increment 1

analysis/Compression_Analysis/PSNR.py

@@ -0,0 +1,38 @@
+import numpy as np
+import math
+import cv2
+
+def Representational(r,g,b):
+	return (0.299*r+0.287*g+0.114*b)
+
+def calculate(img):
+	b,g,r = cv2.split(img)
+	pixelAt = Representational(r,g,b)
+	return pixelAt
+
+def main():
+	
+	#Loading images (orignal image and compressed image)
+	orignal_image = cv2.imread('orignal_image.png',1)
+	compressed_image = cv2.imread('compressed_image.png',1)
+
+	#Getting image height and width
+	height,width = orignal_image.shape[:2]
+
+	orignalPixelAt = calculate(orignal_image)
+	compressedPixelAt = calculate(compressed_image)
+
+	diff = orignalPixelAt - compressedPixelAt
+	error = np.sum(np.abs(diff) ** 2)
+
+	error = error/(height*width)
+
+	#MSR = error_sum/(height*width)
+	PSNR = -(10*math.log10(error/(255*255)))
+
+	print("PSNR value is {}".format(PSNR))
+
+
+if __name__ == '__main__':
+	main()
+

arithmetic_analysis/bisection.py

@@ -0,0 +1,33 @@
+import math
+
+
+def bisection(function, a, b):  # finds where the function becomes 0 in [a,b] using bolzano
+
+    start = a
+    end = b
+    if function(a) == 0:  # one of the a or b is a root for the function
+        return a
+    elif function(b) == 0:
+        return b
+    elif function(a) * function(b) > 0:  # if none of these are root and they are both positive or negative,
+        # then his algorithm can't find the root
+        print("couldn't find root in [a,b]")
+        return
+    else:
+        mid = (start + end) / 2
+        while abs(start - mid) > 0.0000001:  # until we achieve precise equals to 10^-7
+            if function(mid) == 0:
+                return mid
+            elif function(mid) * function(start) < 0:
+                end = mid
+            else:
+                start = mid
+            mid = (start + end) / 2
+        return mid
+
+
+def f(x):
+    return math.pow(x, 3) - 2*x - 5
+
+
+print(bisection(f, 1, 1000))

arithmetic_analysis/intersection.py

@@ -0,0 +1,16 @@
+import math
+
+def intersection(function,x0,x1): #function is the f we want to find its root and x0 and x1 are two random starting points
+    x_n = x0
+    x_n1 = x1
+    while True:
+        x_n2 = x_n1-(function(x_n1)/((function(x_n1)-function(x_n))/(x_n1-x_n)))
+        if abs(x_n2 - x_n1)<0.00001 :
+            return x_n2
+        x_n=x_n1
+        x_n1=x_n2
+
+def f(x):
+    return math.pow(x,3)-2*x-5
+
+print(intersection(f,3,3.5))

arithmetic_analysis/lu_decomposition.py

@@ -0,0 +1,34 @@
+import numpy
+
+def LUDecompose (table):
+    #table that contains our data
+    #table has to be a square array so we need to check first
+    rows,columns=numpy.shape(table)
+    L=numpy.zeros((rows,columns))
+    U=numpy.zeros((rows,columns))
+    if rows!=columns:
+        return
+    for i in range (columns):
+        for j in range(i-1):
+            sum=0
+            for k in range (j-1):
+                sum+=L[i][k]*U[k][j]
+            L[i][j]=(table[i][j]-sum)/U[j][j]
+        L[i][i]=1
+        for j in range(i-1,columns):
+            sum1=0
+            for k in range(i-1):
+                sum1+=L[i][k]*U[k][j]
+            U[i][j]=table[i][j]-sum1
+    return L,U
+
+
+
+
+
+
+
+matrix =numpy.array([[2,-2,1],[0,1,2],[5,3,1]])
+L,U = LUDecompose(matrix)
+print(L)
+print(U)

arithmetic_analysis/newton_method.py

@@ -0,0 +1,15 @@
+def newton(function,function1,startingInt): #function is the f(x) and function1 is the f'(x)
+  x_n=startingInt
+  while True:
+      x_n1=x_n-function(x_n)/function1(x_n)
+      if abs(x_n-x_n1)<0.00001:
+          return x_n1
+      x_n=x_n1
+      
+def f(x):
+    return (x**3)-2*x-5
+
+def f1(x):
+    return 3*(x**2)-2
+
+print(newton(f,f1,3))

arithmetic_analysis/newton_raphson_method.py

@@ -0,0 +1,36 @@
+# Implementing Newton Raphson method in Python
+# Author: Haseeb
+
+from sympy import diff
+from decimal import Decimal
+
+def NewtonRaphson(func, a):
+    ''' Finds root from the point 'a' onwards by Newton-Raphson method '''
+    while True:
+        c = Decimal(a) - ( Decimal(eval(func)) / Decimal(eval(str(diff(func)))) )
+        
+        a = c
+
+        # This number dictates the accuracy of the answer
+        if  abs(eval(func)) < 10**-15:
+            return  c
+    
+
+# Let's Execute
+if __name__ == '__main__':
+    # Find root of trigonometric function
+    # Find value of pi
+    print ('sin(x) = 0', NewtonRaphson('sin(x)', 2))
+    
+    # Find root of polynomial
+    print ('x**2 - 5*x +2 = 0', NewtonRaphson('x**2 - 5*x +2', 0.4))
+    
+    # Find Square Root of 5
+    print ('x**2 - 5 = 0', NewtonRaphson('x**2 - 5', 0.1))
+
+    # Exponential Roots
+    print ('exp(x) - 1 = 0', NewtonRaphson('exp(x) - 1', 0))
+    
+    
+    
+

boolean_algebra/quine_mc_cluskey.py

@@ -0,0 +1,116 @@
+def compare_string(string1, string2):
+	l1 = list(string1); l2 = list(string2)
+	count = 0
+	for i in range(len(l1)):
+		if l1[i] != l2[i]:
+			count += 1
+			l1[i] = '_'
+	if count > 1:
+		return -1
+	else:
+		return("".join(l1))
+
+def check(binary):
+	pi = []
+	while 1:
+		check1 = ['$']*len(binary)
+		temp = []
+		for i in range(len(binary)):
+			for j in range(i+1, len(binary)):
+				k=compare_string(binary[i], binary[j])
+				if k != -1:
+					check1[i] = '*'
+					check1[j] = '*'
+					temp.append(k)
+		for  i in range(len(binary)):
+			if check1[i] == '$':
+				pi.append(binary[i])
+		if len(temp) == 0:
+			return pi
+		binary = list(set(temp))
+
+def decimal_to_binary(no_of_variable, minterms):
+	temp = []
+	s = ''
+	for m in minterms:
+		for i in range(no_of_variable):
+			s = str(m%2) + s
+			m //= 2
+		temp.append(s)
+		s = ''
+	return temp
+
+def is_for_table(string1, string2, count):
+	l1 = list(string1);l2=list(string2)
+	count_n = 0
+	for i in range(len(l1)):
+		if l1[i] != l2[i]:
+			count_n += 1
+	if count_n == count:
+		return True
+	else:
+		return False 
+
+def selection(chart, prime_implicants):
+	temp = []
+	select = [0]*len(chart)
+	for i in range(len(chart[0])):
+		count = 0
+		rem = -1
+		for j in range(len(chart)):
+			if chart[j][i] == 1:
+				count += 1
+				rem = j
+		if count == 1:
+			select[rem] = 1
+	for i in range(len(select)):
+		if select[i] == 1:
+			for j in range(len(chart[0])):
+				if chart[i][j] == 1:
+					for k in range(len(chart)):
+						chart[k][j] = 0 
+			temp.append(prime_implicants[i])
+	while 1:
+		max_n = 0; rem = -1; count_n = 0
+		for i in range(len(chart)):
+			count_n = chart[i].count(1)
+			if count_n > max_n:
+				max_n = count_n
+				rem = i
+		
+		if max_n == 0:
+			return temp
+		
+		temp.append(prime_implicants[rem])
+		
+		for i in range(len(chart[0])):
+			if chart[rem][i] == 1:
+				for j in range(len(chart)):
+					chart[j][i] = 0
+		
+def prime_implicant_chart(prime_implicants, binary):
+	chart = [[0 for x in range(len(binary))] for x in range(len(prime_implicants))]
+	for i in range(len(prime_implicants)):
+		count = prime_implicants[i].count('_')
+		for j in range(len(binary)):
+			if(is_for_table(prime_implicants[i], binary[j], count)):
+				chart[i][j] = 1
+	
+	return chart
+
+def main():
+	no_of_variable = int(raw_input("Enter the no. of variables\n"))
+	minterms = [int(x) for x in raw_input("Enter the decimal representation of Minterms 'Spaces Seprated'\n").split()]
+	binary = decimal_to_binary(no_of_variable, minterms)
+	
+	prime_implicants = check(binary)
+	print("Prime Implicants are:")
+	print(prime_implicants)
+	chart = prime_implicant_chart(prime_implicants, binary)
+	
+	essential_prime_implicants = selection(chart,prime_implicants)
+	print("Essential Prime Implicants are:")
+	print(essential_prime_implicants)
+
+if __name__ == '__main__':
+	main()

ciphers/brute_force_caesar_cipher.py

@@ -0,0 +1,54 @@
+from __future__ import print_function
+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 = raw_input("Encrypted message: ")
+    message = message.upper()
+    decrypt(message)
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+    main()

