, First Out (LIFO). + + https://en.wikipedia.org/wiki/Stack_(abstract_data_type) + """ + + def __init__(self, limit=10): + self.stack = [] + self.limit = limit + + def __bool__(self): + return not bool(self.stack) + + def __str__(self): + return str(self.stack) + + def push(self, data): + """ Push an element to the top of the stack.""" + if len(self.stack) >= self.limit: + raise StackOverflowError + self.stack.append(data) + + def pop(self): + """ Pop an element off of the top of the stack.""" + if self.stack: + return self.stack.pop() + else: + raise IndexError('pop from an empty stack') + + def peek(self): + """ Peek at the top-most element of the stack.""" + if self.stack: + return self.stack[-1] + + def is_empty(self): + """ Check if a stack is empty.""" + return not bool(self.stack) + + def size(self): + """ Return the size of the stack.""" + return len(self.stack) + + +class StackOverflowError(BaseException): + pass + + +if __name__ == '__main__': + stack = Stack() + for i in range(10): + stack.push(i) + + print('Stack demonstration:\n') + print('Initial stack: ' + str(stack)) + print('pop(): ' + str(stack.pop())) + print('After pop(), the stack is now: ' + str(stack)) + print('peek(): ' + str(stack.peek())) + stack.push(100) + print('After push(100), the stack is now: ' + str(stack)) + print('is_empty(): ' + str(stack.is_empty())) + print('size(): ' + str(stack.size())) diff --git a/data_structures/Trie/Trie.py b/data_structures/Trie/Trie.py new file mode 100644 index 000000000..7c886144d --- /dev/null +++ b/data_structures/Trie/Trie.py @@ -0,0 +1,75 @@ +""" +A Trie/Prefix Tree is a kind of search tree used to provide quick lookup +of words/patterns in a set of words. A basic Trie however has O(n^2) space complexity +making it impractical in practice. It however provides O(max(search_string, length of longest word)) lookup +time making it an optimal approach when space is not an issue. + +""" + + +class TrieNode: + def __init__(self): + self.nodes = dict() # Mapping from char to TrieNode + self.is_leaf = False + + def insert_many(self, words: [str]): + """ + Inserts a list of words into the Trie + :param words: list of string words + :return: None + """ + for word in words: + self.insert(word) + + def insert(self, word: str): + """ + Inserts a word into the Trie + :param word: word to be inserted + :return: None + """ + curr = self + for char in word: + if char not in curr.nodes: + curr.nodes[char] = TrieNode() + curr = curr.nodes[char] + curr.is_leaf = True + + def find(self, word: str) -> bool: + """ + Tries to find word in a Trie + :param word: word to look for + :return: Returns True if word is found, False otherwise + """ + curr = self + for char in word: + if char not in curr.nodes: + return False + curr = curr.nodes[char] + return curr.is_leaf + + +def print_words(node: TrieNode, word: str): + """ + Prints all the words in a Trie + :param node: root node of Trie + :param word: Word variable should be empty at start + :return: None + """ + if node.is_leaf: + print(word, end=' ') + + for key, value in node.nodes.items(): + print_words(value, word + key) + + +def test(): + words = ['banana', 'bananas', 'bandana', 'band', 'apple', 'all', 'beast'] + root = TrieNode() + root.insert_many(words) + # print_words(root, '') + assert root.find('banana') + assert not root.find('bandanas') + assert not root.find('apps') + assert root.find('apple') + +test() diff --git a/data_structures/__init__.py b/data_structures/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/dynamic_programming/FloydWarshall.py b/dynamic_programming/FloydWarshall.py new file mode 100644 index 000000000..bf7714124 --- /dev/null +++ b/dynamic_programming/FloydWarshall.py @@ -0,0 +1,37 @@ +import math + +class Graph: + + def __init__(self, N = 0): # a graph with Node 0,1,...,N-1 + self.N = N + self.W = [[math.inf for j in range(0,N)] for i in range(0,N)] # adjacency matrix for weight + self.dp = [[math.inf for j in range(0,N)] for i in range(0,N)] # dp[i][j] stores minimum distance from i to j + + def addEdge(self, u, v, w): + self.dp[u][v] = w; + + def floyd_warshall(self): + for k in range(0,self.N): + for i in range(0,self.N): + for j in range(0,self.N): + self.dp[i][j] = min(self.dp[i][j], self.dp[i][k] + self.dp[k][j]) + + def showMin(self, u, v): + return self.dp[u][v] + +if __name__ == '__main__': + graph = Graph(5) + graph.addEdge(0,2,9) + graph.addEdge(0,4,10) + graph.addEdge(1,3,5) + graph.addEdge(2,3,7) + graph.addEdge(3,0,10) + graph.addEdge(3,1,2) + graph.addEdge(3,2,1) + graph.addEdge(3,4,6) + graph.addEdge(4,1,3) + graph.addEdge(4,2,4) + graph.addEdge(4,3,9) + graph.floyd_warshall() + graph.showMin(1,4) + graph.showMin(0,3) diff --git a/dynamic_programming/edit_distance.py b/dynamic_programming/edit_distance.py new file mode 100644 index 000000000..05682d2c6 --- /dev/null +++ b/dynamic_programming/edit_distance.py @@ -0,0 +1,74 @@ +""" +Author : Turfa Auliarachman +Date : October 12, 2016 + +This is a pure Python implementation of Dynamic Programming solution to the edit distance problem. + +The problem is : +Given two strings A and B. Find the minimum number of operations to string B such that A = B. The permitted operations are removal, insertion, and substitution. +""" + +class EditDistance: + """ + Use : + solver = EditDistance() + editDistanceResult = solver.solve(firstString, secondString) + """ + + def __init__(self): + self.__prepare__() + + def __prepare__(self, N = 0, M = 0): + self.dp = [[-1 for y in range(0,M)] for x in range(0,N)] + + def __solveDP(self, x, y): + if (x==-1): + return y+1 + elif (y==-1): + return x+1 + elif (self.dp[x][y]>-1): + return self.dp[x][y] + else: + if (self.A[x]==self.B[y]): + self.dp[x][y] = self.__solveDP(x-1,y-1) + else: + self.dp[x][y] = 1+min(self.__solveDP(x,y-1), self.__solveDP(x-1,y), self.__solveDP(x-1,y-1)) + + return self.dp[x][y] + + def solve(self, A, B): + if isinstance(A,bytes): + A = A.decode('ascii') + + if isinstance(B,bytes): + B = B.decode('ascii') + + self.A = str(A) + self.B = str(B) + + self.__prepare__(len(A), len(B)) + + return self.__solveDP(len(A)-1, len(B)-1) + +if __name__ == '__main__': + import sys + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + solver = EditDistance() + + print("****************** Testing Edit Distance DP Algorithm ******************") + print() + + print("Enter the first string: ", end="") + S1 = input_function() + + print("Enter the second string: ", end="") + S2 = input_function() + + print() + print("The minimum Edit Distance is: %d" % (solver.solve(S1, S2))) + print() + print("*************** End of Testing Edit Distance DP Algorithm ***************") diff --git a/dynamic_programming/fastfibonacci.py b/dynamic_programming/fastfibonacci.py new file mode 100644 index 000000000..5957fbe0d --- /dev/null +++ b/dynamic_programming/fastfibonacci.py @@ -0,0 +1,42 @@ +""" +This program calculates the nth Fibonacci number in O(log(n)). +It's possible to calculate F(1000000) in less than a second. +""" +import sys + + +# returns F(n) +def fibonacci(n: int): + if n < 0: + raise ValueError("Negative arguments are not supported") + return _fib(n)[0] + + +# returns (F(n), F(n-1)) +def _fib(n: int): + if n == 0: + # (F(0), F(1)) + return (0, 1) + else: + # F(2n) = F(n)[2F(n+1) − F(n)] + # F(2n+1) = F(n+1)^2+F(n)^2 + a, b = _fib(n // 2) + c = a * (b * 2 - a) + d = a * a + b * b + if n % 2 == 0: + return (c, d) + else: + return (d, c + d) + + +if __name__ == "__main__": + args = sys.argv[1:] + if len(args) != 1: + print("Too few or too much parameters given.") + exit(1) + try: + n = int(args[0]) + except ValueError: + print("Could not convert data to an integer.") + exit(1) + print("F(%d) = %d" % (n, fibonacci(n))) diff --git a/dynamic_programming/fibonacci.py b/dynamic_programming/fibonacci.py new file mode 100644 index 000000000..5eaa81b3e --- /dev/null +++ b/dynamic_programming/fibonacci.py @@ -0,0 +1,57 @@ +""" +This is a pure Python implementation of Dynamic Programming solution to the fibonacci sequence problem. +""" + + +class Fibonacci: + + def __init__(self, N=None): + self.fib_array = [] + if N: + N = int(N) + self.fib_array.append(0) + self.fib_array.append(1) + for i in range(2, N + 1): + self.fib_array.append(self.fib_array[i - 1] + self.fib_array[i - 2]) + elif N == 0: + self.fib_array.append(0) + + def get(self, sequence_no=None): + if sequence_no != None: + if sequence_no < len(self.fib_array): + return print(self.fib_array[:sequence_no + 1]) + else: + print("Out of bound.") + else: + print("Please specify a value") + + +if __name__ == '__main__': + import sys + + print("\n********* Fibonacci Series Using Dynamic Programming ************\n") + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + print("\n Enter the upper limit for the fibonacci sequence: ", end="") + try: + N = eval(input()) + fib = Fibonacci(N) + print( + "\n********* Enter different values to get the corresponding fibonacci sequence, enter any negative number to exit. ************\n") + while True: + print("Enter value: ", end=" ") + try: + i = eval(input()) + if i < 0: + print("\n********* Good Bye!! ************\n") + break + fib.get(i) + except NameError: + print("\nInvalid input, please try again.") + except NameError: + print("\n********* Invalid input, good bye!! ************\n") diff --git a/dynamic_programming/k_means_clustering_tensorflow.py b/dynamic_programming/k_means_clustering_tensorflow.py new file mode 100644 index 000000000..ad495c71a --- /dev/null +++ b/dynamic_programming/k_means_clustering_tensorflow.py @@ -0,0 +1,141 @@ +import tensorflow as tf +from random import choice, shuffle +from numpy import array + + +def TFKMeansCluster(vectors, noofclusters): + """ + K-Means Clustering using TensorFlow. + 'vectors' should be a n*k 2-D NumPy array, where n is the number + of vectors of dimensionality k. + 'noofclusters' should be an integer. + """ + + noofclusters = int(noofclusters) + assert noofclusters < len(vectors) + + #Find out the dimensionality + dim = len(vectors[0]) + + #Will help select random centroids from among the available vectors + vector_indices = list(range(len(vectors))) + shuffle(vector_indices) + + #GRAPH OF COMPUTATION + #We initialize a new graph and set it as the default during each run + #of this algorithm. This ensures that as this function is called + #multiple times, the default graph doesn't keep getting crowded with + #unused ops and Variables from previous function calls. + + graph = tf.Graph() + + with graph.as_default(): + + #SESSION OF COMPUTATION + + sess = tf.Session() + + ##CONSTRUCTING THE ELEMENTS OF COMPUTATION + + ##First lets ensure we have a Variable vector for each centroid, + ##initialized to one of the vectors from the available data points + centroids = [tf.Variable((vectors[vector_indices[i]])) + for i in range(noofclusters)] + ##These nodes will assign the centroid Variables the appropriate + ##values + centroid_value = tf.placeholder("float64", [dim]) + cent_assigns = [] + for centroid in centroids: + cent_assigns.append(tf.assign(centroid, centroid_value)) + + ##Variables for cluster assignments of individual vectors(initialized + ##to 0 at first) + assignments = [tf.Variable(0) for i in range(len(vectors))] + ##These nodes will assign an assignment Variable the appropriate + ##value + assignment_value = tf.placeholder("int32") + cluster_assigns = [] + for assignment in assignments: + cluster_assigns.append(tf.assign(assignment, + assignment_value)) + + ##Now lets construct the node that will compute the mean + #The placeholder for the input + mean_input = tf.placeholder("float", [None, dim]) + #The Node/op takes the input and computes a mean along the 0th + #dimension, i.e. the list of input vectors + mean_op = tf.reduce_mean(mean_input, 0) + + ##Node for computing Euclidean distances + #Placeholders for input + v1 = tf.placeholder("float", [dim]) + v2 = tf.placeholder("float", [dim]) + euclid_dist = tf.sqrt(tf.reduce_sum(tf.pow(tf.sub( + v1, v2), 2))) + + ##This node will figure out which cluster to assign a vector to, + ##based on Euclidean distances of the vector from the centroids. + #Placeholder for input + centroid_distances = tf.placeholder("float", [noofclusters]) + cluster_assignment = tf.argmin(centroid_distances, 0) + + ##INITIALIZING STATE VARIABLES + + ##This will help initialization of all Variables defined with respect + ##to the graph. The Variable-initializer should be defined after + ##all the Variables have been constructed, so that each of them + ##will be included in the initialization. + init_op = tf.initialize_all_variables() + + #Initialize all variables + sess.run(init_op) + + ##CLUSTERING ITERATIONS + + #Now perform the Expectation-Maximization steps of K-Means clustering + #iterations. To keep things simple, we will only do a set number of + #iterations, instead of using a Stopping Criterion. + noofiterations = 100 + for iteration_n in range(noofiterations): + + ##EXPECTATION STEP + ##Based on the centroid locations till last iteration, compute + ##the _expected_ centroid assignments. + #Iterate over each vector + for vector_n in range(len(vectors)): + vect = vectors[vector_n] + #Compute Euclidean distance between this vector and each + #centroid. Remember that this list cannot be named + #'centroid_distances', since that is the input to the + #cluster assignment node. + distances = [sess.run(euclid_dist, feed_dict={ + v1: vect, v2: sess.run(centroid)}) + for centroid in centroids] + #Now use the cluster assignment node, with the distances + #as the input + assignment = sess.run(cluster_assignment, feed_dict = { + centroid_distances: distances}) + #Now assign the value to the appropriate state variable + sess.run(cluster_assigns[vector_n], feed_dict={ + assignment_value: assignment}) + + ##MAXIMIZATION STEP + #Based on the expected state computed from the Expectation Step, + #compute the locations of the centroids so as to maximize the + #overall objective of minimizing within-cluster Sum-of-Squares + for cluster_n in range(noofclusters): + #Collect all the vectors assigned to this cluster + assigned_vects = [vectors[i] for i in range(len(vectors)) + if sess.run(assignments[i]) == cluster_n] + #Compute new centroid location + new_location = sess.run(mean_op, feed_dict={ + mean_input: array(assigned_vects)}) + #Assign value to appropriate variable + sess.run(cent_assigns[cluster_n], feed_dict={ + centroid_value: new_location}) + + #Return centroids and assignments + centroids = sess.run(centroids) + assignments = sess.run(assignments) + return centroids, assignments + diff --git a/dynamic_programming/knapsack.py b/dynamic_programming/knapsack.py new file mode 100644 index 000000000..a1e4f0d80 --- /dev/null +++ b/dynamic_programming/knapsack.py @@ -0,0 +1,14 @@ +""" +Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. +""" +def knapsack(W, wt, val, n): + dp = [[0 for i in range(W+1)]for j in range(n+1)] + + for i in range(1,n+1): + for w in range(1,W+1): + if(wt[i-1]<=w): + dp[i][w] = max(val[i-1]+dp[i-1][w-wt[i-1]],dp[i-1][w]) + else: + dp[i][w] = dp[i-1][w] + + return dp[n][w] diff --git a/dynamic_programming/longest common subsequence.py b/dynamic_programming/longest common subsequence.py new file mode 100644 index 000000000..da95561ed --- /dev/null +++ b/dynamic_programming/longest common subsequence.py @@ -0,0 +1,48 @@ +""" +LCS Problem Statement: Given two sequences, find the length of longest subsequence present in both of them. +A subsequence is a sequence that appears in the same relative order, but not necessarily continious. +Example:"abc", "abg" are subsequences of "abcdefgh". +""" +def LCS(x,y): + b=[[] for j in range(len(x)+1)] + c=[[] for i in range(len(x))] + for i in range(len(x)+1): + b[i].append(0) + for i in range(1,len(y)+1): + b[0].append(0) + for i in range(len(x)): + for j in range(len(y)): + if x[i]==y[j]: + b[i+1].append(b[i][j]+1) + c[i].append('/') + elif b[i][j+1]>=b[i+1][j]: + b[i+1].append(b[i][j+1]) + c[i].append('|') + else : + b[i+1].append(b[i+1][j]) + c[i].append('-') + return b,c + + +def print_lcs(x,c,n,m): + n,m=n-1,m-1 + ans=[] + while n>=0 and m>=0: + if c[n][m]=='/': + ans.append(x[n]) + n,m=n-1,m-1 + elif c[n][m]=='|': + n=n-1 + else: + m=m-1 + ans=ans[::-1] + return ans + + +if __name__=='__main__': + x=['a','b','c','b','d','a','b'] + y=['b','d','c','a','b','a'] + b,c=LCS(x,y) + print('Given \nX : ',x) + print('Y : ',y) + print('LCS : ',print_lcs(x,c,len(x),len(y))) diff --git a/dynamic_programming/longest_increasing_subsequence.py b/dynamic_programming/longest_increasing_subsequence.py new file mode 100644 index 000000000..c04f6673f --- /dev/null +++ b/dynamic_programming/longest_increasing_subsequence.py @@ -0,0 +1,41 @@ +''' +Author : Mehdi ALAOUI + +This is a pure Python implementation of Dynamic Programming solution to the longest increasing subsequence of a given sequence. + +The problem is : +Given an ARRAY, to find the longest and increasing sub ARRAY in that given ARRAY and return it. +Example: [10, 22, 9, 33, 21, 50, 41, 60, 80] as input will return [10, 22, 33, 41, 60, 80] as output +''' + +def longestSub(ARRAY): #This function is recursive + + ARRAY_LENGTH = len(ARRAY) + if(ARRAY_LENGTH <= 1): #If the array contains only one element, we return it (it's the stop condition of recursion) + return ARRAY + #Else + PIVOT=ARRAY[0] + isFound=False + i=1 + LONGEST_SUB=[] + while(not isFound and i= ARRAY[i] ] + TEMPORARY_ARRAY = longestSub(TEMPORARY_ARRAY) + if ( len(TEMPORARY_ARRAY) > len(LONGEST_SUB) ): + LONGEST_SUB = TEMPORARY_ARRAY + else: + i+=1 + + TEMPORARY_ARRAY = [ element for element in ARRAY[1:] if element >= PIVOT ] + TEMPORARY_ARRAY = [PIVOT] + longestSub(TEMPORARY_ARRAY) + if ( len(TEMPORARY_ARRAY) > len(LONGEST_SUB) ): + return TEMPORARY_ARRAY + else: + return LONGEST_SUB + +#Some examples + +print(longestSub([4,8,7,5,1,12,2,3,9])) +print(longestSub([9,8,7,6,5,7])) \ No newline at end of file diff --git a/dynamic_programming/longest_increasing_subsequence_O(nlogn).py b/dynamic_programming/longest_increasing_subsequence_O(nlogn).py new file mode 100644 index 000000000..3ebb4a137 --- /dev/null +++ b/dynamic_programming/longest_increasing_subsequence_O(nlogn).py @@ -0,0 +1,40 @@ +############################# +# Author: Aravind Kashyap +# File: lis.py +# comments: This programme outputs the Longest Strictly Increasing Subsequence in O(NLogN) +# Where N is the Number of elements in the list +############################# +def CeilIndex(v,l,r,key): + while r-l > 1: + m = (l + r)/2 + if v[m] >= key: + r = m + else: + l = m + + return r + + +def LongestIncreasingSubsequenceLength(v): + if(len(v) == 0): + return 0 + + tail = [0]*len(v) + length = 1 + + tail[0] = v[0] + + for i in range(1,len(v)): + if v[i] < tail[0]: + tail[0] = v[i] + elif v[i] > tail[length-1]: + tail[length] = v[i] + length += 1 + else: + tail[CeilIndex(tail,-1,length-1,v[i])] = v[i] + + return length + + +v = [2, 5, 3, 7, 11, 8, 10, 13, 6] +print LongestIncreasingSubsequenceLength(v) diff --git a/dynamic_programming/longest_sub_array.py b/dynamic_programming/longest_sub_array.py new file mode 100644 index 000000000..988041ed0 --- /dev/null +++ b/dynamic_programming/longest_sub_array.py @@ -0,0 +1,32 @@ +''' +Auther : Yvonne + +This is a pure Python implementation of Dynamic Programming solution to the longest_sub_array problem. + +The problem is : +Given an array, to find the longest and continuous sub array and get the max sum of the sub array in the given array. +''' + + +class SubArray: + + def __init__(self, arr): + # we need a list not a string, so do something to change the type + self.array = arr.split(',') + print("the input array is:", self.array) + + def solve_sub_array(self): + rear = [int(self.array[0])]*len(self.array) + sum_value = [int(self.array[0])]*len(self.array) + for i in range(1, len(self.array)): + sum_value[i] = max(int(self.array[i]) + sum_value[i-1], int(self.array[i])) + rear[i] = max(sum_value[i], rear[i-1]) + return rear[len(self.array)-1] + + +if __name__ == '__main__': + whole_array = input("please input some numbers:") + array = SubArray(whole_array) + re = array.solve_sub_array() + print("the results is:", re) + diff --git a/dynamic_programming/max_sub_array.py b/dynamic_programming/max_sub_array.py new file mode 100644 index 000000000..653bb66e0 --- /dev/null +++ b/dynamic_programming/max_sub_array.py @@ -0,0 +1,59 @@ +""" +author : Mayank Kumar Jha (mk9440) +""" + +import time +import matplotlib.pyplot as plt +from random import randint +def find_max_sub_array(A,low,high): + if low==high: + return low,high,A[low] + else : + mid=(low+high)//2 + left_low,left_high,left_sum=find_max_sub_array(A,low,mid) + right_low,right_high,right_sum=find_max_sub_array(A,mid+1,high) + cross_left,cross_right,cross_sum=find_max_cross_sum(A,low,mid,high) + if left_sum>=right_sum and left_sum>=cross_sum: + return left_low,left_high,left_sum + elif right_sum>=left_sum and right_sum>=cross_sum : + return right_low,right_high,right_sum + else: + return cross_left,cross_right,cross_sum + +def find_max_cross_sum(A,low,mid,high): + left_sum,max_left=-999999999,-1 + right_sum,max_right=-999999999,-1 + summ=0 + for i in range(mid,low-1,-1): + summ+=A[i] + if summ > left_sum: + left_sum=summ + max_left=i + summ=0 + for i in range(mid+1,high+1): + summ+=A[i] + if summ > right_sum: + right_sum=summ + max_right=i + return max_left,max_right,(left_sum+right_sum) + + +if __name__=='__main__': + inputs=[10,100,1000,10000,50000,100000,200000,300000,400000,500000] + tim=[] + for i in inputs: + li=[randint(1,i) for j in range(i)] + strt=time.time() + (find_max_sub_array(li,0,len(li)-1)) + end=time.time() + tim.append(end-strt) + print("No of Inputs Time Taken") + for i in range(len(inputs)): + print(inputs[i],'\t\t',tim[i]) + plt.plot(inputs,tim) + plt.xlabel("Number of Inputs");plt.ylabel("Time taken in seconds ") + plt.show() + + + + diff --git a/dynamic_programming/minimum_partition.py b/dynamic_programming/minimum_partition.py new file mode 100644 index 000000000..25b7621e1 --- /dev/null +++ b/dynamic_programming/minimum_partition.py @@ -0,0 +1,28 @@ +""" +Partition a set into two subsets such that the difference of subset sums is minimum +""" +def findMin(arr): + n = len(arr) + s = sum(arr) + + dp = [[False for x in range(s+1)]for y in range(n+1)] + + for i in range(1, n+1): + dp[i][0] = True + + for i in range(1, s+1): + dp[0][i] = False + + for i in range(1, n+1): + for j in range(1, s+1): + dp[i][j]= dp[i][j-1] + + if (arr[i-1] <= j): + dp[i][j] = dp[i][j] or dp[i-1][j-arr[i-1]] + + for j in range(s/2, -1, -1): + if dp[n][j] == True: + diff = s-2*j + break; + + return diff diff --git a/hashes/md5.py b/hashes/md5.py new file mode 100644 index 000000000..ff32f4c2e --- /dev/null +++ b/hashes/md5.py @@ -0,0 +1,107 @@ +import math + +def rearrange(bitString32): + if len(bitString32) != 32: + raise ValueError("Need length 32") + newString = "" + for i in [3,2,1,0]: + newString += bitString32[8*i:8*i+8] + return newString + +def reformatHex(i): + hexrep = format(i,'08x') + thing = "" + for i in [3,2,1,0]: + thing += hexrep[2*i:2*i+2] + return thing + +def pad(bitString): + startLength = len(bitString) + bitString += '1' + while len(bitString) % 512 != 448: + bitString += '0' + lastPart = format(startLength,'064b') + bitString += rearrange(lastPart[32:]) + rearrange(lastPart[:32]) + return bitString + +def getBlock(bitString): + currPos = 0 + while currPos < len(bitString): + currPart = bitString[currPos:currPos+512] + mySplits = [] + for i in range(16): + mySplits.append(int(rearrange(currPart[32*i:32*i+32]),2)) + yield mySplits + currPos += 512 +def not32(i): + i_str = format(i,'032b') + new_str = '' + for c in i_str: + new_str += '1' if c=='0' else '0' + return int(new_str,2) + +def sum32(a,b): + return (a + b) % 2**32 + +def leftrot32(i,s): + return (i << s) ^ (i >> (32-s)) + +def md5me(testString): + bs ='' + for i in testString: + bs += format(ord(i),'08b') + bs = pad(bs) + + tvals = [int(2**32 * abs(math.sin(i+1))) for i in range(64)] + + a0 = 0x67452301 + b0 = 0xefcdab89 + c0 = 0x98badcfe + d0 = 0x10325476 + + s = [7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, \ + 5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20, \ + 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, \ + 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21 ] + + for m in getBlock(bs): + A = a0 + B = b0 + C = c0 + D = d0 + for i in range(64): + if i <= 15: + #f = (B & C) | (not32(B) & D) + f = D ^ (B & (C ^ D)) + g = i + elif i<= 31: + #f = (D & B) | (not32(D) & C) + f = C ^ (D & (B ^ C)) + g = (5*i+1) % 16 + elif i <= 47: + f = B ^ C ^ D + g = (3*i+5) % 16 + else: + f = C ^ (B | not32(D)) + g = (7*i) % 16 + dtemp = D + D = C + C = B + B = sum32(B,leftrot32((A + f + tvals[i] + m[g]) % 2**32, s[i])) + A = dtemp + a0 = sum32(a0, A) + b0 = sum32(b0, B) + c0 = sum32(c0, C) + d0 = sum32(d0, D) + + digest = reformatHex(a0) + reformatHex(b0) + reformatHex(c0) + reformatHex(d0) + return digest + +def test(): + assert md5me("") == "d41d8cd98f00b204e9800998ecf8427e" + assert md5me("The quick brown fox jumps over the lazy dog") == "9e107d9d372bb6826bd81d3542a419d6" + print("Success.") + + +if __name__ == "__main__": + test() diff --git a/machine_learning/decision_tree.py b/machine_learning/decision_tree.py new file mode 100644 index 000000000..51f600cac --- /dev/null +++ b/machine_learning/decision_tree.py @@ -0,0 +1,139 @@ +""" +Implementation of a basic regression decision tree. +Input data set: The input data set must be 1-dimensional with continuous labels. +Output: The decision tree maps a real number input to a real number output. +""" + +import numpy as np + +class Decision_Tree: + def __init__(self, depth = 5, min_leaf_size = 5): + self.depth = depth + self.decision_boundary = 0 + self.left = None + self.right = None + self.min_leaf_size = min_leaf_size + self.prediction = None + + def mean_squared_error(self, labels, prediction): + """ + mean_squared_error: + @param labels: a one dimensional numpy array + @param prediction: a floating point value + return value: mean_squared_error calculates the error if prediction is used to estimate the labels + """ + if labels.ndim != 1: + print("Error: Input labels must be one dimensional") + + return np.mean((labels - prediction) ** 2) + + def train(self, X, y): + """ + train: + @param X: a one dimensional numpy array + @param y: a one dimensional numpy array. + The contents of y are the labels for the corresponding X values + + train does not have a return value + """ + + """ + this section is to check that the inputs conform to our dimensionality constraints + """ + if X.ndim != 1: + print("Error: Input data set must be one dimensional") + return + if len(X) != len(y): + print("Error: X and y have different lengths") + return + if y.ndim != 1: + print("Error: Data set labels must be one dimensional") + return + + if len(X) < 2 * self.min_leaf_size: + self.prediction = np.mean(y) + return + + if self.depth == 1: + self.prediction = np.mean(y) + return + + best_split = 0 + min_error = self.mean_squared_error(X,np.mean(y)) * 2 + + + """ + loop over all possible splits for the decision tree. find the best split. + if no split exists that is less than 2 * error for the entire array + then the data set is not split and the average for the entire array is used as the predictor + """ + for i in range(len(X)): + if len(X[:i]) < self.min_leaf_size: + continue + elif len(X[i:]) < self.min_leaf_size: + continue + else: + error_left = self.mean_squared_error(X[:i], np.mean(y[:i])) + error_right = self.mean_squared_error(X[i:], np.mean(y[i:])) + error = error_left + error_right + if error < min_error: + best_split = i + min_error = error + + if best_split != 0: + left_X = X[:best_split] + left_y = y[:best_split] + right_X = X[best_split:] + right_y = y[best_split:] + + self.decision_boundary = X[best_split] + self.left = Decision_Tree(depth = self.depth - 1, min_leaf_size = self.min_leaf_size) + self.right = Decision_Tree(depth = self.depth - 1, min_leaf_size = self.min_leaf_size) + self.left.train(left_X, left_y) + self.right.train(right_X, right_y) + else: + self.prediction = np.mean(y) + + return + + def predict(self, x): + """ + predict: + @param x: a floating point value to predict the label of + the prediction function works by recursively calling the predict function + of the appropriate subtrees based on the tree's decision boundary + """ + if self.prediction is not None: + return self.prediction + elif self.left or self.right is not None: + if x >= self.decision_boundary: + return self.right.predict(x) + else: + return self.left.predict(x) + else: + print("Error: Decision tree not yet trained") + return None + +def main(): + """ + In this demonstration we're generating a sample data set from the sin function in numpy. + We then train a decision tree on the data set and use the decision tree to predict the + label of 10 different test values. Then the mean squared error over this test is displayed. + """ + X = np.arange(-1., 1., 0.005) + y = np.sin(X) + + tree = Decision_Tree(depth = 10, min_leaf_size = 10) + tree.train(X,y) + + test_cases = (np.random.rand(10) * 2) - 1 + predictions = np.array([tree.predict(x) for x in test_cases]) + avg_error = np.mean((predictions - test_cases) ** 2) + + print("Test values: " + str(test_cases)) + print("Predictions: " + str(predictions)) + print("Average error: " + str(avg_error)) + + +if __name__ == '__main__': + main() \ No newline at end of file diff --git a/machine_learning/gradient_descent.py b/machine_learning/gradient_descent.py new file mode 100644 index 000000000..1e771b072 --- /dev/null +++ b/machine_learning/gradient_descent.py @@ -0,0 +1,121 @@ +""" +Implementation of gradient descent algorithm for minimizing cost of a linear hypothesis function. +""" +import numpy + +# List of input, output pairs +train_data = (((5, 2, 3), 15), ((6, 5, 9), 25), + ((11, 12, 13), 41), ((1, 1, 1), 8), ((11, 12, 13), 41)) +test_data = (((515, 22, 13), 555), ((61, 35, 49), 150)) +parameter_vector = [2, 4, 1, 5] +m = len(train_data) +LEARNING_RATE = 0.009 + + +def _error(example_no, data_set='train'): + """ + :param data_set: train data or test data + :param example_no: example number whose error has to be checked + :return: error in example pointed by example number. + """ + return calculate_hypothesis_value(example_no, data_set) - output(example_no, data_set) + + +def _hypothesis_value(data_input_tuple): + """ + Calculates hypothesis function value for a given input + :param data_input_tuple: Input tuple of a particular example + :return: Value of hypothesis function at that point. + Note that there is an 'biased input' whose value is fixed as 1. + It is not explicitly mentioned in input data.. But, ML hypothesis functions use it. + So, we have to take care of it separately. Line 36 takes care of it. + """ + hyp_val = 0 + for i in range(len(parameter_vector) - 1): + hyp_val += data_input_tuple[i]*parameter_vector[i+1] + hyp_val += parameter_vector[0] + return hyp_val + + +def output(example_no, data_set): + """ + :param data_set: test data or train data + :param example_no: example whose output is to be fetched + :return: output for that example + """ + if data_set == 'train': + return train_data[example_no][1] + elif data_set == 'test': + return test_data[example_no][1] + + +def calculate_hypothesis_value(example_no, data_set): + """ + Calculates hypothesis value for a given example + :param data_set: test data or train_data + :param example_no: example whose hypothesis value is to be calculated + :return: hypothesis value for that example + """ + if data_set == "train": + return _hypothesis_value(train_data[example_no][0]) + elif data_set == "test": + return _hypothesis_value(test_data[example_no][0]) + + +def summation_of_cost_derivative(index, end=m): + """ + Calculates the sum of cost function derivative + :param index: index wrt derivative is being calculated + :param end: value where summation ends, default is m, number of examples + :return: Returns the summation of cost derivative + Note: If index is -1, this means we are calculating summation wrt to biased parameter. + """ + summation_value = 0 + for i in range(end): + if index == -1: + summation_value += _error(i) + else: + summation_value += _error(i)*train_data[i][0][index] + return summation_value + + +def get_cost_derivative(index): + """ + :param index: index of the parameter vector wrt to derivative is to be calculated + :return: derivative wrt to that index + Note: If index is -1, this means we are calculating summation wrt to biased parameter. + """ + cost_derivative_value = summation_of_cost_derivative(index, m)/m + return cost_derivative_value + + +def run_gradient_descent(): + global parameter_vector + # Tune these values to set a tolerance value for predicted output + absolute_error_limit = 0.000002 + relative_error_limit = 0 + j = 0 + while True: + j += 1 + temp_parameter_vector = [0, 0, 0, 0] + for i in range(0, len(parameter_vector)): + cost_derivative = get_cost_derivative(i-1) + temp_parameter_vector[i] = parameter_vector[i] - \ + LEARNING_RATE*cost_derivative + if numpy.allclose(parameter_vector, temp_parameter_vector, + atol=absolute_error_limit, rtol=relative_error_limit): + break + parameter_vector = temp_parameter_vector + print("Number of iterations:", j) + + +def test_gradient_descent(): + for i in range(len(test_data)): + print("Actual output value:", output(i, 'test')) + print("Hypothesis output:", calculate_hypothesis_value(i, 'test')) + + +if __name__ == '__main__': + run_gradient_descent() + print("\nTesting gradient descent for a linear hypothesis function.