ciphers/onepad_cipher.py

@@ -0,0 +1,32 @@
+from __future__ import print_function
+
+import random
+
+
+class Onepad:
+    def encrypt(self, text):
+        '''Function to encrypt text using psedo-random numbers'''
+        plain = [ord(i) for i in text]
+        key = []
+        cipher = []
+        for i in plain:
+            k = random.randint(1, 300)
+            c = (i+k)*k
+            cipher.append(c)
+            key.append(k)
+        return cipher, key
+    
+    def decrypt(self, cipher, key):
+        '''Function to decrypt text using psedo-random numbers.'''
+        plain = []
+        for i in range(len(key)):
+            p = (cipher[i]-(key[i])**2)/key[i]
+            plain.append(chr(p))
+        plain = ''.join([i for i in plain])
+        return plain
+
+
+if __name__ == '__main__':
+    c, k = Onepad().encrypt('Hello')
+    print(c, k)
+    print(Onepad().decrypt(c, k))

ciphers/transposition_cipher_encrypt_decrypt_file.py

@@ -0,0 +1,36 @@
+from __future__ import print_function
+import time, os, sys
+import transposition_cipher as transCipher
+
+def main():
+    inputFile = 'Prehistoric Men.txt'
+    outputFile = 'Output.txt'
+    key = int(raw_input('Enter key: '))
+    mode = raw_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 = raw_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()

ciphers/xor_cipher.py

@@ -0,0 +1,209 @@
+"""
+	author: Christian Bender
+	date: 21.12.2017
+	class: XORCipher
+
+	This class implements the XOR-cipher algorithm and provides
+	some useful methods for encrypting and decrypting strings and
+	files.
+
+	Overview about methods
+
+	- encrypt : list of char
+	- decrypt : list of char
+	- encrypt_string : str
+	- decrypt_string : str
+	- encrypt_file : boolean
+	- decrypt_file : boolean
+"""
+class XORCipher(object):
+
+	def __init__(self, key = 0):
+		"""
+			simple constructor that receives a key or uses
+			default key = 0
+		"""
+
+		#private field
+		self.__key = key
+
+	def encrypt(self, content, key):
+		"""
+			input: 'content' of type string and 'key' of type int
+			output: encrypted string 'content' as a list of chars
+			if key not passed the method uses the key by the constructor.
+			otherwise key = 1
+		"""
+
+		# precondition
+		assert (isinstance(key,int) and isinstance(content,str))
+
+		key = key or self.__key or 1
+
+		# make sure key can be any size
+		while (key > 255):
+			key -= 255
+
+		# This will be returned
+		ans = []
+
+		for ch in content:
+			ans.append(chr(ord(ch) ^ key))
+
+		return ans
+
+	def decrypt(self,content,key):
+		"""
+			input: 'content' of type list and 'key' of type int
+			output: decrypted string 'content' as a list of chars
+			if key not passed the method uses the key by the constructor.
+			otherwise key = 1
+		"""
+
+		# precondition
+		assert (isinstance(key,int) and isinstance(content,list))
+
+		key = key or self.__key or 1
+
+		# make sure key can be any size
+		while (key > 255):
+			key -= 255
+
+		# This will be returned
+		ans = []
+
+		for ch in content:
+			ans.append(chr(ord(ch) ^ key))
+
+		return ans
+
+
+	def encrypt_string(self,content, key = 0):
+		"""
+			input: 'content' of type string and 'key' of type int
+			output: encrypted string 'content'
+			if key not passed the method uses the key by the constructor.
+			otherwise key = 1
+		"""
+
+		# precondition
+		assert (isinstance(key,int) and isinstance(content,str))
+
+		key = key or self.__key or 1
+
+		# make sure key can be any size
+		while (key > 255):
+			key -= 255
+
+		# This will be returned
+		ans = ""
+
+		for ch in content:
+			ans += chr(ord(ch) ^ key)
+
+		return ans
+
+	def decrypt_string(self,content,key = 0):
+		"""
+			input: 'content' of type string and 'key' of type int
+			output: decrypted string 'content'
+			if key not passed the method uses the key by the constructor.
+			otherwise key = 1
+		"""
+
+		# precondition
+		assert (isinstance(key,int) and isinstance(content,str))
+
+		key = key or self.__key or 1
+
+		# make sure key can be any size
+		while (key > 255):
+			key -= 255
+
+		# This will be returned
+		ans = ""
+		
+		for ch in content:
+			ans += chr(ord(ch) ^ key)
+
+		return ans
+
+
+	def encrypt_file(self, file, key = 0):
+		"""
+			input: filename (str) and a key (int)
+			output: returns true if encrypt process was
+			successful otherwise false
+			if key not passed the method uses the key by the constructor.
+			otherwise key = 1
+		"""
+
+		#precondition
+		assert (isinstance(file,str) and isinstance(key,int))
+
+		try:
+			with open(file,"r") as fin:
+				with open("encrypt.out","w+") as fout:
+
+					# actual encrypt-process
+					for line in fin:
+						fout.write(self.encrypt_string(line,key))
+
+		except:
+			return False
+
+		return True
+
+
+	def decrypt_file(self,file, key):
+		"""
+			input: filename (str) and a key (int)
+			output: returns true if decrypt process was
+			successful otherwise false
+			if key not passed the method uses the key by the constructor.
+			otherwise key = 1
+		"""
+
+		#precondition
+		assert (isinstance(file,str) and isinstance(key,int))
+
+		try:
+			with open(file,"r") as fin:
+				with open("decrypt.out","w+") as fout:
+
+					# actual encrypt-process
+					for line in fin:
+						fout.write(self.decrypt_string(line,key))
+
+		except:
+			return False
+
+		return True
+
+
+
+
+# Tests
+# crypt = XORCipher()
+# key = 67
+
+# # test enrcypt
+# print crypt.encrypt("hallo welt",key)
+# # test decrypt
+# print crypt.decrypt(crypt.encrypt("hallo welt",key), key)
+
+# # test encrypt_string
+# print crypt.encrypt_string("hallo welt",key)
+
+# # test decrypt_string
+# print crypt.decrypt_string(crypt.encrypt_string("hallo welt",key),key)
+
+# if (crypt.encrypt_file("test.txt",key)):
+# 	print "encrypt successful"
+# else:
+# 	print "encrypt unsuccessful"
+
+# if (crypt.decrypt_file("encrypt.out",key)):
+# 	print "decrypt successful"
+# else:
+# 	print "decrypt unsuccessful"

data_structures/arrays.py

@@ -0,0 +1,3 @@
+arr = [10, 20, 30, 40]
+arr[1] = 30
+print(arr)

data_structures/avl.py

@@ -0,0 +1,181 @@
+"""
+An AVL tree
+"""
+from __future__ import print_function
+
+
+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 = (left_child.right.height
+                                    if (left_child.right is not None) else 0)
+                        h_left = (left_child.left.height
+                                    if (left_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)

data_structures/binary tree/FenwickTree.py

@@ -0,0 +1,29 @@
+from __future__ import print_function
+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))

data_structures/binary tree/LazySegmentTree.py

@@ -0,0 +1,91 @@
+from __future__ import print_function
+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()

data_structures/binary tree/SegmentTree.py

@@ -0,0 +1,71 @@
+from __future__ import print_function
+import math
+
+class SegmentTree:
+    
+    def __init__(self, A):
+        self.N = len(A)
+        self.st = [0] * (4 * self.N) # approximate the overall size of segment tree with array N
+        self.build(1, 0, self.N - 1)
+        
+    def left(self, idx):
+        return idx * 2
+
+    def right(self, idx):
+        return idx * 2 + 1
+
+    def build(self, idx, l, r):
+        if l == r:
+            self.st[idx] = A[l]
+        else:
+            mid = (l + r) // 2
+            self.build(self.left(idx), l, mid)
+            self.build(self.right(idx), mid + 1, r)
+            self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)])
+    
+    def update(self, a, b, val):
+        return self.update_recursive(1, 0, self.N - 1, a - 1, b - 1, val)
+    
+    def update_recursive(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_recursive(self.left(idx), l, mid, a, b, val)
+        self.update_recursive(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, a, b):
+        return self.query_recursive(1, 0, self.N - 1, a - 1, b - 1)
+
+    def query_recursive(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_recursive(self.left(idx), l, mid, a, b)
+        q2 = self.query_recursive(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(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(A)
+    print (segt.query(4, 6))
+    print (segt.query(7, 11))
+    print (segt.query(7, 12))
+    segt.update(1,3,111)
+    print (segt.query(1, 15))
+    segt.update(7,8,235)
+    segt.showData()

data_structures/binary tree/binary_search_tree.py

@@ -0,0 +1,258 @@
+'''
+A binary search Tree
+'''
+from __future__ import print_function
+class Node:
+
+    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
+
+    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
+
+    def getParent(self):
+        return self.parent
+
+    def setParent(self, parent):
+        self.parent = parent
+
+class BinarySearchTree:
+
+    def __init__(self):
+        self.root = None
+
+    def insert(self, label):
+        # Create a new Node
+        new_node = Node(label, None)
+        # If Tree is empty
+        if self.empty():
+            self.root = new_node
+        else:
+            #If Tree is not empty
+            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)
+            #Set parent to the new node
+            new_node.setParent(parent_node)      
+    
+    def delete(self, label):
+        if (not self.empty()):
+            #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:
+                    #Gets the max value of the left branch
+                    tmpNode = self.getMax(node.getLeft())
+                    #Deletes the tmpNode
+                    self.delete(tmpNode.getLabel())
+                    #Assigns the value to the node to delete and keesp tree structure
+                    node.setLabel(tmpNode.getLabel())
+    
+    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 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, 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):
+                curr_node = curr_node.getLeft()
+        return curr_node
+
+    def empty(self):
+        if self.root is None:
+            return True
+        return False
+
+    def __InOrderTraversal(self, curr_node):
+        nodeList = []
+        if curr_node is not None:
+            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
+
+    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)):
+                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:
+            #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():
+    '''
+    Example
+                  8
+                 / \
+                3   10
+               / \    \
+              1   6    14
+                 / \   /
+                4   7 13 
+    '''
+
+    '''
+    Example After Deletion
+                  7
+                 / \
+                1   4
+
+    '''
+    t = BinarySearchTree()
+    t.insert(8)
+    t.insert(3)
+    t.insert(6)
+    t.insert(1)
+    t.insert(10)
+    t.insert(14)
+    t.insert(13)
+    t.insert(4)
+    t.insert(7)
+
+    #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")
+    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")
+    
+    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.delete(3)
+    t.delete(6)
+    t.delete(14)
+
+    #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()

data_structures/graph/bellman_ford.py

@@ -0,0 +1,54 @@
+from __future__ import print_function
+
+def printDist(dist, V):
+	print("\nVertex Distance")
+	for i in range(V):
+		if dist[i] != float('inf') :
+			print(i,"\t",int(dist[i]),end = "\t")
+		else:
+			print(i,"\t","INF",end="\t")
+		print()
+
+def BellmanFord(graph, V, E, src):
+	mdist=[float('inf') for i in range(V)]
+	mdist[src] = 0.0
+	
+	for i in range(V-1):
+		for j in range(V):
+			u = graph[j]["src"]
+			v = graph[j]["dst"]
+			w = graph[j]["weight"]
+
+			if mdist[u] != float('inf') and mdist[u] + w < mdist[v]:
+				mdist[v] = mdist[u] + w 
+	for j in range(V):
+			u = graph[j]["src"]
+			v = graph[j]["dst"]
+			w = graph[j]["weight"]
+
+			if mdist[u] != float('inf') and mdist[u] + w < mdist[v]:
+				print("Negative cycle found. Solution not possible.")
+				return
+	
+	printDist(mdist, V)	
+
+			
+
+#MAIN
+V = int(raw_input("Enter number of vertices: "))
+E = int(raw_input("Enter number of edges: "))
+
+graph = [dict() for j in range(E)]
+
+for i in range(V):
+	graph[i][i] = 0.0
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(raw_input("Enter source:"))
+	dst = int(raw_input("Enter destination:"))
+	weight = float(raw_input("Enter weight:"))
+	graph[i] = {"src": src,"dst": dst, "weight": weight}
+	
+gsrc = int(raw_input("\nEnter shortest path source:"))
+BellmanFord(graph, V, E, gsrc)

data_structures/graph/breadth_first_search.py

@@ -0,0 +1,67 @@
+#!/usr/bin/python
+# encoding=utf8
+
+""" Author: OMKAR PATHAK """
+
+from __future__ import print_function
+
+
+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

data_structures/graph/depth_first_search.py

@@ -0,0 +1,66 @@
+#!/usr/bin/python
+# encoding=utf8
+
+""" Author: OMKAR PATHAK """
+from __future__ import print_function
+
+
+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

data_structures/graph/dijkstra.py

@@ -0,0 +1,57 @@
+from __future__ import print_function
+
+def printDist(dist, V):
+	print("\nVertex Distance")
+	for i in range(V):
+		if dist[i] != float('inf') :
+			print(i,"\t",int(dist[i]),end = "\t")
+		else:
+			print(i,"\t","INF",end="\t")
+		print()
+
+def minDist(mdist, vset, V):
+	minVal = float('inf')
+	minInd = -1
+	for i in range(V):
+		if (not vset[i]) and mdist[i] < minVal :
+			minInd = i
+			minVal = mdist[i]
+	return minInd
+
+def Dijkstra(graph, V, src):
+	mdist=[float('inf') for i in range(V)]
+	vset = [False for i in range(V)]
+	mdist[src] = 0.0;
+	
+	for i in range(V-1):
+		u = minDist(mdist, vset, V)
+		vset[u] = True
+		
+		for v in range(V):
+			if (not vset[v]) and graph[u][v]!=float('inf') and mdist[u] + graph[u][v] < mdist[v]:
+				mdist[v] = mdist[u] + graph[u][v] 
+
+	
+
+	printDist(mdist, V)	
+
+			
+
+#MAIN
+V = int(raw_input("Enter number of vertices: "))
+E = int(raw_input("Enter number of edges: "))
+
+graph = [[float('inf') for i in range(V)] for j in range(V)]
+
+for i in range(V):
+	graph[i][i] = 0.0
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(raw_input("Enter source:"))
+	dst = int(raw_input("Enter destination:"))
+	weight = float(raw_input("Enter weight:"))
+	graph[src][dst] = weight
+
+gsrc = int(raw_input("\nEnter shortest path source:"))
+Dijkstra(graph, V, gsrc)

data_structures/graph/dijkstra_algorithm.py

@@ -0,0 +1,212 @@
+# Title: Dijkstra's Algorithm for finding single source shortest path from scratch
+# Author: Shubham Malik
+# References: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
+
+from __future__ import print_function
+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

data_structures/graph/even_tree.py

@@ -0,0 +1,70 @@
+"""
+You are given a tree(a simple connected graph with no cycles). The tree has N
+nodes numbered from 1 to N and is rooted at node 1.
+
+Find the maximum number of edges you can remove from the tree to get a forest
+such that each connected component of the forest contains an even number of
+nodes.
+
+Constraints
+2 <= 2 <= 100
+
+Note: The tree input will be such that it can always be decomposed into
+components containing an even number of nodes.
+"""
+from __future__ import print_function
+# pylint: disable=invalid-name
+from collections import defaultdict
+
+
+def dfs(start):
+    """DFS traversal"""
+    # pylint: disable=redefined-outer-name
+    ret = 1
+    visited[start] = True
+    for v in tree.get(start):
+        if v not in visited:
+            ret += dfs(v)
+    if ret % 2 == 0:
+        cuts.append(start)
+    return ret
+
+
+def even_tree():
+    """
+    2 1
+    3 1
+    4 3
+    5 2
+    6 1
+    7 2
+    8 6
+    9 8
+    10 8
+    On removing edges (1,3) and (1,6), we can get the desired result 2.
+    """
+    dfs(1)
+
+
+if __name__ == '__main__':
+    n, m = 10, 9
+    tree = defaultdict(list)
+    visited = {}
+    cuts = []
+    count = 0
+    edges = [
+        (2, 1),
+        (3, 1),
+        (4, 3),
+        (5, 2),
+        (6, 1),
+        (7, 2),
+        (8, 6),
+        (9, 8),
+        (10, 8),
+    ]
+    for u, v in edges:
+        tree[u].append(v)
+        tree[v].append(u)
+    even_tree()
+    print(len(cuts) - 1)

data_structures/graph/floyd_warshall.py

@@ -0,0 +1,48 @@
+from __future__ import print_function
+
+def printDist(dist, V):
+	print("\nThe shortest path matrix using Floyd Warshall algorithm\n")
+	for i in range(V):
+		for j in range(V):
+			if dist[i][j] != float('inf') :
+				print(int(dist[i][j]),end = "\t")
+			else:
+				print("INF",end="\t")
+		print()
+
+
+
+def FloydWarshall(graph, V):
+	dist=[[float('inf') for i in range(V)] for j in range(V)]
+	
+	for i in range(V):
+		for j in range(V):
+			dist[i][j] = graph[i][j]
+
+	for k in range(V):
+		for i in range(V):
+			for j in range(V):
+				if dist[i][k]!=float('inf') and dist[k][j]!=float('inf') and dist[i][k]+dist[k][j] < dist[i][j]:
+					dist[i][j] = dist[i][k] + dist[k][j]
+
+	printDist(dist, V)	
+
+			
+
+#MAIN
+V = int(raw_input("Enter number of vertices: "))
+E = int(raw_input("Enter number of edges: "))
+
+graph = [[float('inf') for i in range(V)] for j in range(V)]
+
+for i in range(V):
+	graph[i][i] = 0.0
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(raw_input("Enter source:"))
+	dst = int(raw_input("Enter destination:"))
+	weight = float(raw_input("Enter weight:"))
+	graph[src][dst] = weight
+
+FloydWarshall(graph, V)

data_structures/graph/graph.py

@@ -0,0 +1,44 @@
+#!/usr/bin/python
+# encoding=utf8
+
+from __future__ import print_function
+# 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

data_structures/graph/graph_list.py

@@ -0,0 +1,31 @@
+from __future__ import print_function
+
+
+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()
+

data_structures/graph/graph_matrix.py

@@ -0,0 +1,32 @@
+from __future__ import print_function
+
+
+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()
+

data_structures/heap/heap.py

@@ -0,0 +1,90 @@
+#!/usr/bin/python
+
+from __future__ import print_function, division
+
+try:
+    raw_input          # Python 2
+except NameError:
+    raw_input = input  # Python 3
+
+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()
+
+

data_structures/linked_list/DoublyLinkedList.py

@@ -0,0 +1,76 @@
+'''
+- 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.
+'''
+from __future__ import print_function
+
+
+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 is 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 is 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=" ")

data_structures/linked_list/__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 is None

data_structures/linked_list/singly_LinkedList.py

@@ -0,0 +1,70 @@
+from __future__ import print_function
+
+
+class Node:  # create a Node
+    def __init__(self, data):
+        self.data = data  # given data
+        self.next = None  # given next to None
+
+
+class Linked_List:
+    def insert_tail(Head, data):
+        if Head.next is None:
+            Head.next = Node(data)
+        else:
+            Head.next.insert_tail(data)
+
+    def insert_head(Head, data):
+        tamp = Head
+        if tamp is 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 is not None:
+            print(tamp.data)
+            tamp = tamp.next
+
+    def delete_head(Head):  # delete from head
+        if Head is not None:
+            Head = Head.next
+        return Head  # return new Head
+
+    def delete_tail(Head):  # delete from tail
+        if Head is not None:
+            tamp = Node()
+            tamp = Head
+            while tamp.next.next is not None:  # find the 2nd last element
+                tamp = tamp.next
+            # delete the last element by give next None to 2nd last Element
+            tamp.next = None
+        return Head
+
+    def isEmpty(Head):
+        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
+        return Head

data_structures/queue/DeQueue.py

@@ -0,0 +1,40 @@
+from __future__ import print_function
+# 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)