\n") + test_gradient_descent() diff --git a/machine_learning/k_means_clust.py b/machine_learning/k_means_clust.py new file mode 100644 index 000000000..c19832726 --- /dev/null +++ b/machine_learning/k_means_clust.py @@ -0,0 +1,172 @@ +'''README, Author - Anurag Kumar(mailto:anuragkumarak95@gmail.com) + +Requirements: + - sklearn + - numpy + - matplotlib + +Python: + - 3.5 + +Inputs: + - X , a 2D numpy array of features. + - k , number of clusters to create. + - initial_centroids , initial centroid values generated by utility function(mentioned in usage). + - maxiter , maximum number of iterations to process. + - heterogeneity , empty list that will be filled with hetrogeneity values if passed to kmeans func. + +Usage: + 1. define 'k' value, 'X' features array and 'hetrogeneity' empty list + + 2. create initial_centroids, + initial_centroids = get_initial_centroids( + X, + k, + seed=0 # seed value for initial centroid generation, None for randomness(default=None) + ) + + 3. find centroids and clusters using kmeans function. + + centroids, cluster_assignment = kmeans( + X, + k, + initial_centroids, + maxiter=400, + record_heterogeneity=heterogeneity, + verbose=True # whether to print logs in console or not.(default=False) + ) + + + 4. Plot the loss function, hetrogeneity values for every iteration saved in hetrogeneity list. + plot_heterogeneity( + heterogeneity, + k + ) + + 5. Have fun.. + +''' +from sklearn.metrics import pairwise_distances +import numpy as np + +TAG = 'K-MEANS-CLUST/ ' + +def get_initial_centroids(data, k, seed=None): + '''Randomly choose k data points as initial centroids''' + if seed is not None: # useful for obtaining consistent results + np.random.seed(seed) + n = data.shape[0] # number of data points + + # Pick K indices from range [0, N). + rand_indices = np.random.randint(0, n, k) + + # Keep centroids as dense format, as many entries will be nonzero due to averaging. + # As long as at least one document in a cluster contains a word, + # it will carry a nonzero weight in the TF-IDF vector of the centroid. + centroids = data[rand_indices,:] + + return centroids + +def centroid_pairwise_dist(X,centroids): + return pairwise_distances(X,centroids,metric='euclidean') + +def assign_clusters(data, centroids): + + # Compute distances between each data point and the set of centroids: + # Fill in the blank (RHS only) + distances_from_centroids = centroid_pairwise_dist(data,centroids) + + # Compute cluster assignments for each data point: + # Fill in the blank (RHS only) + cluster_assignment = np.argmin(distances_from_centroids,axis=1) + + return cluster_assignment + +def revise_centroids(data, k, cluster_assignment): + new_centroids = [] + for i in range(k): + # Select all data points that belong to cluster i. Fill in the blank (RHS only) + member_data_points = data[cluster_assignment==i] + # Compute the mean of the data points. Fill in the blank (RHS only) + centroid = member_data_points.mean(axis=0) + new_centroids.append(centroid) + new_centroids = np.array(new_centroids) + + return new_centroids + +def compute_heterogeneity(data, k, centroids, cluster_assignment): + + heterogeneity = 0.0 + for i in range(k): + + # Select all data points that belong to cluster i. Fill in the blank (RHS only) + member_data_points = data[cluster_assignment==i, :] + + if member_data_points.shape[0] > 0: # check if i-th cluster is non-empty + # Compute distances from centroid to data points (RHS only) + distances = pairwise_distances(member_data_points, [centroids[i]], metric='euclidean') + squared_distances = distances**2 + heterogeneity += np.sum(squared_distances) + + return heterogeneity + +from matplotlib import pyplot as plt +def plot_heterogeneity(heterogeneity, k): + plt.figure(figsize=(7,4)) + plt.plot(heterogeneity, linewidth=4) + plt.xlabel('# Iterations') + plt.ylabel('Heterogeneity') + plt.title('Heterogeneity of clustering over time, K={0:d}'.format(k)) + plt.rcParams.update({'font.size': 16}) + plt.show() + +def kmeans(data, k, initial_centroids, maxiter=500, record_heterogeneity=None, verbose=False): + '''This function runs k-means on given data and initial set of centroids. + maxiter: maximum number of iterations to run.(default=500) + record_heterogeneity: (optional) a list, to store the history of heterogeneity as function of iterations + if None, do not store the history. + verbose: if True, print how many data points changed their cluster labels in each iteration''' + centroids = initial_centroids[:] + prev_cluster_assignment = None + + for itr in range(maxiter): + if verbose: + print(itr, end='') + + # 1. Make cluster assignments using nearest centroids + cluster_assignment = assign_clusters(data,centroids) + + # 2. Compute a new centroid for each of the k clusters, averaging all data points assigned to that cluster. + centroids = revise_centroids(data,k, cluster_assignment) + + # Check for convergence: if none of the assignments changed, stop + if prev_cluster_assignment is not None and \ + (prev_cluster_assignment==cluster_assignment).all(): + break + + # Print number of new assignments + if prev_cluster_assignment is not None: + num_changed = np.sum(prev_cluster_assignment!=cluster_assignment) + if verbose: + print(' {0:5d} elements changed their cluster assignment.'.format(num_changed)) + + # Record heterogeneity convergence metric + if record_heterogeneity is not None: + # YOUR CODE HERE + score = compute_heterogeneity(data,k,centroids,cluster_assignment) + record_heterogeneity.append(score) + + prev_cluster_assignment = cluster_assignment[:] + + return centroids, cluster_assignment + +# Mock test below +if False: # change to true to run this test case. + import sklearn.datasets as ds + dataset = ds.load_iris() + k = 3 + heterogeneity = [] + initial_centroids = get_initial_centroids(dataset['data'], k, seed=0) + centroids, cluster_assignment = kmeans(dataset['data'], k, initial_centroids, maxiter=400, + record_heterogeneity=heterogeneity, verbose=True) + plot_heterogeneity(heterogeneity, k) \ No newline at end of file diff --git a/machine_learning/linear_regression.py b/machine_learning/linear_regression.py new file mode 100644 index 000000000..fd33c3580 --- /dev/null +++ b/machine_learning/linear_regression.py @@ -0,0 +1,108 @@ +""" +Linear regression is the most basic type of regression commonly used for +predictive analysis. The idea is preety simple, we have a dataset and we have +a feature's associated with it. The Features should be choose very cautiously +as they determine, how much our model will be able to make future predictions. +We try to set these Feature weights, over many iterations, so that they best +fits our dataset. In this particular code, i had used a CSGO dataset (ADR vs +Rating). We try to best fit a line through dataset and estimate the parameters. +""" + +import requests +import numpy as np + + +def collect_dataset(): + """ Collect dataset of CSGO + The dataset contains ADR vs Rating of a Player + :return : dataset obtained from the link, as matrix + """ + response = requests.get('https://raw.githubusercontent.com/yashLadha/' + + 'The_Math_of_Intelligence/master/Week1/ADRvs' + + 'Rating.csv') + lines = response.text.splitlines() + data = [] + for item in lines: + item = item.split(',') + data.append(item) + data.pop(0) # This is for removing the labels from the list + dataset = np.matrix(data) + return dataset + + +def run_steep_gradient_descent(data_x, data_y, + len_data, alpha, theta): + """ Run steep gradient descent and updates the Feature vector accordingly_ + :param data_x : contains the dataset + :param data_y : contains the output associated with each data-entry + :param len_data : length of the data_ + :param alpha : Learning rate of the model + :param theta : Feature vector (weight's for our model) + ;param return : Updated Feature's, using + curr_features - alpha_ * gradient(w.r.t. feature) + """ + n = len_data + + prod = np.dot(theta, data_x.transpose()) + prod -= data_y.transpose() + sum_grad = np.dot(prod, data_x) + theta = theta - (alpha / n) * sum_grad + return theta + + +def sum_of_square_error(data_x, data_y, len_data, theta): + """ Return sum of square error for error calculation + :param data_x : contains our dataset + :param data_y : contains the output (result vector) + :param len_data : len of the dataset + :param theta : contains the feature vector + :return : sum of square error computed from given feature's + """ + error = 0.0 + prod = np.dot(theta, data_x.transpose()) + prod -= data_y.transpose() + sum_elem = np.sum(np.square(prod)) + error = sum_elem / (2 * len_data) + return error + + +def run_linear_regression(data_x, data_y): + """ Implement Linear regression over the dataset + :param data_x : contains our dataset + :param data_y : contains the output (result vector) + :return : feature for line of best fit (Feature vector) + """ + iterations = 100000 + alpha = 0.0001550 + + no_features = data_x.shape[1] + len_data = data_x.shape[0] - 1 + + theta = np.zeros((1, no_features)) + + for i in range(0, iterations): + theta = run_steep_gradient_descent(data_x, data_y, + len_data, alpha, theta) + error = sum_of_square_error(data_x, data_y, len_data, theta) + print('At Iteration %d - Error is %.5f ' % (i + 1, error)) + + return theta + + +def main(): + """ Driver function """ + data = collect_dataset() + + len_data = data.shape[0] + data_x = np.c_[np.ones(len_data), data[:, :-1]].astype(float) + data_y = data[:, -1].astype(float) + + theta = run_linear_regression(data_x, data_y) + len_result = theta.shape[1] + print('Resultant Feature vector : ') + for i in range(0, len_result): + print('%.5f' % (theta[0, i])) + + +if __name__ == '__main__': + main() diff --git a/machine_learning/perceptron.py b/machine_learning/perceptron.py new file mode 100644 index 000000000..0cd89df16 --- /dev/null +++ b/machine_learning/perceptron.py @@ -0,0 +1,123 @@ +''' + + Perceptron + w = w + N * (d(k) - y) * x(k) + + Using perceptron network for oil analysis, + with Measuring of 3 parameters that represent chemical characteristics we can classify the oil, in p1 or p2 + p1 = -1 + p2 = 1 + +''' + +import random + + +class Perceptron: + def __init__(self, sample, exit, learn_rate=0.01, epoch_number=1000, bias=-1): + self.sample = sample + self.exit = exit + self.learn_rate = learn_rate + self.epoch_number = epoch_number + self.bias = bias + self.number_sample = len(sample) + self.col_sample = len(sample[0]) + self.weight = [] + + def trannig(self): + for sample in self.sample: + sample.insert(0, self.bias) + + for i in range(self.col_sample): + self.weight.append(random.random()) + + self.weight.insert(0, self.bias) + + epoch_count = 0 + + while True: + erro = False + for i in range(self.number_sample): + u = 0 + for j in range(self.col_sample + 1): + u = u + self.weight[j] * self.sample[i][j] + y = self.sign(u) + if y != self.exit[i]: + + for j in range(self.col_sample + 1): + + self.weight[j] = self.weight[j] + self.learn_rate * (self.exit[i] - y) * self.sample[i][j] + erro = True + #print('Epoch: \n',epoch_count) + epoch_count = epoch_count + 1 + # if you want controle the epoch or just by erro + if erro == False: + print('\nEpoch:\n',epoch_count) + print('------------------------\n') + #if epoch_count > self.epoch_number or not erro: + break + + def sort(self, sample): + sample.insert(0, self.bias) + u = 0 + for i in range(self.col_sample + 1): + u = u + self.weight[i] * sample[i] + + y = self.sign(u) + + if y == -1: + print('Sample: ', sample) + print('classification: P1') + else: + print('Sample: ', sample) + print('classification: P2') + + def sign(self, u): + return 1 if u >= 0 else -1 + + +samples = [ + [-0.6508, 0.1097, 4.0009], + [-1.4492, 0.8896, 4.4005], + [2.0850, 0.6876, 12.0710], + [0.2626, 1.1476, 7.7985], + [0.6418, 1.0234, 7.0427], + [0.2569, 0.6730, 8.3265], + [1.1155, 0.6043, 7.4446], + [0.0914, 0.3399, 7.0677], + [0.0121, 0.5256, 4.6316], + [-0.0429, 0.4660, 5.4323], + [0.4340, 0.6870, 8.2287], + [0.2735, 1.0287, 7.1934], + [0.4839, 0.4851, 7.4850], + [0.4089, -0.1267, 5.5019], + [1.4391, 0.1614, 8.5843], + [-0.9115, -0.1973, 2.1962], + [0.3654, 1.0475, 7.4858], + [0.2144, 0.7515, 7.1699], + [0.2013, 1.0014, 6.5489], + [0.6483, 0.2183, 5.8991], + [-0.1147, 0.2242, 7.2435], + [-0.7970, 0.8795, 3.8762], + [-1.0625, 0.6366, 2.4707], + [0.5307, 0.1285, 5.6883], + [-1.2200, 0.7777, 1.7252], + [0.3957, 0.1076, 5.6623], + [-0.1013, 0.5989, 7.1812], + [2.4482, 0.9455, 11.2095], + [2.0149, 0.6192, 10.9263], + [0.2012, 0.2611, 5.4631] + +] + +exit = [-1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1] + +network = Perceptron(sample=samples, exit = exit, learn_rate=0.01, epoch_number=1000, bias=-1) + +network.trannig() + +while True: + sample = [] + for i in range(3): + sample.insert(i, float(input('value: '))) + network.sort(sample) \ No newline at end of file diff --git a/machine_learning/scoring_functions.py b/machine_learning/scoring_functions.py new file mode 100644 index 000000000..4204716cd --- /dev/null +++ b/machine_learning/scoring_functions.py @@ -0,0 +1,63 @@ +import numpy + +""" Here I implemented the scoring functions. + MAE, MSE, RMSE, RMSLE are included. + + Those are used for calculating differences between + predicted values and actual values. + + Metrics are slightly differentiated. Sometimes squared, rooted, + even log is used. + + Using log and roots can be perceived as tools for penalizing big + erors. However, using appropriate metrics depends on the situations, + and types of data +""" + +#Mean Absolute Error +def mae(predict, actual): + predict = np.array(predict) + actual = np.array(actual) + + difference = abs(predict - actual) + score = difference.mean() + + return score + +#Mean Squared Error +def mse(predict, actual): + predict = np.array(predict) + actual = np.array(actual) + + difference = predict - actual + square_diff = np.square(difference) + + score = square_diff.mean() + return score + +#Root Mean Squared Error +def rmse(predict, actual): + predict = np.array(predict) + actual = np.array(actual) + + difference = predict - actual + square_diff = np.square(dfference) + mean_square_diff = square_diff.mean() + score = np.sqrt(mean_square_diff) + return score + +#Root Mean Square Logarithmic Error +def rmsle(predict, actual): + predict = np.array(predict) + actual = np.array(actual) + + log_predict = np.log(predict+1) + log_actual = np.log(actual+1) + + difference = log_predict - log_actual + square_diff = np.square(difference) + mean_square_diff = square_diff.mean() + + score = np.sqrt(mean_square_diff) + + return score diff --git a/other/Dictionary.txt b/other/Dictionary.txt new file mode 100644 index 000000000..14528efe8 --- /dev/null +++ b/other/Dictionary.txt @@ -0,0 +1,45333 @@ +AARHUS +AARON +ABABA +ABACK +ABAFT +ABANDON +ABANDONED +ABANDONING +ABANDONMENT +ABANDONS +ABASE +ABASED +ABASEMENT +ABASEMENTS +ABASES +ABASH +ABASHED +ABASHES +ABASHING +ABASING +ABATE +ABATED +ABATEMENT +ABATEMENTS +ABATER +ABATES +ABATING +ABBA +ABBE +ABBEY +ABBEYS +ABBOT +ABBOTS +ABBOTT +ABBREVIATE +ABBREVIATED +ABBREVIATES +ABBREVIATING +ABBREVIATION +ABBREVIATIONS +ABBY +ABDOMEN +ABDOMENS +ABDOMINAL +ABDUCT +ABDUCTED +ABDUCTION +ABDUCTIONS +ABDUCTOR +ABDUCTORS +ABDUCTS +ABE +ABED +ABEL +ABELIAN +ABELSON +ABERDEEN +ABERNATHY +ABERRANT +ABERRATION +ABERRATIONS +ABET +ABETS +ABETTED +ABETTER +ABETTING +ABEYANCE +ABHOR +ABHORRED +ABHORRENT +ABHORRER +ABHORRING 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+ZOMBA +ZONAL +ZONALLY +ZONE +ZONED +ZONES +ZONING +ZOO +ZOOLOGICAL +ZOOLOGICALLY +ZOOM +ZOOMS +ZOOS +ZORN +ZOROASTER +ZOROASTRIAN +ZULU +ZULUS +ZURICH \ No newline at end of file diff --git a/other/FindingPrimes.py b/other/FindingPrimes.py new file mode 100644 index 000000000..3cb10f701 --- /dev/null +++ b/other/FindingPrimes.py @@ -0,0 +1,18 @@ +''' +-The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or equal to a given value. +-Illustration: https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif +''' +from math import sqrt +def SOE(n): + check = round(sqrt(n)) #Need not check for multiples past the square root of n + + sieve = [False if i <2 else True for i in range(n+1)] #Set every index to False except for index 0 and 1 + + for i in range(2, check): + if(sieve[i] == True): #If i is a prime + for j in range(i+i, n+1, i): #Step through the list in increments of i(the multiples of the prime) + sieve[j] = False #Sets every multiple of i to False + + for i in range(n+1): + if(sieve[i] == True): + print(i, end=" ") diff --git a/other/LinearCongruentialGenerator.py b/other/LinearCongruentialGenerator.py new file mode 100644 index 000000000..b1eaa6119 --- /dev/null +++ b/other/LinearCongruentialGenerator.py @@ -0,0 +1,34 @@ +__author__ = "Tobias Carryer" + +from time import time + +class LinearCongruentialGenerator(object): + """ + A pseudorandom number generator. + """ + + def __init__( self, multiplier, increment, modulo, seed=int(time()) ): + """ + These parameters are saved and used when nextNumber() is called. + + modulo is the largest number that can be generated (exclusive). The most + efficent values are powers of 2. 2^32 is a common value. + """ + self.multiplier = multiplier + self.increment = increment + self.modulo = modulo + self.seed = seed + + def next_number( self ): + """ + The smallest number that can be generated is zero. + The largest number that can be generated is modulo-1. modulo is set in the constructor. + """ + self.seed = (self.multiplier * self.seed + self.increment) % self.modulo + return self.seed + +if __name__ == "__main__": + # Show the LCG in action. + lcg = LinearCongruentialGenerator(1664525, 1013904223, 2<<31) + while True : + print lcg.next_number() \ No newline at end of file diff --git a/other/anagrams.py b/other/anagrams.py new file mode 100644 index 000000000..6150ea8e6 --- /dev/null +++ b/other/anagrams.py @@ -0,0 +1,28 @@ +import collections, pprint, time, os + +start_time = time.time() +print('creating word list...') +path = os.path.split(os.path.realpath(__file__)) +word_list = sorted(list(set([word.strip().lower() for word in open(path[0] + '/words')]))) + +def signature(word): + return ''.join(sorted(word)) + +word_bysig = collections.defaultdict(list) +for word in word_list: + word_bysig[signature(word)].append(word) + +def anagram(myword): + return word_bysig[signature(myword)] + +print('finding anagrams...') +all_anagrams = {word: anagram(word) + for word in word_list if len(anagram(word)) > 1} + +print('writing anagrams to file...') +with open('anagrams.txt', 'w') as file: + file.write('all_anagrams = ') + file.write(pprint.pformat(all_anagrams)) + +total_time = round(time.time() - start_time, 2) +print('Done [', total_time, 'seconds ]') diff --git a/other/binary_exponentiation.py b/other/binary_exponentiation.py new file mode 100644 index 000000000..1a30fb8fd --- /dev/null +++ b/other/binary_exponentiation.py @@ -0,0 +1,49 @@ +""" +* Binary Exponentiation for Powers +* This is a method to find a^b in a time complexity of O(log b) +* This is one of the most commonly used methods of finding powers. +* Also useful in cases where solution to (a^b)%c is required, +* where a,b,c can be numbers over the computers calculation limits. +* Done using iteration, can also be done using recursion + +* @author chinmoy159 +* @version 1.0 dated 10/08/2017 +""" + + +def b_expo(a, b): + res = 1 + while b > 0: + if b&1: + res *= a + + a *= a + b >>= 1 + + return res + + +def b_expo_mod(a, b, c): + res = 1 + while b > 0: + if b&1: + res = ((res%c) * (a%c)) % c + + a *= a + b >>= 1 + + return res + +""" +* Wondering how this method works ! +* It's pretty simple. +* Let's say you need to calculate a ^ b +* RULE 1 : a ^ b = (a*a) ^ (b/2) ---- example : 4 ^ 4 = (4*4) ^ (4/2) = 16 ^ 2 +* RULE 2 : IF b is ODD, then ---- a ^ b = a * (a ^ (b - 1)) :: where (b - 1) is even. +* Once b is even, repeat the process to get a ^ b +* Repeat the process till b = 1 OR b = 0, because a^1 = a AND a^0 = 1 +* +* As far as the modulo is concerned, +* the fact : (a*b) % c = ((a%c) * (b%c)) % c +* Now apply RULE 1 OR 2 whichever is required. +""" diff --git a/other/binary_exponentiation_2.py b/other/binary_exponentiation_2.py new file mode 100644 index 000000000..217a616c9 --- /dev/null +++ b/other/binary_exponentiation_2.py @@ -0,0 +1,50 @@ +""" +* Binary Exponentiation with Multiplication +* This is a method to find a*b in a time complexity of O(log b) +* This is one of the most commonly used methods of finding result of multiplication. +* Also useful in cases where solution to (a*b)%c is required, +* where a,b,c can be numbers over the computers calculation limits. +* Done using iteration, can also be done using recursion + +* @author chinmoy159 +* @version 1.0 dated 10/08/2017 +""" + + +def b_expo(a, b): + res = 0 + while b > 0: + if b&1: + res += a + + a += a + b >>= 1 + + return res + + +def b_expo_mod(a, b, c): + res = 0 + while b > 0: + if b&1: + res = ((res%c) + (a%c)) % c + + a += a + b >>= 1 + + return res + + +""" +* Wondering how this method works ! +* It's pretty simple. +* Let's say you need to calculate a ^ b +* RULE 1 : a * b = (a+a) * (b/2) ---- example : 4 * 4 = (4+4) * (4/2) = 8 * 2 +* RULE 2 : IF b is ODD, then ---- a * b = a + (a * (b - 1)) :: where (b - 1) is even. +* Once b is even, repeat the process to get a * b +* Repeat the process till b = 1 OR b = 0, because a*1 = a AND a*0 = 0 +* +* As far as the modulo is concerned, +* the fact : (a+b) % c = ((a%c) + (b%c)) % c +* Now apply RULE 1 OR 2, whichever is required. +""" diff --git a/other/detecting_english_programmatically.py b/other/detecting_english_programmatically.py new file mode 100644 index 000000000..305174e31 --- /dev/null +++ b/other/detecting_english_programmatically.py @@ -0,0 +1,55 @@ +import os + +UPPERLETTERS = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' +LETTERS_AND_SPACE = UPPERLETTERS + UPPERLETTERS.lower() + ' \t\n' + +def loadDictionary(): + path = os.path.split(os.path.realpath(__file__)) + dictionaryFile = open(path[0] + '/Dictionary.txt') + englishWords = {} + for word in dictionaryFile.read().split('\n'): + englishWords[word] = None + dictionaryFile.close() + return englishWords + +ENGLISH_WORDS = loadDictionary() + +def getEnglishCount(message): + message = message.upper() + message = removeNonLetters(message) + possibleWords = message.split() + + if possibleWords == []: + return 0.0 + + matches = 0 + for word in possibleWords: + if word in ENGLISH_WORDS: + matches += 1 + + return float(matches) / len(possibleWords) + +def removeNonLetters(message): + lettersOnly = [] + for symbol in message: + if symbol in LETTERS_AND_SPACE: + lettersOnly.append(symbol) + return ''.join(lettersOnly) + +def isEnglish(message, wordPercentage = 20, letterPercentage = 85): + """ + >>> isEnglish('Hello World') + True + + >>> isEnglish('llold HorWd') + False + """ + wordsMatch = getEnglishCount(message) * 100 >= wordPercentage + numLetters = len(removeNonLetters(message)) + messageLettersPercentage = (float(numLetters) / len(message)) * 100 + lettersMatch = messageLettersPercentage >= letterPercentage + return wordsMatch and lettersMatch + + +import doctest +doctest.testmod() diff --git a/other/euclidean_gcd.py b/other/euclidean_gcd.py new file mode 100644 index 000000000..13378379f --- /dev/null +++ b/other/euclidean_gcd.py @@ -0,0 +1,18 @@ +# https://en.wikipedia.org/wiki/Euclidean_algorithm + +def euclidean_gcd(a, b): + while b: + t = b + b = a % b + a = t + return a + +def main(): + print("GCD(3, 5) = " + str(euclidean_gcd(3, 5))) + print("GCD(5, 3) = " + str(euclidean_gcd(5, 3))) + print("GCD(1, 3) = " + str(euclidean_gcd(1, 3))) + print("GCD(3, 6) = " + str(euclidean_gcd(3, 6))) + print("GCD(6, 3) = " + str(euclidean_gcd(6, 3))) + +if __name__ == '__main__': + main() diff --git a/other/frequency_finder.py b/other/frequency_finder.py new file mode 100644 index 000000000..6264b25bf --- /dev/null +++ b/other/frequency_finder.py @@ -0,0 +1,68 @@ +# Frequency Finder + +# frequency taken from http://en.wikipedia.org/wiki/Letter_frequency +englishLetterFreq = {'E': 12.70, 'T': 9.06, 'A': 8.17, 'O': 7.51, 'I': 6.97, + 'N': 6.75, 'S': 6.33, 'H': 6.09, 'R': 5.99, 'D': 4.25, + 'L': 4.03, 'C': 2.78, 'U': 2.76, 'M': 2.41, 'W': 2.36, + 'F': 2.23, 'G': 2.02, 'Y': 1.97, 'P': 1.93, 'B': 1.29, + 'V': 0.98, 'K': 0.77, 'J': 0.15, 'X': 0.15, 'Q': 0.10, + 'Z': 0.07} +ETAOIN = 'ETAOINSHRDLCUMWFGYPBVKJXQZ' +LETTERS = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' + +def getLetterCount(message): + letterCount = {'A': 0, 'B': 0, 'C': 0, 'D': 0, 'E': 0, 'F': 0, 'G': 0, 'H': 0, + 'I': 0, 'J': 0, 'K': 0, 'L': 0, 'M': 0, 'N': 0, 'O': 0, 'P': 0, + 'Q': 0, 'R': 0, 'S': 0, 'T': 0, 'U': 0, 'V': 0, 'W': 0, 'X': 0, + 'Y': 0, 'Z': 0} + for letter in message.upper(): + if letter in LETTERS: + letterCount[letter] += 1 + + return letterCount + +def getItemAtIndexZero(x): + return x[0] + +def getFrequencyOrder(message): + letterToFreq = getLetterCount(message) + freqToLetter = {} + for letter in LETTERS: + if letterToFreq[letter] not in freqToLetter: + freqToLetter[letterToFreq[letter]] = [letter] + else: + freqToLetter[letterToFreq[letter]].append(letter) + + for freq in freqToLetter: + freqToLetter[freq].sort(key = ETAOIN.find, reverse = True) + freqToLetter[freq] = ''.join(freqToLetter[freq]) + + freqPairs = list(freqToLetter.items()) + freqPairs.sort(key = getItemAtIndexZero, reverse = True) + + freqOrder = [] + for freqPair in freqPairs: + freqOrder.append(freqPair[1]) + + return ''.join(freqOrder) + +def englishFreqMatchScore(message): + ''' + >>> englishFreqMatchScore('Hello World') + 1 + ''' + freqOrder = getFrequencyOrder(message) + matchScore = 0 + for commonLetter in ETAOIN[:6]: + if commonLetter in freqOrder[:6]: + matchScore += 1 + + for uncommonLetter in ETAOIN[-6:]: + if uncommonLetter in freqOrder[-6:]: + matchScore += 1 + + return matchScore + +if __name__ == '__main__': + import doctest + doctest.testmod() diff --git a/other/nested_brackets.py b/other/nested_brackets.py new file mode 100644 index 000000000..f486190f4 --- /dev/null +++ b/other/nested_brackets.py @@ -0,0 +1,49 @@ +''' +The nested brackets problem is a problem that determines if a sequence of +brackets are properly nested. A sequence of brackets s is considered properly nested +if any of the following conditions are true: + + - s is empty + - s has the form (U) or [U] or {U} where U is a properly nested string + - s has the form VW where V and W are properly nested strings + +For example, the string "()()[()]" is properly nested but "[(()]" is not. + +The function called is_balanced takes as input a string S which is a sequence of brackets and +returns true if S is nested and false otherwise. + +''' + + +def is_balanced(S): + + stack = [] + open_brackets = set({'(', '[', '{'}) + closed_brackets = set({')', ']', '}'}) + open_to_closed = dict({'{':'}', '[':']', '(':')'}) + + for i in range(len(S)): + + if S[i] in open_brackets: + stack.append(S[i]) + + elif S[i] in closed_brackets: + if len(stack) == 0 or (len(stack) > 0 and open_to_closed[stack.pop()] != S[i]): + return False + + return len(stack) == 0 + + +def main(): + + S = input("Enter sequence of brackets: ") + + if is_balanced(S): + print(S, "is balanced") + + else: + print(S, "is not balanced") + + +if __name__ == "__main__": + main() diff --git a/other/password_generator.py b/other/password_generator.py new file mode 100644 index 000000000..10ba77088 --- /dev/null +++ b/other/password_generator.py @@ -0,0 +1,14 @@ +import string +import random + +letters = [letter for letter in string.ascii_letters] +digits = [digit for digit in string.digits] +symbols = [symbol for symbol in string.punctuation] +chars = letters + digits + symbols +random.shuffle(chars) + +min_length = 8 +max_length = 16 +password = ''.join(random.choice(chars) for x in range(random.randint(min_length, max_length))) +print('Password: ' + password) +print('[ If you are thinking of using this passsword, You better save it. ]') diff --git a/other/tower_of_hanoi.py b/other/tower_of_hanoi.py new file mode 100644 index 000000000..de0cb6218 --- /dev/null +++ b/other/tower_of_hanoi.py @@ -0,0 +1,25 @@ +def moveTower(height, fromPole, toPole, withPole): + ''' + >>> moveTower(3, 'A', 'B', 'C') + moving disk from A to B + moving disk from A to C + moving disk from B to C + moving disk from A to B + moving disk from C to A + moving disk from C to B + moving disk from A to B + ''' + if height >= 1: + moveTower(height-1, fromPole, withPole, toPole) + moveDisk(fromPole, toPole) + moveTower(height-1, withPole, toPole, fromPole) + +def moveDisk(fp,tp): + print('moving disk from', fp, 'to', tp) + +def main(): + height = int(input('Height of hanoi: ')) + moveTower(height, 'A', 'B', 'C') + +if __name__ == '__main__': + main() diff --git a/other/word_patterns.py b/other/word_patterns.py new file mode 100644 index 000000000..827c9fa8b --- /dev/null +++ b/other/word_patterns.py @@ -0,0 +1,38 @@ +import pprint, time + +def getWordPattern(word): + word = word.upper() + nextNum = 0 + letterNums = {} + wordPattern = [] + + for letter in word: + if letter not in letterNums: + letterNums[letter] = str(nextNum) + nextNum += 1 + wordPattern.append(letterNums[letter]) + return '.'.join(wordPattern) + +def main(): + startTime = time.time() + allPatterns = {} + + with open('Dictionary.txt') as fo: + wordList = fo.read().split('\n') + + for word in wordList: + pattern = getWordPattern(word) + + if pattern not in allPatterns: + allPatterns[pattern] = [word] + else: + allPatterns[pattern].append(word) + + with open('Word Patterns.txt', 'w') as fo: + fo.write(pprint.pformat(allPatterns)) + + totalTime = round(time.time() - startTime, 2) + print('Done! [', totalTime, 'seconds ]') + +if __name__ == '__main__': + main() diff --git a/other/words b/other/words new file mode 100644 index 000000000..4be557ed6 --- /dev/null +++ b/other/words @@ -0,0 +1,235886 @@ +A +a +aa +aal +aalii +aam +Aani +aardvark +aardwolf +Aaron +Aaronic +Aaronical +Aaronite +Aaronitic +Aaru +Ab +aba +Ababdeh +Ababua +abac +abaca +abacate +abacay +abacinate +abacination +abaciscus +abacist +aback +abactinal +abactinally +abaction +abactor +abaculus +abacus +Abadite +abaff +abaft +abaisance +abaiser +abaissed +abalienate +abalienation +abalone +Abama +abampere +abandon +abandonable +abandoned +abandonedly +abandonee +abandoner +abandonment +Abanic +Abantes +abaptiston +Abarambo +Abaris +abarthrosis +abarticular +abarticulation +abas +abase +abased +abasedly +abasedness +abasement +abaser +Abasgi +abash +abashed +abashedly +abashedness +abashless +abashlessly +abashment +abasia +abasic +abask +Abassin +abastardize +abatable +abate +abatement +abater +abatis +abatised 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+zygomaticofrontal +zygomaticomaxillary +zygomaticoorbital +zygomaticosphenoid +zygomaticotemporal +zygomaticum +zygomaticus +zygomaxillare +zygomaxillary +zygomorphic +zygomorphism +zygomorphous +zygomycete +Zygomycetes +zygomycetous +zygon +zygoneure +zygophore +zygophoric +Zygophyceae +zygophyceous +Zygophyllaceae +zygophyllaceous +Zygophyllum +zygophyte +zygopleural +Zygoptera +Zygopteraceae +zygopteran +zygopterid +Zygopterides +Zygopteris +zygopteron +zygopterous +Zygosaccharomyces +zygose +zygosis +zygosperm +zygosphenal +zygosphene +zygosphere +zygosporange +zygosporangium +zygospore +zygosporic +zygosporophore +zygostyle +zygotactic +zygotaxis +zygote +zygotene +zygotic +zygotoblast +zygotoid +zygotomere +zygous +zygozoospore +zymase +zyme +zymic +zymin +zymite +zymogen +zymogene +zymogenesis +zymogenic +zymogenous +zymoid +zymologic +zymological +zymologist +zymology +zymolyis +zymolysis +zymolytic +zymome +zymometer +zymomin +zymophore +zymophoric +zymophosphate +zymophyte +zymoplastic +zymoscope +zymosimeter +zymosis +zymosterol +zymosthenic +zymotechnic +zymotechnical +zymotechnics +zymotechny +zymotic +zymotically +zymotize +zymotoxic +zymurgy +Zyrenian +Zyrian +Zyryan +zythem +Zythia +zythum +Zyzomys +Zyzzogeton diff --git a/searches/binary_search.py