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

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

data_structures/stacks/Stock-Span-Problem.py

@@ -0,0 +1,52 @@
+'''
+The stock span problem is a financial problem where we have a series of n daily 
+price quotes for a stock and we need to calculate span of stock's price for all n days.
+
+The span Si of the stock's price on a given day i is defined as the maximum 
+number of consecutive days just before the given day, for which the price of the stock 
+on the current day is less than or equal to its price on the given day.
+'''
+from __future__ import print_function
+def calculateSpan(price, S): 
+      
+    n = len(price) 
+    # Create a stack and push index of fist element to it 
+    st = []  
+    st.append(0) 
+  
+    # Span value of first element is always 1 
+    S[0] = 1 
+  
+    # Calculate span values for rest of the elements 
+    for i in range(1, n): 
+          
+        # Pop elements from stack whlie stack is not 
+        # empty and top of stack is smaller than price[i] 
+        while( len(st) > 0 and price[st[0]] <= price[i]): 
+            st.pop() 
+  
+        # If stack becomes empty, then price[i] is greater 
+        # than all elements on left of it, i.e. price[0], 
+        # price[1], ..price[i-1]. Else the price[i]  is 
+        # greater than elements after top of stack 
+        S[i] = i+1 if len(st) <= 0 else (i - st[0]) 
+  
+        # Push this element to stack 
+        st.append(i) 
+  
+  
+# A utility function to print elements of array 
+def printArray(arr, n): 
+    for i in range(0,n): 
+        print (arr[i],end =" ") 
+  
+  
+# Driver program to test above function 
+price = [10, 4, 5, 90, 120, 80] 
+S = [0 for i in range(len(price)+1)] 
+  
+# Fill the span values in array S[] 
+calculateSpan(price, S) 
+  
+# Print the calculated span values 
+printArray(S, len(price)) 

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]

data_structures/stacks/balanced_parentheses.py

@@ -0,0 +1,23 @@
+from __future__ import print_function
+from __future__ import absolute_import
+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)))

data_structures/stacks/infix_to_postfix_conversion.py

@@ -0,0 +1,64 @@
+from __future__ import print_function
+from __future__ import absolute_import
+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))

data_structures/stacks/next.py

@@ -0,0 +1,17 @@
+from __future__ import print_function
+# 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)

data_structures/stacks/stack.py

@@ -0,0 +1,69 @@
+from __future__ import print_function
+__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()))

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]):  # noqa: E999 This syntax is Python 3 only
+        """
+        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):  # noqa: E999 This syntax is Python 3 only
+        """
+        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:  # noqa: E999 This syntax is Python 3 only
+        """
+        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):  # noqa: E999 This syntax is Python 3 only
+    """
+    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()

data_structures/union_find/tests_union_find.py

@@ -0,0 +1,78 @@
+from __future__ import absolute_import
+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()

data_structures/union_find/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)

dynamic_programming/floyd_warshall.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)

file_transfer_protocol/ftp_client_server.py

@@ -0,0 +1,58 @@
+# server
+
+import socket                   # Import socket module
+
+port = 60000                    # Reserve a port for your service.
+s = socket.socket()             # Create a socket object
+host = socket.gethostname()     # Get local machine name
+s.bind((host, port))            # Bind to the port
+s.listen(5)                     # Now wait for client connection.
+
+print('Server listening....')
+
+while True:
+    conn, addr = s.accept()     # Establish connection with client.
+    print('Got connection from', addr)
+    data = conn.recv(1024)
+    print('Server received', repr(data))
+
+    filename = 'mytext.txt'
+    f = open(filename, 'rb')
+    in_data = f.read(1024)
+    while (in_data):
+       conn.send(in_data)
+       print('Sent ', repr(in_data))
+       in_data = f.read(1024)
+    f.close()
+
+    print('Done sending')
+    conn.send('Thank you for connecting')
+    conn.close()
+
+
+# client side server
+
+import socket                   # Import socket module
+
+s = socket.socket()             # Create a socket object
+host = socket.gethostname()     # Get local machine name
+port = 60000                    # Reserve a port for your service.
+
+s.connect((host, port))
+s.send("Hello server!")
+
+with open('received_file', 'wb') as f:
+    print('file opened')
+    while True:
+        print('receiving data...')
+        data = s.recv(1024)
+        print('data=%s', (data))
+        if not data:
+            break
+        # write data to a file
+        f.write(data)
+
+f.close()
+print('Successfully get the file')
+s.close()
+print('connection closed')

file_transfer_protocol/ftp_send_receive.py

@@ -0,0 +1,36 @@
+"""
+	File transfer protocol used to send and receive files using FTP server.
+	Use credentials to provide access to the FTP client
+
+	Note: Do not use root username & password for security reasons
+	  Create a seperate user and provide access to a home directory of the user
+	  Use login id and password of the user created 
+	  cwd here stands for current working directory
+"""
+
+from ftplib import FTP
+ftp = FTP('xxx.xxx.x.x')  # Enter the ip address or the domain name here
+ftp.login(user='username', passwd='password')
+ftp.cwd('/Enter the directory here/')
+
+"""
+	The file which will be received via the FTP server
+	Enter the location of the file where the file is received
+"""
+
+def ReceiveFile():
+	FileName = 'example.txt'   """ Enter the location of the file """
+	LocalFile = open(FileName, 'wb')
+	ftp.retrbinary('RETR ' + FileName, LocalFile.write, 1024)
+	ftp.quit()
+	LocalFile.close()
+
+"""
+	The file which will be sent via the FTP server
+	The file send will be send to the current working directory
+"""
+
+def SendFile():
+	FileName = 'example.txt'   """ Enter the name of the file """
+	ftp.storbinary('STOR ' + FileName, open(FileName, 'rb'))
+	ftp.quit()

graphs/ArticulationPoints.py

@@ -0,0 +1,44 @@
+# Finding Articulation Points in Undirected Graph
+def computeAP(l):
+    n = len(l)
+    outEdgeCount = 0
+    low = [0] * n
+    visited = [False] * n
+    isArt = [False] * n
+
+    def dfs(root, at, parent, outEdgeCount):
+        if parent == root:
+            outEdgeCount += 1
+        visited[at] = True
+        low[at] = at
+
+        for to in l[at]:
+            if to == parent:
+                pass
+            elif not visited[to]:
+                outEdgeCount = dfs(root, to, at, outEdgeCount)
+                low[at] = min(low[at], low[to])
+
+                # AP found via bridge
+                if at < low[to]:
+                    isArt[at] = True
+                # AP found via cycle
+                if at == low[to]:
+                    isArt[at] = True
+            else:
+                low[at] = min(low[at], to)
+        return outEdgeCount
+
+    for i in range(n):
+        if not visited[i]:
+            outEdgeCount = 0
+            outEdgeCount = dfs(i, i, -1, outEdgeCount)
+            isArt[i] = (outEdgeCount > 1)
+
+    for x in range(len(isArt)):
+        if isArt[x] == True:
+            print(x)
+
+# Adjacency list of graph
+l = {0:[1,2], 1:[0,2], 2:[0,1,3,5], 3:[2,4], 4:[3], 5:[2,6,8], 6:[5,7], 7:[6,8], 8:[5,7]}
+computeAP(l)

graphs/CheckBipartiteGraph_BFS.py

@@ -0,0 +1,43 @@
+# Check whether Graph is Bipartite or Not using BFS
+
+# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
+# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
+# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
+# or u belongs to V and v to U. We can also say that there is no edge that connects
+# vertices of same set.
+def checkBipartite(l):
+    queue = []
+    visited = [False] * len(l)
+    color = [-1] * len(l)
+
+    def bfs():
+        while(queue):
+            u = queue.pop(0)
+            visited[u] = True
+
+            for neighbour in l[u]:
+
+                if neighbour == u:
+                    return False
+
+                if color[neighbour] == -1:
+                    color[neighbour] = 1 - color[u]
+                    queue.append(neighbour)
+
+                elif color[neighbour] == color[u]:
+                    return False
+
+        return True
+
+    for i in range(len(l)):
+        if not visited[i]:
+            queue.append(i)
+            color[i] = 0
+            if bfs() == False:
+                return False
+
+    return True
+
+# Adjacency List of graph
+l = {0:[1,3], 1:[0,2], 2:[1,3], 3:[0,2]}
+print(checkBipartite(l))

graphs/FindingBridges.py

@@ -0,0 +1,31 @@
+# Finding Bridges in Undirected Graph
+def computeBridges(l):
+    id = 0
+    n = len(l) # No of vertices in graph
+    low = [0] * n
+    visited = [False] * n
+
+    def dfs(at, parent, bridges, id):
+        visited[at] = True
+        low[at] = id
+        id += 1
+        for to in l[at]:
+            if to == parent:
+                pass
+            elif not visited[to]:
+                dfs(to, at, bridges, id)
+                low[at] = min(low[at], low[to])
+                if at < low[to]:
+                    bridges.append([at, to])
+            else:
+                # This edge is a back edge and cannot be a bridge
+                low[at] = min(low[at], to)
+
+    bridges = []
+    for i in range(n):
+        if (not visited[i]):
+            dfs(i, -1, bridges, id)
+    print(bridges)
+            
+l = {0:[1,2], 1:[0,2], 2:[0,1,3,5], 3:[2,4], 4:[3], 5:[2,6,8], 6:[5,7], 7:[6,8], 8:[5,7]}
+computeBridges(l)

graphs/KahnsAlgorithm_long.py

@@ -0,0 +1,30 @@
+# Finding longest distance in Directed Acyclic Graph using KahnsAlgorithm
+def longestDistance(l):
+    indegree = [0] * len(l)
+    queue = []
+    longDist = [1] * len(l)
+
+    for key, values in l.items():
+        for i in values:
+            indegree[i] += 1
+
+    for i in range(len(indegree)):
+        if indegree[i] == 0:
+            queue.append(i)
+
+    while(queue):
+        vertex = queue.pop(0)
+        for x in l[vertex]:
+            indegree[x] -= 1
+
+            if longDist[vertex] + 1 > longDist[x]:
+                longDist[x] =  longDist[vertex] + 1
+
+            if indegree[x] == 0:
+                queue.append(x)
+
+    print(max(longDist))
+
+# Adjacency list of Graph
+l = {0:[2,3,4], 1:[2,7], 2:[5], 3:[5,7], 4:[7], 5:[6], 6:[7], 7:[]}
+longestDistance(l)

graphs/KahnsAlgorithm_topo.py

@@ -0,0 +1,32 @@
+# Kahn's Algorithm is used to find Topological ordering of Directed Acyclic Graph using BFS
+def topologicalSort(l):
+    indegree = [0] * len(l)
+    queue = []
+    topo = []
+    cnt = 0
+
+    for key, values in l.items():
+        for i in values:
+            indegree[i] += 1
+
+    for i in range(len(indegree)):
+        if indegree[i] == 0:
+            queue.append(i)
+
+    while(queue):
+        vertex = queue.pop(0)
+        cnt += 1
+        topo.append(vertex)
+        for x in l[vertex]:
+            indegree[x] -= 1
+            if indegree[x] == 0:
+                queue.append(x)
+
+    if cnt != len(l):
+        print("Cycle exists")
+    else:
+        print(topo)
+
+# Adjacency List of Graph
+l = {0:[1,2], 1:[3], 2:[3], 3:[4,5], 4:[], 5:[]}
+topologicalSort(l)

graphs/MinimumSpanningTree_Prims.py

@@ -0,0 +1,111 @@
+import sys
+from collections import defaultdict
+
+def PrimsAlgorithm(l):
+
+    nodePosition = []
+    def getPosition(vertex):
+        return nodePosition[vertex]
+
+    def setPosition(vertex, pos):
+        nodePosition[vertex] = pos
+
+    def topToBottom(heap, start, size, positions):
+        if start > size // 2 - 1:
+            return
+        else:
+            if 2 * start + 2 >= size:
+                m = 2 * start + 1
+            else:
+                if heap[2 * start + 1] < heap[2 * start + 2]:
+                    m = 2 * start + 1
+                else:
+                    m = 2 * start + 2
+            if heap[m] < heap[start]:
+                temp, temp1 = heap[m], positions[m]
+                heap[m], positions[m] = heap[start], positions[start]
+                heap[start], positions[start] = temp, temp1
+
+                temp = getPosition(positions[m])
+                setPosition(positions[m], getPosition(positions[start]))
+                setPosition(positions[start], temp)
+
+                topToBottom(heap, m, size, positions)
+
+    # Update function if value of any node in min-heap decreases
+    def bottomToTop(val, index, heap, position):
+        temp = position[index]
+
+        while(index != 0):
+            if index % 2 == 0:
+                parent = int( (index-2) / 2 )
+            else:
+                parent = int( (index-1) / 2 )
+
+            if val < heap[parent]:
+                heap[index] = heap[parent]
+                position[index] = position[parent]
+                setPosition(position[parent], index)
+            else:
+                heap[index] = val
+                position[index] = temp
+                setPosition(temp, index)
+                break
+            index = parent
+        else:
+            heap[0] = val
+            position[0] = temp
+            setPosition(temp, 0)
+
+    def heapify(heap, positions):
+        start = len(heap) // 2 - 1
+        for i in range(start, -1, -1):
+            topToBottom(heap, i, len(heap), positions)
+
+    def deleteMinimum(heap, positions):
+        temp = positions[0]
+        heap[0] = sys.maxsize
+        topToBottom(heap, 0, len(heap), positions)
+        return temp
+
+    visited = [0 for i in range(len(l))]
+    Nbr_TV  = [-1 for i in range(len(l))] # Neighboring Tree Vertex of selected vertex
+    # Minimum Distance of explored vertex with neighboring vertex of partial tree formed in graph
+    Distance_TV = [] # Heap of Distance of vertices from their neighboring vertex
+    Positions = []
+
+    for x in range(len(l)):
+        p = sys.maxsize
+        Distance_TV.append(p)
+        Positions.append(x)
+        nodePosition.append(x)
+
+    TreeEdges = []
+    visited[0] = 1
+    Distance_TV[0] = sys.maxsize
+    for x in l[0]:
+        Nbr_TV[ x[0] ] = 0
+        Distance_TV[ x[0] ] = x[1]
+    heapify(Distance_TV, Positions)
+
+    for i in range(1, len(l)):
+        vertex = deleteMinimum(Distance_TV, Positions)
+        if visited[vertex] == 0:
+            TreeEdges.append((Nbr_TV[vertex], vertex))
+            visited[vertex] = 1
+            for v in l[vertex]:
+                if visited[v[0]] == 0 and v[1] < Distance_TV[ getPosition(v[0]) ]:
+                    Distance_TV[ getPosition(v[0]) ] = v[1]
+                    bottomToTop(v[1], getPosition(v[0]), Distance_TV, Positions)
+                    Nbr_TV[ v[0] ] = vertex
+    return TreeEdges
+
+# < --------- Prims Algorithm --------- >
+n = int(raw_input("Enter number of vertices: "))
+e = int(raw_input("Enter number of edges: "))
+adjlist = defaultdict(list)
+for x in range(e):
+    l = [int(x) for x in input().split()]
+    adjlist[l[0]].append([ l[1], l[2] ])
+    adjlist[l[1]].append([ l[0], l[2] ])
+print(PrimsAlgorithm(adjlist))

graphs/Multi_Hueristic_Astar.py

@@ -0,0 +1,266 @@
+from __future__ import print_function
+import heapq
+import numpy as np
+
+try:
+    xrange          # Python 2
+except NameError:
+    xrange = range  # Python 3
+
+
+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], end=' ')
+				print("<-- End position", end=' ')
+			else:
+				print(grid[i][j], end=' ')
+		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, end=' ') 
+		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('#', end=' ')
+			elif (j, i) in back_pointer:
+				if (j, i) == (n-1, n-1):
+					print('*', end=' ')
+				else:
+					print('-', end=' ')
+			else:
+				print('*', end=' ')
+			if (j, i) == (n-1, n-1):
+				print('<-- End position', end=' ')
+		print()
+	print("^")
+	print("Start position")
+	print()
+	print("# is an obstacle")
+	print("- is the path taken by algorithm")
+multi_a_star(start, goal, n_hueristic)

graphs/a_star.py

@@ -0,0 +1,102 @@
+from __future__ import print_function
+
+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]) 
+

graphs/basic-graphs.py

@@ -0,0 +1,281 @@
+from __future__ import print_function
+
+try:
+    raw_input          # Python 2
+except NameError:
+    raw_input = input  # Python 3
+
+try:
+    xrange             # Python 2
+except NameError:
+    xrange = range     # Python 3
+
+# 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 is 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 = raw_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_and_n):
+    (A, n) = A_and_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_and_n):
+    # Sort edges on the basis of distance
+    (E, n) = E_and_n
+    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

graphs/minimum_spanning_tree_kruskal.py

@@ -0,0 +1,32 @@
+from __future__ import print_function
+num_nodes, num_edges = list(map(int,raw_input().split()))
+
+edges = []
+
+for i in range(num_edges):
+	node1, node2, cost = list(map(int,raw_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)

graphs/scc_kosaraju.py

@@ -0,0 +1,46 @@
+from __future__ import print_function
+# n - no of nodes, m - no of edges
+n, m = list(map(int,raw_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,raw_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())