b/searches/binary_search.py new file mode 100644 index 000000000..c54aa96a1 --- /dev/null +++ b/searches/binary_search.py @@ -0,0 +1,162 @@ +""" +This is pure python implementation of binary search algorithm + +For doctests run following command: +python -m doctest -v binary_search.py +or +python3 -m doctest -v binary_search.py + +For manual testing run: +python binary_search.py +""" +from __future__ import print_function +import bisect + + +def binary_search(sorted_collection, item): + """Pure implementation of binary search algorithm in Python + + Be careful collection must be sorted, otherwise result will be + unpredictable + + :param sorted_collection: some sorted collection with comparable items + :param item: item value to search + :return: index of found item or None if item is not found + + Examples: + >>> binary_search([0, 5, 7, 10, 15], 0) + 0 + + >>> binary_search([0, 5, 7, 10, 15], 15) + 4 + + >>> binary_search([0, 5, 7, 10, 15], 5) + 1 + + >>> binary_search([0, 5, 7, 10, 15], 6) + + """ + left = 0 + right = len(sorted_collection) - 1 + + while left <= right: + midpoint = (left + right) // 2 + current_item = sorted_collection[midpoint] + if current_item == item: + return midpoint + else: + if item < current_item: + right = midpoint - 1 + else: + left = midpoint + 1 + return None + + +def binary_search_std_lib(sorted_collection, item): + """Pure implementation of binary search algorithm in Python using stdlib + + Be careful collection must be sorted, otherwise result will be + unpredictable + + :param sorted_collection: some sorted collection with comparable items + :param item: item value to search + :return: index of found item or None if item is not found + + Examples: + >>> binary_search_std_lib([0, 5, 7, 10, 15], 0) + 0 + + >>> binary_search_std_lib([0, 5, 7, 10, 15], 15) + 4 + + >>> binary_search_std_lib([0, 5, 7, 10, 15], 5) + 1 + + >>> binary_search_std_lib([0, 5, 7, 10, 15], 6) + + """ + index = bisect.bisect_left(sorted_collection, item) + if index != len(sorted_collection) and sorted_collection[index] == item: + return index + return None + +def binary_search_by_recursion(sorted_collection, item, left, right): + + """Pure implementation of binary search algorithm in Python by recursion + + Be careful collection must be sorted, otherwise result will be + unpredictable + First recursion should be started with left=0 and right=(len(sorted_collection)-1) + + :param sorted_collection: some sorted collection with comparable items + :param item: item value to search + :return: index of found item or None if item is not found + + Examples: + >>> binary_search_std_lib([0, 5, 7, 10, 15], 0) + 0 + + >>> binary_search_std_lib([0, 5, 7, 10, 15], 15) + 4 + + >>> binary_search_std_lib([0, 5, 7, 10, 15], 5) + 1 + + >>> binary_search_std_lib([0, 5, 7, 10, 15], 6) + + """ + midpoint = left + (right - left) // 2 + + if sorted_collection[midpoint] == item: + return midpoint + elif sorted_collection[midpoint] > item: + return binary_search_by_recursion(sorted_collection, item, left, midpoint-1) + else: + return binary_search_by_recursion(sorted_collection, item, midpoint+1, right) + +def __assert_sorted(collection): + """Check if collection is sorted, if not - raises :py:class:`ValueError` + + :param collection: collection + :return: True if collection is sorted + :raise: :py:class:`ValueError` if collection is not sorted + + Examples: + >>> __assert_sorted([0, 1, 2, 4]) + True + + >>> __assert_sorted([10, -1, 5]) + Traceback (most recent call last): + ... + ValueError: Collection must be sorted + """ + if collection != sorted(collection): + raise ValueError('Collection must be sorted') + return True + + +if __name__ == '__main__': + import sys + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by comma:\n') + collection = [int(item) for item in user_input.split(',')] + try: + __assert_sorted(collection) + except ValueError: + sys.exit('Sequence must be sorted to apply binary search') + + target_input = input_function( + 'Enter a single number to be found in the list:\n' + ) + target = int(target_input) + result = binary_search(collection, target) + if result is not None: + print('{} found at positions: {}'.format(target, result)) + else: + print('Not found') diff --git a/searches/interpolation_search.py b/searches/interpolation_search.py new file mode 100644 index 000000000..068d9c554 --- /dev/null +++ b/searches/interpolation_search.py @@ -0,0 +1,102 @@ +""" +This is pure python implementation of interpolation search algorithm +""" +from __future__ import print_function +import bisect + + +def interpolation_search(sorted_collection, item): + """Pure implementation of interpolation search algorithm in Python + Be careful collection must be sorted, otherwise result will be + unpredictable + :param sorted_collection: some sorted collection with comparable items + :param item: item value to search + :return: index of found item or None if item is not found + """ + left = 0 + right = len(sorted_collection) - 1 + + while left <= right: + point = left + ((item - sorted_collection[left]) * (right - left)) // (sorted_collection[right] - sorted_collection[left]) + + #out of range check + if point<0 or point>=len(sorted_collection): + return None + + current_item = sorted_collection[point] + if current_item == item: + return point + else: + if item < current_item: + right = point - 1 + else: + left = point + 1 + return None + + +def interpolation_search_by_recursion(sorted_collection, item, left, right): + + """Pure implementation of interpolation search algorithm in Python by recursion + Be careful collection must be sorted, otherwise result will be + unpredictable + First recursion should be started with left=0 and right=(len(sorted_collection)-1) + :param sorted_collection: some sorted collection with comparable items + :param item: item value to search + :return: index of found item or None if item is not found + """ + point = left + ((item - sorted_collection[left]) * (right - left)) // (sorted_collection[right] - sorted_collection[left]) + + #out of range check + if point<0 or point>=len(sorted_collection): + return None + + if sorted_collection[point] == item: + return point + elif sorted_collection[point] > item: + return interpolation_search_by_recursion(sorted_collection, item, left, point-1) + else: + return interpolation_search_by_recursion(sorted_collection, item, point+1, right) + +def __assert_sorted(collection): + """Check if collection is sorted, if not - raises :py:class:`ValueError` + :param collection: collection + :return: True if collection is sorted + :raise: :py:class:`ValueError` if collection is not sorted + Examples: + >>> __assert_sorted([0, 1, 2, 4]) + True + >>> __assert_sorted([10, -1, 5]) + Traceback (most recent call last): + ... + ValueError: Collection must be sorted + """ + if collection != sorted(collection): + raise ValueError('Collection must be sorted') + return True + + +if __name__ == '__main__': + import sys + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by comma:\n') + collection = [int(item) for item in user_input.split(',')] + try: + __assert_sorted(collection) + except ValueError: + sys.exit('Sequence must be sorted to apply interpolation search') + + target_input = input_function( + 'Enter a single number to be found in the list:\n' + ) + target = int(target_input) + result = interpolation_search(collection, target) + if result is not None: + print('{} found at positions: {}'.format(target, result)) + else: + print('Not found') \ No newline at end of file diff --git a/searches/linear_search.py b/searches/linear_search.py new file mode 100644 index 000000000..ce8098b1a --- /dev/null +++ b/searches/linear_search.py @@ -0,0 +1,62 @@ +""" +This is pure python implementation of linear search algorithm + +For doctests run following command: +python -m doctest -v linear_search.py +or +python3 -m doctest -v linear_search.py + +For manual testing run: +python linear_search.py +""" +from __future__ import print_function + + +def linear_search(sequence, target): + """Pure implementation of linear search algorithm in Python + + :param sequence: some sorted collection with comparable items + :param target: item value to search + :return: index of found item or None if item is not found + + Examples: + >>> linear_search([0, 5, 7, 10, 15], 0) + 0 + + >>> linear_search([0, 5, 7, 10, 15], 15) + 4 + + >>> linear_search([0, 5, 7, 10, 15], 5) + 1 + + >>> linear_search([0, 5, 7, 10, 15], 6) + + """ + for index, item in enumerate(sequence): + if item == target: + return index + return None + + +if __name__ == '__main__': + import sys + + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by coma:\n') + sequence = [int(item) for item in user_input.split(',')] + + target_input = input_function( + 'Enter a single number to be found in the list:\n' + ) + target = int(target_input) + result = linear_search(sequence, target) + if result is not None: + print('{} found at positions: {}'.format(target, result)) + else: + print('Not found') diff --git a/searches/quick_select.py b/searches/quick_select.py new file mode 100644 index 000000000..e5e2ce99c --- /dev/null +++ b/searches/quick_select.py @@ -0,0 +1,47 @@ +import collections +import sys +import random +import time +import math +""" +A python implementation of the quick select algorithm, which is efficient for calculating the value that would appear in the index of a list if it would be sorted, even if it is not already sorted +https://en.wikipedia.org/wiki/Quickselect +""" +def _partition(data, pivot): + """ + Three way partition the data into smaller, equal and greater lists, + in relationship to the pivot + :param data: The data to be sorted (a list) + :param pivot: The value to partition the data on + :return: Three list: smaller, equal and greater + """ + less, equal, greater = [], [], [] + for element in data: + if element.address < pivot.address: + less.append(element) + elif element.address > pivot.address: + greater.append(element) + else: + equal.append(element) + return less, equal, greater + + def quickSelect(list, k): + #k = len(list) // 2 when trying to find the median (index that value would be when list is sorted) + smaller = [] + larger = [] + pivot = random.randint(0, len(list) - 1) + pivot = list[pivot] + count = 0 + smaller, equal, larger =_partition(list, pivot) + count = len(equal) + m = len(smaller) + + #k is the pivot + if m <= k < m + count: + return pivot + # must be in smaller + elif m > k: + return quickSelect(smaller, k) + #must be in larger + else: + return quickSelect(larger, k - (m + count)) diff --git a/searches/ternary_search.py b/searches/ternary_search.py new file mode 100644 index 000000000..3b1c75314 --- /dev/null +++ b/searches/ternary_search.py @@ -0,0 +1,112 @@ +''' +This is a type of divide and conquer algorithm which divides the search space into +3 parts and finds the target value based on the property of the array or list +(usually monotonic property). + +Time Complexity : O(log3 N) +Space Complexity : O(1) +''' + +import sys + +# This is the precision for this function which can be altered. +# It is recommended for users to keep this number greater than or equal to 10. +precision = 10 + +# This is the linear search that will occur after the search space has become smaller. +def lin_search(left, right, A, target): + for i in range(left, right+1): + if(A[i] == target): + return i + +# This is the iterative method of the ternary search algorithm. +def ite_ternary_search(A, target): + left = 0 + right = len(A) - 1; + while(True): + if(left>> bogosort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + >>> bogosort([]) + [] + >>> bogosort([-2, -5, -45]) + [-45, -5, -2] + """ + + def isSorted(collection): + if len(collection) < 2: + return True + for i in range(len(collection) - 1): + if collection[i] > collection[i + 1]: + return False + return True + + while not isSorted(collection): + random.shuffle(collection) + return collection + +if __name__ == '__main__': + import sys + + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + print(bogosort(unsorted)) diff --git a/sorts/bubble_sort.py b/sorts/bubble_sort.py new file mode 100644 index 000000000..d26adc89c --- /dev/null +++ b/sorts/bubble_sort.py @@ -0,0 +1,53 @@ +""" +This is pure python implementation of bubble sort algorithm + +For doctests run following command: +python -m doctest -v bubble_sort.py +or +python3 -m doctest -v bubble_sort.py + +For manual testing run: +python bubble_sort.py +""" + +from __future__ import print_function + + +def bubble_sort(collection): + """Pure implementation of bubble sort algorithm in Python + + :param collection: some mutable ordered collection with heterogeneous + comparable items inside + :return: the same collection ordered by ascending + + Examples: + >>> bubble_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + + >>> bubble_sort([]) + [] + + >>> bubble_sort([-2, -5, -45]) + [-45, -5, -2] + """ + length = len(collection) + for i in range(length-1, -1, -1):#range(length-1, -1, -1) + for j in range(i):#range(1, i) + if collection[j] > collection[j+1]: + collection[j], collection[j+1] = collection[j+1], collection[j] + + return collection + + +if __name__ == '__main__': + import sys + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + print(bubble_sort(unsorted)) diff --git a/sorts/bucket_sort.py b/sorts/bucket_sort.py new file mode 100644 index 000000000..e378d65f4 --- /dev/null +++ b/sorts/bucket_sort.py @@ -0,0 +1,56 @@ +#!/usr/bin/env python +# Author: OMKAR PATHAK +# This program will illustrate how to implement bucket sort algorithm + +# Wikipedia says: Bucket sort, or bin sort, is a sorting algorithm that works by distributing the +# elements of an array into a number of buckets. Each bucket is then sorted individually, either using +# a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a +# distribution sort, and is a cousin of radix sort in the most to least significant digit flavour. +# Bucket sort is a generalization of pigeonhole sort. Bucket sort can be implemented with comparisons +# and therefore can also be considered a comparison sort algorithm. The computational complexity estimates +# involve the number of buckets. + +# Time Complexity of Solution: +# Best Case O(n); Average Case O(n); Worst Case O(n) + +from P26_InsertionSort import insertionSort +import math + +DEFAULT_BUCKET_SIZE = 5 + +def bucketSort(myList, bucketSize=DEFAULT_BUCKET_SIZE): + if(len(myList) == 0): + print('You don\'t have any elements in array!') + + minValue = myList[0] + maxValue = myList[0] + + # For finding minimum and maximum values + for i in range(0, len(myList)): + if myList[i] < minValue: + minValue = myList[i] + elif myList[i] > maxValue: + maxValue = myList[i] + + # Initialize buckets + bucketCount = math.floor((maxValue - minValue) / bucketSize) + 1 + buckets = [] + for i in range(0, bucketCount): + buckets.append([]) + + # For putting values in buckets + for i in range(0, len(myList)): + buckets[math.floor((myList[i] - minValue) / bucketSize)].append(myList[i]) + + # Sort buckets and place back into input array + sortedArray = [] + for i in range(0, len(buckets)): + insertionSort(buckets[i]) + for j in range(0, len(buckets[i])): + sortedArray.append(buckets[i][j]) + + return sortedArray + +if __name__ == '__main__': + sortedArray = bucketSort([12, 23, 4, 5, 3, 2, 12, 81, 56, 95]) + print(sortedArray) diff --git a/sorts/cocktail_shaker_sort.py b/sorts/cocktail_shaker_sort.py new file mode 100644 index 000000000..c09d64408 --- /dev/null +++ b/sorts/cocktail_shaker_sort.py @@ -0,0 +1,36 @@ +from __future__ import print_function + +def cocktail_shaker_sort(unsorted): + """ + Pure implementation of the cocktail shaker sort algorithm in Python. + """ + for i in range(len(unsorted)-1, 0, -1): + swapped = False + + for j in range(i, 0, -1): + if unsorted[j] < unsorted[j-1]: + unsorted[j], unsorted[j-1] = unsorted[j-1], unsorted[j] + swapped = True + + for j in range(i): + if unsorted[j] > unsorted[j+1]: + unsorted[j], unsorted[j+1] = unsorted[j+1], unsorted[j] + swapped = True + + if not swapped: + return unsorted + +if __name__ == '__main__': + import sys + + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + cocktail_shaker_sort(unsorted) + print(unsorted) \ No newline at end of file diff --git a/sorts/counting_sort.py b/sorts/counting_sort.py new file mode 100644 index 000000000..13e4554ae --- /dev/null +++ b/sorts/counting_sort.py @@ -0,0 +1,72 @@ +""" +This is pure python implementation of counting sort algorithm +For doctests run following command: +python -m doctest -v counting_sort.py +or +python3 -m doctest -v counting_sort.py +For manual testing run: +python counting_sort.py +""" + +from __future__ import print_function + + +def counting_sort(collection): + """Pure implementation of counting sort algorithm in Python + :param collection: some mutable ordered collection with heterogeneous + comparable items inside + :return: the same collection ordered by ascending + Examples: + >>> counting_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + >>> counting_sort([]) + [] + >>> counting_sort([-2, -5, -45]) + [-45, -5, -2] + """ + # if the collection is empty, returns empty + if collection == []: + return [] + + # get some information about the collection + coll_len = len(collection) + coll_max = max(collection) + coll_min = min(collection) + + # create the counting array + counting_arr_length = coll_max + 1 - coll_min + counting_arr = [0] * counting_arr_length + + # count how much a number appears in the collection + for number in collection: + counting_arr[number - coll_min] += 1 + + # sum each position with it's predecessors. now, counting_arr[i] tells + # us how many elements <= i has in the collection + for i in range(1, counting_arr_length): + counting_arr[i] = counting_arr[i] + counting_arr[i-1] + + # create the output collection + ordered = [0] * coll_len + + # place the elements in the output, respecting the original order (stable + # sort) from end to begin, updating counting_arr + for i in reversed(range(0, coll_len)): + ordered[counting_arr[collection[i] - coll_min]-1] = collection[i] + counting_arr[collection[i] - coll_min] -= 1 + + return ordered + + +if __name__ == '__main__': + import sys + # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + print(counting_sort(unsorted)) diff --git a/sorts/gnome_sort.py b/sorts/gnome_sort.py new file mode 100644 index 000000000..4f04ff384 --- /dev/null +++ b/sorts/gnome_sort.py @@ -0,0 +1,34 @@ +from __future__ import print_function + +def gnome_sort(unsorted): + """ + Pure implementation of the gnome sort algorithm in Python. + """ + if len(unsorted) <= 1: + return unsorted + + i = 1 + + while i < len(unsorted): + if unsorted[i-1] <= unsorted[i]: + i += 1 + else: + unsorted[i-1], unsorted[i] = unsorted[i], unsorted[i-1] + i -= 1 + if (i == 0): + i = 1 + +if __name__ == '__main__': + import sys + + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + gnome_sort(unsorted) + print(unsorted) \ No newline at end of file diff --git a/sorts/heap_sort.py b/sorts/heap_sort.py new file mode 100644 index 000000000..2d9dd844d --- /dev/null +++ b/sorts/heap_sort.py @@ -0,0 +1,65 @@ +''' +This is a pure python implementation of the heap sort algorithm. + +For doctests run following command: +python -m doctest -v heap_sort.py +or +python3 -m doctest -v heap_sort.py + +For manual testing run: +python heap_sort.py +''' + +from __future__ import print_function + + +def heapify(unsorted, index, heap_size): + largest = index + left_index = 2 * index + 1 + right_index = 2 * index + 2 + if left_index < heap_size and unsorted[left_index] > unsorted[largest]: + largest = left_index + + if right_index < heap_size and unsorted[right_index] > unsorted[largest]: + largest = right_index + + if largest != index: + unsorted[largest], unsorted[index] = unsorted[index], unsorted[largest] + heapify(unsorted, largest, heap_size) + + +def heap_sort(unsorted): + ''' + Pure implementation of the heap sort algorithm in Python + :param collection: some mutable ordered collection with heterogeneous + comparable items inside + :return: the same collection ordered by ascending + + Examples: + >>> heap_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + + >>> heap_sort([]) + [] + + >>> heap_sort([-2, -5, -45]) + [-45, -5, -2] + ''' + n = len(unsorted) + for i in range(n // 2 - 1, -1, -1): + heapify(unsorted, i, n) + for i in range(n - 1, 0, -1): + unsorted[0], unsorted[i] = unsorted[i], unsorted[0] + heapify(unsorted, 0, i) + return unsorted + +if __name__ == '__main__': + import sys + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + print(heap_sort(unsorted)) diff --git a/sorts/insertion_sort.py b/sorts/insertion_sort.py new file mode 100644 index 000000000..33bd27c8f --- /dev/null +++ b/sorts/insertion_sort.py @@ -0,0 +1,53 @@ +""" +This is a pure python implementation of the insertion sort algorithm + +For doctests run following command: +python -m doctest -v insertion_sort.py +or +python3 -m doctest -v insertion_sort.py + +For manual testing run: +python insertion_sort.py +""" +from __future__ import print_function + + +def insertion_sort(collection): + """Pure implementation of the insertion sort algorithm in Python + + :param collection: some mutable ordered collection with heterogeneous + comparable items inside + :return: the same collection ordered by ascending + + Examples: + >>> insertion_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + + >>> insertion_sort([]) + [] + + >>> insertion_sort([-2, -5, -45]) + [-45, -5, -2] + """ + for index in range(1, len(collection)): + while 0 < index and collection[index] < collection[index - 1]: + collection[index], collection[ + index - 1] = collection[index - 1], collection[index] + index -= 1 + + return collection + + +if __name__ == '__main__': + import sys + + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + print(insertion_sort(unsorted)) diff --git a/sorts/merge_sort.py b/sorts/merge_sort.py new file mode 100644 index 000000000..ca8dbc33c --- /dev/null +++ b/sorts/merge_sort.py @@ -0,0 +1,76 @@ +""" +This is a pure python implementation of the merge sort algorithm + +For doctests run following command: +python -m doctest -v merge_sort.py +or +python3 -m doctest -v merge_sort.py + +For manual testing run: +python merge_sort.py +""" +from __future__ import print_function + + +def merge_sort(collection): + """Pure implementation of the merge sort algorithm in Python + + :param collection: some mutable ordered collection with heterogeneous + comparable items inside + :return: the same collection ordered by ascending + + Examples: + >>> merge_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + + >>> merge_sort([]) + [] + + >>> merge_sort([-2, -5, -45]) + [-45, -5, -2] + """ + length = len(collection) + if length > 1: + midpoint = length // 2 + left_half = merge_sort(collection[:midpoint]) + right_half = merge_sort(collection[midpoint:]) + i = 0 + j = 0 + k = 0 + left_length = len(left_half) + right_length = len(right_half) + while i < left_length and j < right_length: + if left_half[i] < right_half[j]: + collection[k] = left_half[i] + i += 1 + else: + collection[k] = right_half[j] + j += 1 + k += 1 + + while i < left_length: + collection[k] = left_half[i] + i += 1 + k += 1 + + while j < right_length: + collection[k] = right_half[j] + j += 1 + k += 1 + + return collection + + +if __name__ == '__main__': + import sys + + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + print(merge_sort(unsorted)) diff --git a/sorts/normal_distribution_QuickSort_README.md b/sorts/normal_distribution_QuickSort_README.md new file mode 100644 index 000000000..d56f934cc --- /dev/null +++ b/sorts/normal_distribution_QuickSort_README.md @@ -0,0 +1,76 @@ +#Normal Distribution QuickSort + + +Algorithm implementing QuickSort Algorithm where the pivot element is chosen randomly between first and last elements of the array and the array elements are taken from a Standard Normal Distribution. +This is different from the ordinary quicksort in the sense, that it applies more to real life problems , where elements usually follow a normal distribution. Also the pivot is randomized to make it a more generic one. + + +##Array Elements + +The array elements are taken from a Standard Normal Distribution , having mean = 0 and standard deviation 1. + +####The code + +```python + +>>> import numpy as np +>>> from tempfile import TemporaryFile +>>> outfile = TemporaryFile() +>>> p = 100 # 100 elements are to be sorted +>>> mu, sigma = 0, 1 # mean and standard deviation +>>> X = np.random.normal(mu, sigma, p) +>>> np.save(outfile, X) +>>> print('The array is') +>>> print(X) + +``` + +------ + +#### The Distribution of the Array elements. + +```python +>>> mu, sigma = 0, 1 # mean and standard deviation +>>> s = np.random.normal(mu, sigma, p) +>>> count, bins, ignored = plt.hist(s, 30, normed=True) +>>> plt.plot(bins , 1/(sigma * np.sqrt(2 * np.pi)) *np.exp( - (bins - mu)**2 / (2 * sigma**2) ),linewidth=2, color='r') +>>> plt.show() + +``` + + +----- + + + + +![](https://www.mathsisfun.com/data/images/normal-distrubution-large.gif) + +--- + +--------------------- + +-- + +##Plotting the function for Checking 'The Number of Comparisons' taking place between Normal Distribution QuickSort and Ordinary QuickSort + +```python +>>>import matplotlib.pyplot as plt + + + # Normal Disrtibution QuickSort is red +>>> plt.plot([1,2,4,16,32,64,128,256,512,1024,2048],[1,1,6,15,43,136,340,800,2156,6821,16325],linewidth=2, color='r') + + #Ordinary QuickSort is green +>>> plt.plot([1,2,4,16,32,64,128,256,512,1024,2048],[1,1,4,16,67,122,362,949,2131,5086,12866],linewidth=2, color='g') + +>>> plt.show() + +``` + + +---- + + +------------------ + diff --git a/sorts/quick_sort.py b/sorts/quick_sort.py new file mode 100644 index 000000000..52e37b587 --- /dev/null +++ b/sorts/quick_sort.py @@ -0,0 +1,54 @@ +""" +This is a pure python implementation of the quick sort algorithm + +For doctests run following command: +python -m doctest -v quick_sort.py +or +python3 -m doctest -v quick_sort.py + +For manual testing run: +python quick_sort.py +""" +from __future__ import print_function + + +def quick_sort(ARRAY): + """Pure implementation of quick sort algorithm in Python + + :param collection: some mutable ordered collection with heterogeneous + comparable items inside + :return: the same collection ordered by ascending + + Examples: + >>> quick_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + + >>> quick_sort([]) + [] + + >>> quick_sort([-2, -5, -45]) + [-45, -5, -2] + """ + ARRAY_LENGTH = len(ARRAY) + if( ARRAY_LENGTH <= 1): + return ARRAY + else: + PIVOT = ARRAY[0] + GREATER = [ element for element in ARRAY[1:] if element > PIVOT ] + LESSER = [ element for element in ARRAY[1:] if element <= PIVOT ] + return quick_sort(LESSER) + [PIVOT] + quick_sort(GREATER) + + +if __name__ == '__main__': + import sys + + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [ int(item) for item in user_input.split(',') ] + print( quick_sort(unsorted) ) diff --git a/sorts/radix_sort.py b/sorts/radix_sort.py new file mode 100644 index 000000000..f19bc10e8 --- /dev/null +++ b/sorts/radix_sort.py @@ -0,0 +1,27 @@ +def radixsort(lst): + RADIX = 10 + maxLength = False + tmp , placement = -1, 1 + + while not maxLength: + maxLength = True + # declare and initialize buckets + buckets = [list() for _ in range( RADIX )] + + # split lst between lists + for i in lst: + tmp = i // placement + buckets[tmp % RADIX].append( i ) + if maxLength and tmp > 0: + maxLength = False + + # empty lists into lst array + a = 0 + for b in range( RADIX ): + buck = buckets[b] + for i in buck: + lst[a] = i + a += 1 + + # move to next + placement *= RADIX diff --git a/sorts/random_normaldistribution_quicksort.py b/sorts/random_normaldistribution_quicksort.py new file mode 100644 index 000000000..19b180578 --- /dev/null +++ b/sorts/random_normaldistribution_quicksort.py @@ -0,0 +1,66 @@ +from random import randint +from tempfile import TemporaryFile +import numpy as np +import math + + + +def _inPlaceQuickSort(A,start,end): + count = 0 + if start>> selection_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + + >>> selection_sort([]) + [] + + >>> selection_sort([-2, -5, -45]) + [-45, -5, -2] + """ + + length = len(collection) + for i in range(length): + least = i + for k in range(i + 1, length): + if collection[k] < collection[least]: + least = k + collection[least], collection[i] = ( + collection[i], collection[least] + ) + return collection + + +if __name__ == '__main__': + import sys + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + user_input = input_function('Enter numbers separated by a comma:\n') + unsorted = [int(item) for item in user_input.split(',')] + print(selection_sort(unsorted)) diff --git a/sorts/shell_sort.py b/sorts/shell_sort.py new file mode 100644 index 000000000..de3d84f72 --- /dev/null +++ b/sorts/shell_sort.py @@ -0,0 +1,57 @@ +""" +This is a pure python implementation of the shell sort algorithm + +For doctests run following command: +python -m doctest -v shell_sort.py +or +python3 -m doctest -v shell_sort.py + +For manual testing run: +python shell_sort.py +""" +from __future__ import print_function + + +def shell_sort(collection): + """Pure implementation of shell sort algorithm in Python + :param collection: Some mutable ordered collection with heterogeneous + comparable items inside + :return: the same collection ordered by ascending + + >>> shell_sort([0, 5, 3, 2, 2]) + [0, 2, 2, 3, 5] + + >>> shell_sort([]) + [] + + >>> shell_sort([-2, -5, -45]) + [-45, -5, -2] + """ + # Marcin Ciura's gap sequence + gaps = [701, 301, 132, 57, 23, 10, 4, 1] + + for gap in gaps: + i 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value = lst[index] + pos = binary_search(lst, value, 0, index - 1) + lst = lst[:pos] + [value] + lst[pos:index] + lst[index+1:] + + return lst + + +def merge(left, right): + if not left: + return right + + if not right: + return left + + if left[0] < right[0]: + return [left[0]] + merge(left[1:], right) + + return [right[0]] + merge(left, right[1:]) + + +def timsort(lst): + runs, sorted_runs = [], [] + length = len(lst) + new_run = [lst[0]] + sorted_array = [] + + for i in range(1, length): + if i == length - 1: + new_run.append(lst[i]) + runs.append(new_run) + break + + if lst[i] < lst[i - 1]: + if not new_run: + runs.append([lst[i - 1]]) + new_run.append(lst[i]) + else: + runs.append(new_run) + new_run = [] + else: + new_run.append(lst[i]) + + for run in runs: + sorted_runs.append(insertion_sort(run)) + + for run in sorted_runs: + sorted_array = merge(sorted_array, run) + + return sorted_array + + +def main(): + + lst = [5,9,10,3,-4,5,178,92,46,-18,0,7] + sorted_lst = timsort(lst) + print(sorted_lst) + +if __name__ == '__main__': + main() diff --git a/sorts/topological_sort.py b/sorts/topological_sort.py new file mode 100644 index 000000000..5de1cc2b7 --- /dev/null +++ b/sorts/topological_sort.py @@ -0,0 +1,32 @@ +# a +# / \ +# b c +# / \ +# d e +edges = {'a': ['c', 'b'], 'b': ['d', 'e'], 'c': [], 'd': [], 'e': []} +vertices = ['a', 'b', 'c', 'd', 'e'] + + +def topological_sort(start, visited, sort): + """Perform topolical sort on a directed acyclic graph.""" + current = start + # add current to visited + visited.append(current) + neighbors = edges[current] + for neighbor in neighbors: + # if neighbor not in visited, visit + if neighbor not in visited: + sort = topological_sort(neighbor, visited, sort) + # if all neighbors visited add current to sort + sort.append(current) + # if all vertices haven't been visited select a new one to visit + if len(visited) != len(vertices): + for vertice in vertices: + if vertice not in visited: + sort = topological_sort(vertice, visited, sort) + # return sort + return sort + + +sort = topological_sort('a', [], []) +print(sort) diff --git a/traversals/binary_tree_traversals.py b/traversals/binary_tree_traversals.py new file mode 100644 index 000000000..9d14a1e7e --- /dev/null +++ b/traversals/binary_tree_traversals.py @@ -0,0 +1,109 @@ +""" +This is pure python implementation of tree traversal algorithms +""" +from __future__ import print_function +import queue + + +class TreeNode: + def __init__(self, data): + self.data = data + self.right = None + self.left = None + + +def build_tree(): + print("\n********Press N to stop entering at any point of time********\n") + print("Enter the value of the root node: ", end="") + check=input() + if check=='N' or check=='n': + return None + data=int(check) + q = queue.Queue() + tree_node = TreeNode(data) + q.put(tree_node) + while not q.empty(): + node_found = q.get() + print("Enter the left node of %s: " % node_found.data, end="") + check=input() + if check=='N' or check =='n': + return tree_node + left_data = int(check) + left_node = TreeNode(left_data) + node_found.left = left_node + q.put(left_node) + print("Enter the right node of %s: " % node_found.data, end="") + check = input() + if check == 'N' or check == 'n': + return tree_node + right_data = int(check) + right_node = TreeNode(right_data) + node_found.right = right_node + q.put(right_node) + + +def pre_order(node): + if not isinstance(node, TreeNode) or not node: + return + print(node.data, end=" ") + pre_order(node.left) + pre_order(node.right) + + +def in_order(node): + if not isinstance(node, TreeNode) or not node: + return + in_order(node.left) + print(node.data, end=" ") + in_order(node.right) + + +def post_order(node): + if not isinstance(node, TreeNode) or not node: + return + post_order(node.left) + post_order(node.right) + print(node.data, end=" ") + + +def level_order(node): + if not isinstance(node, TreeNode) or not node: + return + q = queue.Queue() + q.put(node) + while not q.empty(): + node_dequeued = q.get() + print(node_dequeued.data, end=" ") + if node_dequeued.left: + q.put(node_dequeued.left) + if node_dequeued.right: + q.put(node_dequeued.right) + + +if __name__ == '__main__': + import sys + + print("\n********* Binary Tree Traversals ************\n") + # For python 2.x and 3.x compatibility: 3.x has no raw_input builtin + # otherwise 2.x's input builtin function is too "smart" + if sys.version_info.major < 3: + input_function = raw_input + else: + input_function = input + + node = build_tree() + print("\n********* Pre Order Traversal ************") + pre_order(node) + print("\n******************************************\n") + + print("\n********* In Order Traversal ************") + in_order(node) + print("\n******************************************\n") + + print("\n********* Post Order Traversal ************") + post_order(node) + print("\n******************************************\n") + + print("\n********* Level Order Traversal ************") + level_order(node) + print("\n******************************************\n") From 96536ad7617dadb74b89a8ebc14cc239f8f3b294 Mon Sep 17 00:00:00 2001 From: Erdenezul Date: Wed, 25 Oct 2017 09:56:48 +0800 Subject: [PATCH 61/73] add coin change problem --- dynamic_programming/coin_change.py | 25 +++++++++++++++++++++++++ 1 file changed, 25 insertions(+) create mode 100644 dynamic_programming/coin_change.py diff --git a/dynamic_programming/coin_change.py b/dynamic_programming/coin_change.py new file mode 100644 index 000000000..a8af4d5cc --- /dev/null +++ b/dynamic_programming/coin_change.py @@ -0,0 +1,25 @@ +""" +You have m types of coins available in infinite quantities +where the value of each coins is given in the array S=[S0,... Sm-1] +Can you determine number of ways of making change for n units using +the given types of coints? +https://www.hackerrank.com/challenges/coin-change/problem +""" +def dp_count(S, m, n): + table = [0] * (n + 1) + + # Base case (If given value is 0) + table[0] = 1 + + # Pick all coins one by one and update table[] values + # after the index greater than or equal to the value of the + # picked coin + for i in range(0, m): + for j in range(S[i], n + 1): + table[j] += table[j - S[i]] + + return table[n] + +if __name__ == '__main__': + print dp_count([1, 2, 3], 3, 4) # answer 4 + print dp_count([2, 5, 3, 6], 4, 10) # answer 5 From 53ce9b806813ec253aaf6750c595d026fb84a434 Mon Sep 17 00:00:00 2001 From: Erdenezul Date: Wed, 25 Oct 2017 15:58:46 +0800 Subject: [PATCH 62/73] fix typo --- dynamic_programming/coin_change.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/dynamic_programming/coin_change.py b/dynamic_programming/coin_change.py index a8af4d5cc..dca016359 100644 --- a/dynamic_programming/coin_change.py +++ b/dynamic_programming/coin_change.py @@ -2,7 +2,7 @@ You have m types of coins available in infinite quantities where the value of each coins is given in the array S=[S0,... Sm-1] Can you determine number of ways of making change for n units using -the given types of coints? +the given types of coins? https://www.hackerrank.com/challenges/coin-change/problem """ def dp_count(S, m, n): From f1621c4a028de2093409afe7a12d4d9a8375f650 Mon Sep 17 00:00:00 2001 From: Anurag Kumar Date: Thu, 26 Oct 2017 12:11:32 +0530 Subject: [PATCH 63/73] [other] Added Conway's Game of Life Experiment. --- other/game_of_life/game_o_life.py | 118 ++++++++++++++++++++++++++++++ other/game_of_life/sample.gif | Bin 0 -> 228847 bytes 2 files changed, 118 insertions(+) create mode 100644 other/game_of_life/game_o_life.py create mode 100644 other/game_of_life/sample.gif diff --git a/other/game_of_life/game_o_life.py b/other/game_of_life/game_o_life.py new file mode 100644 index 000000000..32ebe0fc1 --- /dev/null +++ b/other/game_of_life/game_o_life.py @@ -0,0 +1,118 @@ +'''Conway's Game Of Life, Author Anurag Kumar(mailto:anuragkumarak95@gmail.com) + +Requirements: + - numpy + - random + - time + - matplotlib + +Python: + - 3.5 + +Usage: + - $python3 game_o_life + +Game-Of-Life Rules: + + 1. + Any live cell with fewer than two live neighbours + dies, as if caused by under-population. + 2. + Any live cell with two or three live neighbours lives + on to the next generation. + 3. + Any live cell with more than three live neighbours + dies, as if by over-population. + 4. + Any dead cell with exactly three live neighbours be- + comes a live cell, as if by reproduction. + ''' +import numpy as np +import random, time, sys +from matplotlib import pyplot as plt +import matplotlib.animation as animation +from matplotlib.colors import ListedColormap + +usage_doc='Usage of script: script_nama ' + +choice = [0]*100 + [1]*10 +random.shuffle(choice) + +def create_canvas(size): + canvas = [ [False for i in range(size)] for j in range(size)] + return canvas + +def seed(canvas): + for i,row in enumerate(canvas): + for j,_ in enumerate(row): + canvas[i][j]=bool(random.getrandbits(1)) + +def run(canvas): + ''' This function runs the rules of game through all points, and changes their status accordingly.(in the same canvas) + @Args: + -- + canvas : canvas of population to run the rules on. + + @returns: + -- + None + ''' + canvas = np.array(canvas) + next_gen_canvas = np.array(create_canvas(canvas.shape[0])) + for r, row in enumerate(canvas): + for c, pt in enumerate(row): + # print(r-1,r+2,c-1,c+2) + next_gen_canvas[r][c] = __judge_point(pt,canvas[r-1:r+2,c-1:c+2]) + + canvas = next_gen_canvas + del next_gen_canvas # cleaning memory as we move on. + return canvas.tolist() + +def __judge_point(pt,neighbours): + dead = 0 + alive = 0 + # finding dead or alive neighbours count. + for i in neighbours: + for status in i: + if status: alive+=1 + else: dead+=1 + + # handling duplicate entry for focus pt. + if pt : alive-=1 + else : dead-=1 + + # running the rules of game here. + state = pt + if pt: + if alive<2: + state=False + elif alive==2 or alive==3: + state=True + elif alive>3: + state=False + else: + if alive==3: + state=True + + return state + + +if __name__=='__main__': + if len(sys.argv) != 2: raise Exception(usage_doc) + + canvas_size = int(sys.argv[1]) + # main working structure of this module. + c=create_canvas(canvas_size) + seed(c) + fig, ax = plt.subplots() + fig.show() + cmap = ListedColormap(['w','k']) + try: + while True: + c = run(c) + ax.matshow(c,cmap=cmap) + fig.canvas.draw() + ax.cla() + except KeyboardInterrupt: + # do nothing. + pass diff --git a/other/game_of_life/sample.gif b/other/game_of_life/sample.gif new file mode 100644 index 0000000000000000000000000000000000000000..0bf2ae1f95e4604f6840d5804846924ed72ea966 GIT binary patch literal 228847 zcmdSALv$rh7`GWa>Dac_v2Aqhq+{E*ZhT|AW81dvq+{FYoB4k;-^?s#&dg>u^Db*u zb*k#rdFuJS(y~%KyvDK+z2L9IVE+|3I5-3Z1SBLR6ciLRG&Bqh3@j`x92^`10s3d)ZkKTuIo(a_M)(a|w5FfcJOv9PePv9WP*aBy*P@$m5Q@$m@=2nY!Y ziHL}ZiHS)_NJvRZ$;ikkC@83?sAygw+9?&0C#>FMd^<>l?|?c?L) 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zI|?5hB3Rs88EPd!jP!E-D|2kmuYG6TxCFE2$@d2%VlN!V{}rhNR{RZB!@~`bFJau` z7>V)2)n)LCTC~g>*;vMFz0r#vl;awWr#Y3(k&k`!%^u6sMz#HskaY~Co(9>cLYi%f z%Zr{P*_T9x+zg8-f#j7WnMeZi?~->kVGsi-B~Dh7HAe#F8B^Fo;E8OKvioGRFv$`N znsSODhbldDu@t3a4ed@}Kz{^O@b`Bf@;Zgg_ui{D4>)zN}} zRA&&S=sSy4(!4d(ne=m5IW5#uho1DB4^!z#HFT(jqHLZypr#G_?ZdpD1#x z8NcW*wzh6$@=D{&z7WI(`-sWYd6J8G*&`9Ely0UTEsxMwKZY>Eo^5?+uGXpwzwT9L7|#k z$n93Fy)~vjyBJ)KG_<%;{Vj5r%iQKV_qouGu5_nM-Rf$IxYnJ>KC`P`>~a?(+x;$h zy-U(rIyNhC&CPkmqDs2rQH<-|nt2fmGx`c9ys87033qj=}LvL_5)x($T~NZm~8S>EWlM7=$WrGTDGE z8D-j$!1|&wWUO2+15YNrU!JCgbL8bJYxyx;W>>+PYkX$Mq04P6RCyBIh)ZZygw+g(_tO`kBgV4s@eYH|YvK`p#EY-lAbVW<34{ zot0J>mI?M(P$QW}qXt;1-&~Y98)(&HPOy4Y%~8mjy3>AKb5^&BXeXXJOTScdR6_ls zVE201za}cL|4VES8JpS39xjc++~rw%xQXH*UMl+gj_Zh{YXZa)a31A4d0x u!Trc))0W+1gE!dZO|^gk03rDV1quMg04x9i000310RR991OST#1OPkWbdkyc literal 0 HcmV?d00001 From 20a45779034e97eaee7830b15ef6247528f01300 Mon Sep 17 00:00:00 2001 From: bT-53 Date: Fri, 27 Oct 2017 09:19:58 +0700 Subject: [PATCH 64/73] Add a soution of ProjectEuler Problem 13 --- Project Euler/Problem 13/sol1.py | 13 +++++++++++++ 1 file changed, 13 insertions(+) create mode 100644 Project Euler/Problem 13/sol1.py diff --git a/Project Euler/Problem 13/sol1.py b/Project Euler/Problem 13/sol1.py new file mode 100644 index 000000000..db8ddce4d --- /dev/null +++ b/Project Euler/Problem 13/sol1.py @@ -0,0 +1,13 @@ +''' +Problem Statement: +Work out the first ten digits of the sum of the N 50-digit numbers. +''' + +n = int(input().strip()) + +array = [] +for i in range(n): + array.append(int(input().strip())) + +print(str(sum(array))[:10]) + From 3cae7967acf2cdef9c65b39547ccec2115c16410 Mon Sep 17 00:00:00 2001 From: bT-53 Date: Fri, 27 Oct 2017 10:10:29 +0700 Subject: [PATCH 65/73] Create scc_kosaraju.py --- Graphs/scc_kosaraju.py | 45 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 45 insertions(+) create mode 100644 Graphs/scc_kosaraju.py diff --git a/Graphs/scc_kosaraju.py b/Graphs/scc_kosaraju.py new file mode 100644 index 000000000..09a05e981 --- /dev/null +++ b/Graphs/scc_kosaraju.py @@ -0,0 +1,45 @@ +# n - no of nodes, m - no of edges +n, m = list(map(int,input().split())) + +g = [[] for i in range(n)] #graph +r = [[] for i in range(n)] #reversed graph +# input graph data (edges) +for i in range(m): + u, v = list(map(int,input().split())) + g[u].append(v) + r[v].append(u) + +stack = [] +visit = [False]*n +scc = [] +component = [] + +def dfs(u): + global g, r, scc, component, visit, stack + if visit[u]: return + visit[u] = True + for v in g[u]: + dfs(v) + stack.append(u) + +def dfs2(u): + global g, r, scc, component, visit, stack + if visit[u]: return + visit[u] = True + component.append(u) + for v in r[u]: + dfs2(v) + +def kosaraju(): + global g, r, scc, component, visit, stack + for i in range(n): + dfs(i) + visit = [False]*n + for i in stack[::-1]: + if visit[i]: continue + component = [] + dfs2(i) + scc.append(component) + return scc + +print(kosaraju()) From 8cd515750715cb5fa170a3e737c09d1784795341 Mon Sep 17 00:00:00 2001 From: Yashasvi Baweja Date: Fri, 27 Oct 2017 11:34:50 +0530 Subject: [PATCH 66/73] Added Multi Heuristic Astar Implemented the paper www.cs.cmu.edu/~venkatrn/papers/ijrr16.pdf --- Multi_Hueristic_Astar.py | 262 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 262 insertions(+) create mode 100644 Multi_Hueristic_Astar.py diff --git a/Multi_Hueristic_Astar.py b/Multi_Hueristic_Astar.py new file mode 100644 index 000000000..03652d35a --- /dev/null +++ b/Multi_Hueristic_Astar.py @@ -0,0 +1,262 @@ +import heapq +import numpy as np +import math +import copy + + +class PriorityQueue: + def __init__(self): + self.elements = [] + self.set = set() + + def minkey(self): + if not self.empty(): + return self.elements[0][0] + else: + return float('inf') + + def empty(self): + return len(self.elements) == 0 + + def put(self, item, priority): + if item not in self.set: + heapq.heappush(self.elements, (priority, item)) + self.set.add(item) + else: + # update + # print("update", item) + temp = [] + (pri, x) = heapq.heappop(self.elements) + while x != item: + temp.append((pri, x)) + (pri, x) = heapq.heappop(self.elements) + temp.append((priority, item)) + for (pro, xxx) in temp: + heapq.heappush(self.elements, (pro, xxx)) + + def remove_element(self, item): + if item in self.set: + self.set.remove(item) + temp = [] + (pro, x) = heapq.heappop(self.elements) + while x != item: + temp.append((pro, x)) + (pro, x) = heapq.heappop(self.elements) + for (prito, yyy) in temp: + heapq.heappush(self.elements, (prito, yyy)) + + def top_show(self): + return self.elements[0][1] + + def get(self): + (priority, item) = heapq.heappop(self.elements) + self.set.remove(item) + return (priority, item) + +def consistent_hueristic(P, goal): + # euclidean distance + a = np.array(P) + b = np.array(goal) + return np.linalg.norm(a - b) + +def hueristic_2(P, goal): + # integer division by time variable + return consistent_hueristic(P, goal) // t + +def hueristic_1(P, goal): + # manhattan distance + return abs(P[0] - goal[0]) + abs(P[1] - goal[1]) + +def key(start, i, goal, g_function): + ans = g_function[start] + W1 * hueristics[i](start, goal) + return ans + +def do_something(back_pointer, goal, start): + grid = np.chararray((n, n)) + for i in range(n): + for j in range(n): + grid[i][j] = '*' + + for i in range(n): + for j in range(n): + if (j, (n-1)-i) in blocks: + grid[i][j] = "#" + + grid[0][(n-1)] = "-" + x = back_pointer[goal] + while x != start: + (x_c, y_c) = x + # print(x) + grid[(n-1)-y_c][x_c] = "-" + x = back_pointer[x] + grid[(n-1)][0] = "-" + + + for i in xrange(n): + for j in range(n): + if (i, j) == (0, n-1): + print grid[i][j], + print "<-- End position", + else: + print grid[i][j], + print + print("^") + print("Start position") + print + print("# is an obstacle") + print("- is the path taken by algorithm") + print("PATH TAKEN BY THE ALGORITHM IS:-") + x = back_pointer[goal] + while x != start: + print x, + x = back_pointer[x] + print x + quit() + +def valid(p): + if p[0] < 0 or p[0] > n-1: + return False + if p[1] < 0 or p[1] > n-1: + return False + return True + +def expand_state(s, j, visited, g_function, close_list_anchor, close_list_inad, open_list, back_pointer): + for itera in range(n_hueristic): + open_list[itera].remove_element(s) + # print("s", s) + # print("j", j) + (x, y) = s + left = (x-1, y) + right = (x+1, y) + up = (x, y+1) + down = (x, y-1) + + for neighbours in [left, right, up, down]: + if neighbours not in blocks: + if valid(neighbours) and neighbours not in visited: + # print("neighbour", neighbours) + visited.add(neighbours) + back_pointer[neighbours] = -1 + g_function[neighbours] = float('inf') + + if valid(neighbours) and g_function[neighbours] > g_function[s] + 1: + g_function[neighbours] = g_function[s] + 1 + back_pointer[neighbours] = s + if neighbours not in close_list_anchor: + open_list[0].put(neighbours, key(neighbours, 0, goal, g_function)) + if neighbours not in close_list_inad: + for var in range(1,n_hueristic): + if key(neighbours, var, goal, g_function) <= W2 * key(neighbours, 0, goal, g_function): + # print("why not plssssssssss") + open_list[j].put(neighbours, key(neighbours, var, goal, g_function)) + + + # print + +def make_common_ground(): + some_list = [] + # block 1 + for x in range(1, 5): + for y in range(1, 6): + some_list.append((x, y)) + + # line + for x in range(15, 20): + some_list.append((x, 17)) + + # block 2 big + for x in range(10, 19): + for y in range(1, 15): + some_list.append((x, y)) + + # L block + for x in range(1, 4): + for y in range(12, 19): + some_list.append((x, y)) + for x in range(3, 13): + for y in range(16, 19): + some_list.append((x, y)) + return some_list + +hueristics = {0: consistent_hueristic, 1: hueristic_1, 2: hueristic_2} + +blocks_blk = [(0, 1),(1, 1),(2, 1),(3, 1),(4, 1),(5, 1),(6, 1),(7, 1),(8, 1),(9, 1),(10, 1),(11, 1),(12, 1),(13, 1),(14, 1),(15, 1),(16, 1),(17, 1),(18, 1), (19, 1)] +blocks_no = [] +blocks_all = make_common_ground() + + + + +blocks = blocks_blk +# hyper parameters +W1 = 1 +W2 = 1 +n = 20 +n_hueristic = 3 # one consistent and two other inconsistent + +# start and end destination +start = (0, 0) +goal = (n-1, n-1) + +t = 1 +def multi_a_star(start, goal, n_hueristic): + g_function = {start: 0, goal: float('inf')} + back_pointer = {start:-1, goal:-1} + open_list = [] + visited = set() + + for i in range(n_hueristic): + open_list.append(PriorityQueue()) + open_list[i].put(start, key(start, i, goal, g_function)) + + close_list_anchor = [] + close_list_inad = [] + while