graphs/tarjans_scc.py

@@ -0,0 +1,78 @@
+from collections import deque
+
+
+def tarjan(g):
+    """
+    Tarjan's algo for finding strongly connected components in a directed graph
+
+    Uses two main attributes of each node to track reachability, the index of that node within a component(index),
+    and the lowest index reachable from that node(lowlink).
+
+    We then perform a dfs of the each component making sure to update these parameters for each node and saving the
+    nodes we visit on the way.
+
+    If ever we find that the lowest reachable node from a current node is equal to the index of the current node then it
+    must be the root of a strongly connected component and so we save it and it's equireachable vertices as a strongly
+    connected component.
+
+    Complexity: strong_connect() is called at most once for each node and has a complexity of O(|E|) as it is DFS.
+    Therefore this has complexity O(|V| + |E|) for a graph G = (V, E)
+
+    """
+
+    n = len(g)
+    stack = deque()
+    on_stack = [False for _ in range(n)]
+    index_of = [-1 for _ in range(n)]
+    lowlink_of = index_of[:]
+
+    def strong_connect(v, index, components):
+        index_of[v] = index  # the number when this node is seen
+        lowlink_of[v] = index  # lowest rank node reachable from here
+        index += 1
+        stack.append(v)
+        on_stack[v] = True
+
+        for w in g[v]:
+            if index_of[w] == -1:
+                index = strong_connect(w, index, components)
+                lowlink_of[v] = lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
+            elif on_stack[w]:
+                lowlink_of[v] = lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
+
+        if lowlink_of[v] == index_of[v]:
+            component = []
+            w = stack.pop()
+            on_stack[w] = False
+            component.append(w)
+            while w != v:
+                w = stack.pop()
+                on_stack[w] = False
+                component.append(w)
+            components.append(component)
+        return index
+
+    components = []
+    for v in range(n):
+        if index_of[v] == -1:
+            strong_connect(v, 0, components)
+
+    return components
+
+
+def create_graph(n, edges):
+    g = [[] for _ in range(n)]
+    for u, v in edges:
+        g[u].append(v)
+    return g
+
+
+if __name__ == '__main__':
+    # Test
+    n_vertices = 7
+    source = [0, 0, 1, 2, 3, 3, 4, 4, 6]
+    target = [1, 3, 2, 0, 1, 4, 5, 6, 5]
+    edges = [(u, v) for u, v in zip(source, target)]
+    g = create_graph(n_vertices, edges)
+
+    assert [[5], [6], [4], [3, 2, 1, 0]] == tarjan(g)

linear_algebra_python/README.md

@@ -0,0 +1,74 @@
+# Linear algebra library for Python  
+
+This module contains some useful classes and functions for dealing with linear algebra in python 2.  
+
+---
+
+## Overview  
+
+- class Vector  
+    - This class represents a vector of arbitray size and operations on it.  
+
+    **Overview about the methods:**    
+        
+    - constructor(components : list) : init the vector  
+    - set(components : list) : changes the vector components.  
+    - __str__() : toString method  
+    - component(i : int): gets the i-th component (start by 0)  
+    - size() : gets the size of the vector (number of components)  
+    - euclidLength() : returns the eulidean length of the vector.  
+    - operator + : vector addition  
+    - operator - : vector subtraction  
+    - operator * : scalar multiplication and dot product  
+    - copy() : copies this vector and returns it.  
+    - changeComponent(pos,value) : changes the specified component.  
+
+- function zeroVector(dimension)  
+    - returns a zero vector of 'dimension'  
+- function unitBasisVector(dimension,pos)  
+    - returns a unit basis vector with a One at index 'pos' (indexing at 0)  
+- function axpy(scalar,vector1,vector2)  
+    - computes the axpy operation  
+- function randomVector(N,a,b)
+    - returns a random vector of size N, with random integer components between 'a' and 'b'.
+- class Matrix
+    - This class represents a matrix of arbitrary size and operations on it.
+
+    **Overview about the methods:**  
+    
+    -  __str__() : returns a string representation  
+    - operator * : implements the matrix vector multiplication  
+                   implements the matrix-scalar multiplication.  
+    - changeComponent(x,y,value) : changes the specified component.  
+    - component(x,y) : returns the specified component.  
+    - width() : returns the width of the matrix  
+    - height() : returns the height of the matrix  
+    - operator + : implements the matrix-addition.  
+    - operator - _ implements the matrix-subtraction  
+- function squareZeroMatrix(N)  
+    - returns a square zero-matrix of dimension NxN  
+- function randomMatrix(W,H,a,b)  
+    - returns a random matrix WxH with integer components between 'a' and 'b'  
+---
+
+## Documentation  
+
+The module is well documented. You can use the python in-built ```help(...)``` function.  
+For instance: ```help(Vector)``` gives you all information about the Vector-class.  
+Or ```help(unitBasisVector)``` gives you all information you needed about the  
+global function ```unitBasisVector(...)```. If you need informations about a certain  
+method you type ```help(CLASSNAME.METHODNAME)```.  
+
+---
+
+## Usage  
+
+You will find the module in the **src** directory its called ```lib.py```. You need to  
+import this module in your project. Alternative you can also use the file ```lib.pyc``` in python-bytecode.   
+
+---
+
+## Tests  
+
+In the **src** directory you also find the test-suite, its called ```tests.py```.  
+The test-suite uses the built-in python-test-framework **unittest**.  

linear_algebra_python/src/lib.py

@@ -0,0 +1,364 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Feb 26 14:29:11 2018
+
+@author: Christian Bender
+@license: MIT-license
+
+This module contains some useful classes and functions for dealing
+with linear algebra in python.
+
+Overview:
+
+- class Vector
+- function zeroVector(dimension)
+- function unitBasisVector(dimension,pos)
+- function axpy(scalar,vector1,vector2)
+- function randomVector(N,a,b)
+- class Matrix
+- function squareZeroMatrix(N)
+- function randomMatrix(W,H,a,b)
+"""
+
+
+import math
+import random
+
+
+class Vector(object):
+    """
+        This class represents a vector of arbitray size.
+        You need to give the vector components. 
+        
+        Overview about the methods:
+        
+        constructor(components : list) : init the vector
+        set(components : list) : changes the vector components.
+        __str__() : toString method
+        component(i : int): gets the i-th component (start by 0)
+        size() : gets the size of the vector (number of components)
+        euclidLength() : returns the eulidean length of the vector.
+        operator + : vector addition
+        operator - : vector subtraction
+        operator * : scalar multiplication and dot product
+        copy() : copies this vector and returns it.
+        changeComponent(pos,value) : changes the specified component.
+        TODO: compare-operator
+    """
+    def __init__(self,components):
+        """
+            input: components or nothing
+            simple constructor for init the vector
+        """
+        self.__components = components
+    def set(self,components):
+        """
+            input: new components
+            changes the components of the vector.
+            replace the components with newer one.
+        """
+        if len(components) > 0:
+            self.__components = components
+        else:
+            raise Exception("please give any vector")
+    def __str__(self):
+        """
+            returns a string representation of the vector
+        """
+        ans = "("
+        length = len(self.__components)
+        for i in range(length):
+            if i != length-1:
+                ans += str(self.__components[i]) + ","
+            else:
+                ans += str(self.__components[i]) + ")"
+        if len(ans) == 1:
+            ans += ")"
+        return ans
+    def component(self,i):
+        """
+            input: index (start at 0)
+            output: the i-th component of the vector.
+        """
+        if i < len(self.__components) and i >= 0:
+            return self.__components[i]
+        else:
+            raise Exception("index out of range")
+    def size(self):
+        """
+            returns the size of the vector
+        """
+        return len(self.__components)
+    def eulidLength(self):
+        """
+            returns the eulidean length of the vector
+        """
+        summe = 0
+        for c in self.__components:
+            summe += c**2
+        return math.sqrt(summe)
+    def __add__(self,other):
+        """
+            input: other vector
+            assumes: other vector has the same size
+            returns a new vector that represents the sum.
+        """
+        size = self.size()
+        result = []
+        if size == other.size():
+            for i in range(size):
+                result.append(self.__components[i] + other.component(i))
+        else:
+            raise Exception("must have the same size")
+        return Vector(result)
+    def __sub__(self,other):
+        """
+            input: other vector
+            assumes: other vector has the same size
+            returns a new vector that represents the differenz.
+        """
+        size = self.size()
+        result = []
+        if size == other.size():
+            for i in range(size):
+                result.append(self.__components[i] - other.component(i))
+        else: # error case
+            raise Exception("must have the same size")
+        return Vector(result)
+    def __mul__(self,other):
+        """
+            mul implements the scalar multiplication 
+            and the dot-product
+        """
+        ans = []
+        if isinstance(other,float) or isinstance(other,int):
+            for c in self.__components:
+                ans.append(c*other)
+        elif (isinstance(other,Vector) and (self.size() == other.size())):
+            size = self.size()
+            summe = 0
+            for i in range(size):
+                summe += self.__components[i] * other.component(i)
+            return summe
+        else: # error case
+            raise Exception("invalide operand!")
+        return Vector(ans)
+    def copy(self):
+        """
+            copies this vector and returns it.
+        """
+        components = [x for x in self.__components]
+        return Vector(components)
+    def changeComponent(self,pos,value):
+        """
+            input: an index (pos) and a value
+            changes the specified component (pos) with the
+            'value'
+        """
+        #precondition
+        assert (pos >= 0 and pos < len(self.__components))
+        self.__components[pos] = value
+    
+def zeroVector(dimension):
+    """
+        returns a zero-vector of size 'dimension'
+    """        
+    #precondition
+    assert(isinstance(dimension,int))
+    ans = []
+    for i in range(dimension):
+        ans.append(0)
+    return Vector(ans)
+
+
+def unitBasisVector(dimension,pos):
+    """
+        returns a unit basis vector with a One 
+        at index 'pos' (indexing at 0)
+    """
+    #precondition
+    assert(isinstance(dimension,int) and (isinstance(pos,int)))
+    ans = []
+    for i in range(dimension):
+        if i != pos:
+            ans.append(0)
+        else:
+            ans.append(1)
+    return Vector(ans)
+        
+
+def axpy(scalar,x,y):
+    """
+        input: a 'scalar' and two vectors 'x' and 'y'
+        output: a vector
+        computes the axpy operation
+    """
+    # precondition
+    assert(isinstance(x,Vector) and (isinstance(y,Vector)) \
+    and (isinstance(scalar,int) or isinstance(scalar,float)))
+    return (x*scalar + y)
+    
+
+def randomVector(N,a,b):
+    """
+        input: size (N) of the vector.
+               random range (a,b)
+        output: returns a random vector of size N, with 
+                random integer components between 'a' and 'b'.
+    """
+    ans = zeroVector(N)
+    random.seed(None)
+    for i in range(N):
+        ans.changeComponent(i,random.randint(a,b))
+    return ans
+
+
+class Matrix(object):
+    """
+    class: Matrix
+    This class represents a arbitrary matrix.
+    
+    Overview about the methods:
+    
+         __str__() : returns a string representation 
+           operator * : implements the matrix vector multiplication
+                        implements the matrix-scalar multiplication.
+           changeComponent(x,y,value) : changes the specified component.
+           component(x,y) : returns the specified component.
+           width() : returns the width of the matrix
+           height() : returns the height of the matrix
+           operator + : implements the matrix-addition.
+           operator - _ implements the matrix-subtraction
+    """
+    def __init__(self,matrix,w,h):
+        """
+            simple constructor for initialzes 
+            the matrix with components.
+        """
+        self.__matrix = matrix
+        self.__width = w
+        self.__height = h
+    def __str__(self):
+        """
+            returns a string representation of this
+            matrix.
+        """
+        ans = ""
+        for i in range(self.__height):
+            ans += "|"
+            for j in range(self.__width):
+                if j < self.__width -1:
+                    ans += str(self.__matrix[i][j]) + ","
+                else:
+                    ans += str(self.__matrix[i][j]) + "|\n"
+        return ans
+    def changeComponent(self,x,y, value):
+        """
+            changes the x-y component of this matrix
+        """
+        if x >= 0 and x < self.__height and y >= 0 and y < self.__width:
+            self.__matrix[x][y] = value
+        else:
+            raise Exception ("changeComponent: indices out of bounds")
+    def component(self,x,y):
+        """
+            returns the specified (x,y) component
+        """
+        if x >= 0 and x < self.__height and y >= 0 and y < self.__width:
+            return self.__matrix[x][y]
+        else:
+            raise Exception ("changeComponent: indices out of bounds")
+    def width(self):
+        """
+            getter for the width
+        """
+        return self.__width
+    def height(self):
+        """
+            getter for the height
+        """
+        return self.__height
+    def __mul__(self,other):
+        """
+            implements the matrix-vector multiplication.
+            implements the matrix-scalar multiplication
+        """
+        if isinstance(other, Vector): # vector-matrix 
+            if (other.size() == self.__width):
+                ans = zeroVector(self.__height)
+                for i in range(self.__height):
+                    summe = 0
+                    for j in range(self.__width):
+                        summe += other.component(j) * self.__matrix[i][j]
+                    ans.changeComponent(i,summe)
+                    summe = 0
+                return ans
+            else:
+                raise Exception("vector must have the same size as the "
+                + "number of columns of the matrix!")
+        elif isinstance(other,int) or isinstance(other,float): # matrix-scalar
+            matrix = []
+            for i in range(self.__height):
+                row = []
+                for j in range(self.__width):
+                    row.append(self.__matrix[i][j] * other)
+                matrix.append(row)
+            return Matrix(matrix,self.__width,self.__height)
+    def __add__(self,other):
+        """
+            implements the matrix-addition.
+        """
+        if (self.__width == other.width() and self.__height == other.height()):
+            matrix = []
+            for i in range(self.__height):
+                row = []
+                for j in range(self.__width):
+                    row.append(self.__matrix[i][j] + other.component(i,j))
+                matrix.append(row)
+            return Matrix(matrix,self.__width,self.__height)
+        else:
+            raise Exception("matrix must have the same dimension!")
+    def __sub__(self,other):
+        """
+            implements the matrix-subtraction.
+        """
+        if (self.__width == other.width() and self.__height == other.height()):
+            matrix = []
+            for i in range(self.__height):
+                row = []
+                for j in range(self.__width):
+                    row.append(self.__matrix[i][j] - other.component(i,j))
+                matrix.append(row)
+            return Matrix(matrix,self.__width,self.__height)
+        else:
+            raise Exception("matrix must have the same dimension!")
+    
+
+def squareZeroMatrix(N):
+    """
+        returns a square zero-matrix of dimension NxN
+    """
+    ans = []
+    for i in range(N):
+        row = []
+        for j in range(N):
+            row.append(0)
+        ans.append(row)
+    return Matrix(ans,N,N)
+    
+    
+def randomMatrix(W,H,a,b):
+    """
+        returns a random matrix WxH with integer components
+        between 'a' and 'b'
+    """
+    matrix = []
+    random.seed(None)
+    for i in range(H):
+        row = []
+        for j in range(W):
+            row.append(random.randint(a,b))
+        matrix.append(row)
+    return Matrix(matrix,W,H)
+            
+        

linear_algebra_python/src/tests.py

@@ -0,0 +1,133 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Feb 26 15:40:07 2018
+
+@author: Christian Bender
+@license: MIT-license
+
+This file contains the test-suite for the linear algebra library.
+"""
+
+import unittest
+from lib import *
+
+class Test(unittest.TestCase):
+    def test_component(self):
+        """
+            test for method component
+        """
+        x = Vector([1,2,3])
+        self.assertEqual(x.component(0),1)
+        self.assertEqual(x.component(2),3)
+        try:
+            y = Vector()
+            self.assertTrue(False)
+        except:
+            self.assertTrue(True)
+    def test_str(self):
+        """
+            test for toString() method
+        """
+        x = Vector([0,0,0,0,0,1])
+        self.assertEqual(x.__str__(),"(0,0,0,0,0,1)")
+    def test_size(self):
+        """
+            test for size()-method
+        """
+        x = Vector([1,2,3,4])
+        self.assertEqual(x.size(),4)
+    def test_euclidLength(self):
+        """
+            test for the eulidean length
+        """
+        x = Vector([1,2])
+        self.assertAlmostEqual(x.eulidLength(),2.236,3)
+    def test_add(self):
+        """
+            test for + operator
+        """
+        x = Vector([1,2,3])
+        y = Vector([1,1,1])
+        self.assertEqual((x+y).component(0),2)
+        self.assertEqual((x+y).component(1),3)
+        self.assertEqual((x+y).component(2),4)
+    def test_sub(self):
+        """
+            test for - operator
+        """
+        x = Vector([1,2,3])
+        y = Vector([1,1,1])
+        self.assertEqual((x-y).component(0),0)
+        self.assertEqual((x-y).component(1),1)
+        self.assertEqual((x-y).component(2),2)
+    def test_mul(self):
+        """
+            test for * operator
+        """
+        x = Vector([1,2,3])
+        a = Vector([2,-1,4]) # for test of dot-product
+        b = Vector([1,-2,-1])
+        self.assertEqual((x*3.0).__str__(),"(3.0,6.0,9.0)")
+        self.assertEqual((a*b),0)
+    def test_zeroVector(self):
+        """
+            test for the global function zeroVector(...)
+        """
+        self.assertTrue(zeroVector(10).__str__().count("0") == 10)
+    def test_unitBasisVector(self):
+        """
+            test for the global function unitBasisVector(...)
+        """
+        self.assertEqual(unitBasisVector(3,1).__str__(),"(0,1,0)")
+    def test_axpy(self):
+        """
+            test for the global function axpy(...) (operation)
+        """
+        x = Vector([1,2,3])
+        y = Vector([1,0,1])
+        self.assertEqual(axpy(2,x,y).__str__(),"(3,4,7)")
+    def test_copy(self):
+        """
+            test for the copy()-method
+        """
+        x = Vector([1,0,0,0,0,0])
+        y = x.copy()
+        self.assertEqual(x.__str__(),y.__str__())
+    def test_changeComponent(self):
+        """
+            test for the changeComponent(...)-method
+        """
+        x = Vector([1,0,0])
+        x.changeComponent(0,0)
+        x.changeComponent(1,1)
+        self.assertEqual(x.__str__(),"(0,1,0)")
+    def test_str_matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        self.assertEqual("|1,2,3|\n|2,4,5|\n|6,7,8|\n",A.__str__())
+    def test__mul__matrix(self):
+        A = Matrix([[1,2,3],[4,5,6],[7,8,9]],3,3)
+        x = Vector([1,2,3])
+        self.assertEqual("(14,32,50)",(A*x).__str__())
+        self.assertEqual("|2,4,6|\n|8,10,12|\n|14,16,18|\n",(A*2).__str__())
+    def test_changeComponent_matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        A.changeComponent(0,2,5)
+        self.assertEqual("|1,2,5|\n|2,4,5|\n|6,7,8|\n",A.__str__())
+    def test_component_matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        self.assertEqual(7,A.component(2,1),0.01)
+    def test__add__matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        B = Matrix([[1,2,7],[2,4,5],[6,7,10]],3,3)
+        self.assertEqual("|2,4,10|\n|4,8,10|\n|12,14,18|\n",(A+B).__str__())
+    def test__sub__matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        B = Matrix([[1,2,7],[2,4,5],[6,7,10]],3,3)
+        self.assertEqual("|0,0,-4|\n|0,0,0|\n|0,0,-2|\n",(A-B).__str__())
+    def test_squareZeroMatrix(self):
+        self.assertEqual('|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|' 
+        +'\n|0,0,0,0,0|\n',squareZeroMatrix(5).__str__())
+        
+
+if __name__ == "__main__":
+    unittest.main()