open_list[0].minkey() < float('inf'): + for i in range(1, n_hueristic): + # print("i", i) + # print(open_list[0].minkey(), open_list[i].minkey()) + if open_list[i].minkey() <= W2 * open_list[0].minkey(): + global t + t += 1 + # print("less prio") + if g_function[goal] <= open_list[i].minkey(): + if g_function[goal] < float('inf'): + do_something(back_pointer, goal, start) + else: + _, get_s = open_list[i].top_show() + visited.add(get_s) + expand_state(get_s, i, visited, g_function, close_list_anchor, close_list_inad, open_list, back_pointer) + close_list_inad.append(get_s) + else: + # print("more prio") + if g_function[goal] <= open_list[0].minkey(): + if g_function[goal] < float('inf'): + do_something(back_pointer, goal, start) + else: + # print("hoolla") + get_s = open_list[0].top_show() + visited.add(get_s) + expand_state(get_s, 0, visited, g_function, close_list_anchor, close_list_inad, open_list, back_pointer) + close_list_anchor.append(get_s) + print("No path found to goal") + print + for i in range(n-1,-1, -1): + for j in range(n): + if (j, i) in blocks: + print '#', + elif (j, i) in back_pointer: + if (j, i) == (n-1, n-1): + print '*', + else: + print '-', + else: + print '*', + if (j, i) == (n-1, n-1): + print '<-- End position', + print + print("^") + print("Start position") + print + print("# is an obstacle") + print("- is the path taken by algorithm") +multi_a_star(start, goal, n_hueristic) \ No newline at end of file From e07e0cb38bf3ea7f7301641fe877fe473248fabb Mon Sep 17 00:00:00 2001 From: Thanapat Katapornsiri Date: Fri, 27 Oct 2017 14:16:26 +0700 Subject: [PATCH 67/73] add minimum spanning tree kruskal --- Graphs/minimum_spanning_tree_kruskal.py | 31 +++++++++++++++++++++++++ 1 file changed, 31 insertions(+) create mode 100644 Graphs/minimum_spanning_tree_kruskal.py diff --git a/Graphs/minimum_spanning_tree_kruskal.py b/Graphs/minimum_spanning_tree_kruskal.py new file mode 100644 index 000000000..d329774c8 --- /dev/null +++ b/Graphs/minimum_spanning_tree_kruskal.py @@ -0,0 +1,31 @@ +num_nodes, num_edges = list(map(int,input().split())) + +edges = [] + +for i in range(num_edges): + node1, node2, cost = list(map(int,input().split())) + edges.append((i,node1,node2,cost)) + +edges = sorted(edges, key=lambda edge: edge[3]) + +parent = [i for i in range(num_nodes)] + +def find_parent(i): + if(i != parent[i]): + parent[i] = find_parent(parent[i]) + return parent[i] + +minimum_spanning_tree_cost = 0 +minimum_spanning_tree = [] + +for edge in edges: + parent_a = find_parent(edge[1]) + parent_b = find_parent(edge[2]) + if(parent_a != parent_b): + minimum_spanning_tree_cost += edge[3] + minimum_spanning_tree.append(edge) + parent[parent_a] = parent_b + +print(minimum_spanning_tree_cost) +for edge in minimum_spanning_tree: + print(edge) \ No newline at end of file From 6393251803b6562d9b2ea98cf1385d1dbb0207d9 Mon Sep 17 00:00:00 2001 From: Thanapat Katapornsiri Date: Fri, 27 Oct 2017 14:34:44 +0700 Subject: [PATCH 68/73] add newline at the end --- Graphs/minimum_spanning_tree_kruskal.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Graphs/minimum_spanning_tree_kruskal.py b/Graphs/minimum_spanning_tree_kruskal.py index d329774c8..d26eb70b2 100644 --- a/Graphs/minimum_spanning_tree_kruskal.py +++ b/Graphs/minimum_spanning_tree_kruskal.py @@ -28,4 +28,4 @@ for edge in edges: print(minimum_spanning_tree_cost) for edge in minimum_spanning_tree: - print(edge) \ No newline at end of file + print(edge) From 8c5fd4b597e7903a18040eff5c7e86aef4b0b030 Mon Sep 17 00:00:00 2001 From: Honey Sharma Date: Fri, 27 Oct 2017 21:00:08 +0530 Subject: [PATCH 69/73] Create cyclesort.py implementation of cycle sort in python3 --- sorts/cyclesort.py | 51 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 51 insertions(+) create mode 100644 sorts/cyclesort.py diff --git a/sorts/cyclesort.py b/sorts/cyclesort.py new file mode 100644 index 000000000..2cc635417 --- /dev/null +++ b/sorts/cyclesort.py @@ -0,0 +1,51 @@ +# Code contributed by Honey Sharma +def cycle_sort(array): + ans = 0 + + # Pass through the array to find cycles to rotate. + for cycleStart in range(0, len(array) - 1): + item = array[cycleStart] + + # finding the position for putting the item. + pos = cycleStart + for i in range(cycleStart + 1, len(array)): + if array[i] < item: + pos += 1 + + # If the item is already present-not a cycle. + if pos == cycleStart: + continue + + # Otherwise, put the item there or right after any duplicates. + while item == array[pos]: + pos += 1 + array[pos], item = item, array[pos] + ans += 1 + + # Rotate the rest of the cycle. + while pos != cycleStart: + + # Find where to put the item. + pos = cycleStart + for i in range(cycleStart + 1, len(array)): + if array[i] < item: + pos += 1 + + # Put the item there or right after any duplicates. + while item == array[pos]: + pos += 1 + array[pos], item = item, array[pos] + ans += 1 + + return ans + + +# Main Code starts here +user_input = input('Enter numbers separated by a comma:\n') +unsorted = [int(item) for item in user_input.split(',')] +n = len(unsorted) +cycle_sort(unsorted) + +print("After sort : ") +for i in range(0, n): + print(unsorted[i], end=' ') From 54700f2c8f0fd75b30b7468d9fea64cdea326b4d Mon Sep 17 00:00:00 2001 From: Pablo Date: Sat, 28 Oct 2017 16:17:55 -0300 Subject: [PATCH 70/73] Added delete function --- .../Binary Tree/binary_search_tree.py | 69 ++++++++++++++----- 1 file changed, 52 insertions(+), 17 deletions(-) diff --git a/data_structures/Binary Tree/binary_search_tree.py b/data_structures/Binary Tree/binary_search_tree.py index 2993c3cdc..c38751ad3 100644 --- a/data_structures/Binary Tree/binary_search_tree.py +++ b/data_structures/Binary Tree/binary_search_tree.py @@ -1,13 +1,14 @@ ''' A binary search Tree ''' - class Node: - def __init__(self, label): + def __init__(self, label, parent): self.label = label self.left = None self.right = None + #Added in order to delete a node easier + self.parent = parent def getLabel(self): return self.label @@ -27,6 +28,11 @@ class Node: def setRight(self, right): self.right = right + def getParent(self): + return self.parent + + def setParent(self, parent): + self.parent = parent class BinarySearchTree: @@ -35,13 +41,12 @@ class BinarySearchTree: def insert(self, label): # Create a new Node - new_node = Node(label) + new_node = Node(label, None) # If Tree is empty if self.empty(): self.root = new_node else: #If Tree is not empty - parent_node = None curr_node = self.root #While we don't get to a leaf while curr_node is not None: @@ -58,8 +63,14 @@ class BinarySearchTree: if new_node.getLabel() < parent_node.getLabel(): parent_node.setLeft(new_node) else: - parent_node.setRight(new_node) - + parent_node.setRight(new_node) + #Set parent to the new node + new_node.setParent(parent_node) + ''' + def delete(self): + if (not self.empty()): + if() + ''' def getNode(self, label): curr_node = None #If the tree is not empty @@ -78,6 +89,24 @@ class BinarySearchTree: curr_node = curr_node.getRight() return curr_node + def getMax(self): + #We go deep on the right branch + curr_node = None + if(not self.empty()): + curr_node = self.getRoot() + while(curr_node.getRight() is not None): + curr_node = curr_node.getRight() + return curr_node + + def getMin(self): + #We go deep on the left branch + curr_node = None + if(not self.empty()): + curr_node = self.getRoot() + while(curr_node.getLeft() is not None): + curr_node = curr_node.getLeft() + return curr_node + def empty(self): if self.root is None: return True @@ -92,19 +121,19 @@ class BinarySearchTree: def getRoot(self): return self.root -''' -Example - 8 - / \ - 3 10 - / \ \ - 1 6 14 - / \ / - 4 7 13 -''' +def testBinarySearchTree(): + ''' + Example + 8 + / \ + 3 10 + / \ \ + 1 6 14 + / \ / + 4 7 13 + ''' -if __name__ == "__main__": t = BinarySearchTree() t.insert(8) t.insert(3) @@ -128,3 +157,9 @@ if __name__ == "__main__": else: print("The label -1 doesn't exist") + if(not t.empty()): + print("Max Value: ", t.getMax().getLabel()) + print("Min Value: ", t.getMin().getLabel()) + +if __name__ == "__main__": + testBinarySearchTree() From f766bb42166b874364f30f022db738110a3dc567 Mon Sep 17 00:00:00 2001 From: Pablo Date: Sat, 28 Oct 2017 16:18:21 -0300 Subject: [PATCH 71/73] Added delete function --- .../Binary Tree/binary_search_tree.py | 100 ++++++++++++++---- 1 file changed, 79 insertions(+), 21 deletions(-) diff --git a/data_structures/Binary Tree/binary_search_tree.py b/data_structures/Binary Tree/binary_search_tree.py index c38751ad3..41ba87436 100644 --- a/data_structures/Binary Tree/binary_search_tree.py +++ b/data_structures/Binary Tree/binary_search_tree.py @@ -66,11 +66,29 @@ class BinarySearchTree: parent_node.setRight(new_node) #Set parent to the new node new_node.setParent(parent_node) - ''' - def delete(self): + + def delete(self, label): if (not self.empty()): - if() - ''' + #Look for the node with that label + node = self.getNode(label) + #If the node exists + if(node is not None): + #If it has no children + if(node.getLeft() is None and node.getRight() is None): + self.__reassignNodes(node, None) + node = None + #Has only right children + elif(node.getLeft() is None and node.getRight() is not None): + self.__reassignNodes(node, node.getRight()) + #Has only left children + elif(node.getLeft() is not None and node.getRight() is None): + self.__reassignNodes(node, node.getLeft()) + #Has two children + else: + tmpNode = self.getMax(node.getLeft()) + self.delete(tmpNode.getLabel()) + self.__reassignNodes(node, tmpNode) + def getNode(self, label): curr_node = None #If the tree is not empty @@ -89,18 +107,23 @@ class BinarySearchTree: curr_node = curr_node.getRight() return curr_node - def getMax(self): - #We go deep on the right branch - curr_node = None - if(not self.empty()): + def getMax(self, root = None): + if(root is not None): + curr_node = root + else: + #We go deep on the right branch curr_node = self.getRoot() + if(not self.empty()): while(curr_node.getRight() is not None): curr_node = curr_node.getRight() return curr_node - def getMin(self): - #We go deep on the left branch - curr_node = None + def getMin(self, root = None): + if(root is not None): + curr_node = root + else: + #We go deep on the left branch + curr_node = self.getRoot() if(not self.empty()): curr_node = self.getRoot() while(curr_node.getLeft() is not None): @@ -121,29 +144,58 @@ class BinarySearchTree: def getRoot(self): return self.root + def __isRightChildren(self, node): + if(node == node.getParent().getRight()): + return True + return False + + def __reassignNodes(self,node, newChildren): + if(newChildren is not None): + newChildren.setParent(node.getParent()) + if(node.getParent() is not None): + #If it is the Right Children + if(self.__isRightChildren(node)):a + node.getParent().setRight(newChildren) + else: + #Else it is the left children + node.getParent().setLeft(newChildren) + else: + #It is the root of the tree + node.setLabel(newChildren.getLabel()) def testBinarySearchTree(): ''' Example - 8 - / \ - 3 10 - / \ \ - 1 6 14 - / \ / - 4 7 13 + 8 + / \ + 3 10 + / \ \ + 1 6 14 + / \ / + 4 7 13 ''' + ''' + Example After Deletion + 7 + / \ + 3 14 + / \ + 1 6 + / + 4 + ''' t = BinarySearchTree() t.insert(8) t.insert(3) - t.insert(1) + t.insert(10) t.insert(6) - t.insert(4) - t.insert(7) + t.insert(1) t.insert(10) t.insert(14) t.insert(13) + t.insert(4) + t.insert(7) t.preShow(t.getRoot()) @@ -160,6 +212,12 @@ def testBinarySearchTree(): if(not t.empty()): print("Max Value: ", t.getMax().getLabel()) print("Min Value: ", t.getMin().getLabel()) + + t.delete(13) + t.delete(10) + t.delete(8) + + t.preShow(t.getRoot()) if __name__ == "__main__": testBinarySearchTree() From 9d8824658af8c657e3cc07e8192765b10d76f4d4 Mon Sep 17 00:00:00 2001 From: Pablo Date: Sat, 28 Oct 2017 18:33:14 -0300 Subject: [PATCH 72/73] Finished delete function and added some prints functions too --- .../Binary Tree/binary_search_tree.py | 70 ++++++++++++++----- 1 file changed, 52 insertions(+), 18 deletions(-) diff --git a/data_structures/Binary Tree/binary_search_tree.py b/data_structures/Binary Tree/binary_search_tree.py index 41ba87436..5290f685b 100644 --- a/data_structures/Binary Tree/binary_search_tree.py +++ b/data_structures/Binary Tree/binary_search_tree.py @@ -85,9 +85,12 @@ class BinarySearchTree: self.__reassignNodes(node, node.getLeft()) #Has two children else: + #Gets the max value of the left branch tmpNode = self.getMax(node.getLeft()) + #Deletes the tmpNode self.delete(tmpNode.getLabel()) - self.__reassignNodes(node, tmpNode) + #Assigns the value to the node to delete and keesp tree structure + node.setLabel(tmpNode.getLabel()) def getNode(self, label): curr_node = None @@ -135,11 +138,13 @@ class BinarySearchTree: return True return False - def preShow(self, curr_node): + def __InOrderTraversal(self, curr_node): + nodeList = [] if curr_node is not None: - print(curr_node.getLabel()) - self.preShow(curr_node.getLeft()) - self.preShow(curr_node.getRight()) + nodeList.insert(0, curr_node) + nodeList = nodeList + self.__InOrderTraversal(curr_node.getLeft()) + nodeList = nodeList + self.__InOrderTraversal(curr_node.getRight()) + return nodeList def getRoot(self): return self.root @@ -149,19 +154,44 @@ class BinarySearchTree: return True return False - def __reassignNodes(self,node, newChildren): + def __reassignNodes(self, node, newChildren): if(newChildren is not None): newChildren.setParent(node.getParent()) if(node.getParent() is not None): #If it is the Right Children - if(self.__isRightChildren(node)):a - node.getParent().setRight(newChildren) + if(self.__isRightChildren(node)): + node.getParent().setRight(newChildren) else: #Else it is the left children node.getParent().setLeft(newChildren) + + #This function traversal the tree. By default it returns an + #In order traversal list. You can pass a function to traversal + #The tree as needed by client code + def traversalTree(self, traversalFunction = None, root = None): + if(traversalFunction is None): + #Returns a list of nodes in preOrder by default + return self.__InOrderTraversal(self.root) else: - #It is the root of the tree - node.setLabel(newChildren.getLabel()) + #Returns a list of nodes in the order that the users wants to + return traversalFunction(self.root) + + #Returns an string of all the nodes labels in the list + #In Order Traversal + def __str__(self): + list = self.__InOrderTraversal(self.root) + str = "" + for x in list: + str = str + " " + x.getLabel().__str__() + return str + +def InPreOrder(curr_node): + nodeList = [] + if curr_node is not None: + nodeList = nodeList + InPreOrder(curr_node.getLeft()) + nodeList.insert(0, curr_node.getLabel()) + nodeList = nodeList + InPreOrder(curr_node.getRight()) + return nodeList def testBinarySearchTree(): ''' @@ -179,16 +209,12 @@ def testBinarySearchTree(): Example After Deletion 7 / \ - 3 14 - / \ - 1 6 - / - 4 + 1 4 + ''' t = BinarySearchTree() t.insert(8) t.insert(3) - t.insert(10) t.insert(6) t.insert(1) t.insert(10) @@ -197,7 +223,8 @@ def testBinarySearchTree(): t.insert(4) t.insert(7) - t.preShow(t.getRoot()) + #Prints all the elements of the list in order traversal + print(t.__str__()) if(t.getNode(6) is not None): print("The label 6 exists") @@ -216,8 +243,15 @@ def testBinarySearchTree(): t.delete(13) t.delete(10) t.delete(8) + t.delete(3) + t.delete(6) + t.delete(14) - t.preShow(t.getRoot()) + #Gets all the elements of the tree In pre order + #And it prints them + list = t.traversalTree(InPreOrder, t.root) + for x in list: + print(x) if __name__ == "__main__": testBinarySearchTree() From 75af340aff08b0b1b20775b447fc6a0766f79518 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Pedro=20T=C3=B4rres?= Date: Sun, 29 Oct 2017 14:44:54 -0300 Subject: [PATCH 73/73] ROT13 --- ciphers/rot13.py | 24 ++++++++++++++++++++++++ 1 file changed, 24 insertions(+) create mode 100644 ciphers/rot13.py diff --git a/ciphers/rot13.py b/ciphers/rot13.py new file mode 100644 index 000000000..208de4890 --- /dev/null +++ b/ciphers/rot13.py @@ -0,0 +1,24 @@ +def dencrypt(s, n): + out = '' + for c in s: + if c >= 'A' and c <= 'Z': + out += chr(ord('A') + (ord(c) - ord('A') + n) % 26) + elif c >= 'a' and c <= 'z': + out += chr(ord('a') + (ord(c) - ord('a') + n) % 26) + else: + out += c + return out + + +def main(): + s0 = 'HELLO' + + s1 = dencrypt(s0, 13) + print(s1) # URYYB + + s2 = dencrypt(s1, 13) + print(s2) # HELLO + + +if __name__ == '__main__': + main()