maths/BasicMaths.py

@@ -0,0 +1,74 @@
+import math
+
+def primeFactors(n):
+    pf = []
+    while n % 2 == 0:
+        pf.append(2)
+        n = int(n / 2)
+        
+    for i in range(3, int(math.sqrt(n))+1, 2):
+        while n % i == 0:
+            pf.append(i)
+            n = int(n / i)
+    
+    if n > 2:
+        pf.append(n)
+    
+    return pf
+
+def numberOfDivisors(n):
+    div = 1
+    
+    temp = 1
+    while n % 2 == 0:
+        temp += 1
+        n = int(n / 2)
+    div = div * (temp) 
+    
+    for i in range(3, int(math.sqrt(n))+1, 2):
+        temp = 1
+        while n % i == 0:
+            temp += 1
+            n = int(n / i)
+        div = div * (temp)
+    
+    return div
+
+def sumOfDivisors(n):
+    s = 1
+    
+    temp = 1
+    while n % 2 == 0:
+        temp += 1
+        n = int(n / 2)
+    if temp > 1:
+        s *= (2**temp - 1) / (2 - 1) 
+    
+    for i in range(3, int(math.sqrt(n))+1, 2):
+        temp = 1
+        while n % i == 0:
+            temp += 1
+            n = int(n / i)
+        if temp > 1:
+            s *= (i**temp - 1) / (i - 1)
+    
+    return s
+
+def eulerPhi(n):
+    l = primeFactors(n)
+    l = set(l)
+    s = n
+    for x in l:
+        s *= (x - 1)/x 
+    return s   
+
+def main():
+    print(primeFactors(100))
+    print(numberOfDivisors(100))
+    print(sumOfDivisors(100))
+    print(eulerPhi(100))
+    
+if __name__ == '__main__':
+    main()
+    
+    

maths/FibonacciSequenceRecursion.py

@@ -0,0 +1,18 @@
+# Fibonacci Sequence Using Recursion
+
+def recur_fibo(n):
+    return n if n <= 1 else (recur_fibo(n-1) + recur_fibo(n-2))
+    
+def isPositiveInteger(limit):
+    return limit >= 0
+
+def main():
+    limit = int(input("How many terms to include in fibonacci series: "))
+    if isPositiveInteger(limit):
+        print("The first {limit} terms of the fibonacci series are as follows:")
+        print([recur_fibo(n) for n in range(limit)])
+    else:
+        print("Please enter a positive integer: ")
+
+if __name__ == '__main__':
+    main()

maths/GreaterCommonDivisor.py

@@ -0,0 +1,15 @@
+# Greater Common Divisor - https://en.wikipedia.org/wiki/Greatest_common_divisor
+def gcd(a, b):
+    return b if a == 0 else gcd(b % a, a)
+
+def main():
+    try:
+        nums = input("Enter two Integers separated by comma (,): ").split(',')
+        num1 = int(nums[0]); num2 = int(nums[1])
+    except (IndexError, UnboundLocalError, ValueError):
+        print("Wrong Input")
+    print(f"gcd({num1}, {num2}) = {gcd(num1, num2)}")
+
+if __name__ == '__main__':
+    main()
+

maths/ModularExponential.py

@@ -0,0 +1,20 @@
+def modularExponential(base, power, mod):
+	if power < 0:
+		return -1
+	base %= mod
+	result = 1
+
+	while power > 0:
+		if power & 1:
+			result = (result * base) % mod
+		power = power >> 1
+		base = (base * base) % mod
+	return result
+
+
+def main():
+	print(modularExponential(3, 200, 13))
+
+
+if __name__ == '__main__':
+	main()

maths/SegmentedSieve.py

@@ -0,0 +1,46 @@
+import math
+
+def sieve(n):
+    in_prime = []
+    start = 2
+    end   = int(math.sqrt(n)) # Size of every segment
+    temp = [True] * (end + 1)
+    prime = []
+    
+    while(start <= end):
+        if temp[start] == True:
+            in_prime.append(start)
+            for i in range(start*start, end+1, start):
+                if temp[i] == True:
+                    temp[i] = False
+        start += 1
+    prime += in_prime
+    
+    low = end + 1
+    high = low + end - 1
+    if high > n:
+        high = n
+    
+    while(low <= n):
+        temp = [True] * (high-low+1)
+        for each in in_prime:
+            
+            t = math.floor(low / each) * each
+            if t < low:
+                t += each
+            
+            for j in range(t, high+1, each):
+                temp[j - low] = False
+                
+        for j in range(len(temp)):
+            if temp[j] == True:
+                prime.append(j+low)
+        
+        low = high + 1
+        high = low + end - 1
+        if high > n:
+            high = n
+            
+    return prime
+
+print(sieve(10**6))

maths/SieveOfEratosthenes.py

@@ -0,0 +1,24 @@
+import math
+n = int(raw_input("Enter n: "))
+
+def sieve(n):
+    l = [True] * (n+1)
+    prime = []
+    start = 2
+    end   = int(math.sqrt(n))
+    while(start <= end):
+        if l[start] == True:
+            prime.append(start)
+            for i in range(start*start, n+1, start):
+                if l[i] == True:
+                    l[i] = False
+        start += 1
+    
+    for j in range(end+1,n+1):
+        if l[j] == True:
+            prime.append(j)
+    
+    return prime
+
+print(sieve(n))
+        

maths/SimpsonRule.py

@@ -0,0 +1,49 @@
+
+'''
+Numerical integration or quadrature for a smooth function f with known values at x_i
+
+This method is the classical approch of suming 'Equally Spaced Abscissas' 
+
+method 2: 
+"Simpson Rule"
+
+'''
+from __future__ import print_function
+
+
+def method_2(boundary, steps):
+# "Simpson Rule"
+# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
+	h = (boundary[1] - boundary[0]) / steps
+	a = boundary[0]
+	b = boundary[1]
+	x_i = makePoints(a,b,h)
+	y = 0.0
+	y += (h/3.0)*f(a)
+	cnt = 2
+	for i in x_i:
+		y += (h/3)*(4-2*(cnt%2))*f(i)	
+		cnt += 1
+	y += (h/3.0)*f(b)
+	return y
+
+def makePoints(a,b,h):
+	x = a + h
+	while x < (b-h):
+		yield x
+		x = x + h
+
+def f(x): #enter your function here
+	y = (x-0)*(x-0)
+	return y
+
+def main():
+	a = 0.0 #Lower bound of integration
+	b = 1.0	#Upper bound of integration
+	steps = 10.0		#define number of steps or resolution
+	boundary = [a, b]	#define boundary of integration
+	y = method_2(boundary, steps)
+	print('y = {0}'.format(y))
+
+if __name__ == '__main__':
+        main()

maths/TrapezoidalRule.py

@@ -0,0 +1,46 @@
+'''
+Numerical integration or quadrature for a smooth function f with known values at x_i
+
+This method is the classical approch of suming 'Equally Spaced Abscissas' 
+
+method 1: 
+"extended trapezoidal rule"
+
+'''
+from __future__ import print_function
+
+def method_1(boundary, steps):
+# "extended trapezoidal rule"
+# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
+	h = (boundary[1] - boundary[0]) / steps
+	a = boundary[0]
+	b = boundary[1]
+	x_i = makePoints(a,b,h)
+	y = 0.0	
+	y += (h/2.0)*f(a)
+	for i in x_i:
+		#print(i)	
+		y += h*f(i)
+	y += (h/2.0)*f(b)	
+	return y	
+
+def makePoints(a,b,h):
+	x = a + h	
+	while x < (b-h):
+		yield x
+		x = x + h
+		
+def f(x): #enter your function here
+	y = (x-0)*(x-0)
+	return y
+
+def main():
+	a = 0.0 #Lower bound of integration
+	b = 1.0	#Upper bound of integration
+	steps = 10.0		#define number of steps or resolution	
+	boundary = [a, b]	#define boundary of integration
+	y = method_1(boundary, steps)
+	print('y = {0}'.format(y))
+
+if __name__ == '__main__':
+	main()

neural_network/bpnn.py

@@ -0,0 +1,193 @@
+#!/usr/bin/python
+# encoding=utf8
+
+'''
+
+A Framework of Back Propagation Neural Network（BP） model
+
+Easy to use:
+    * add many layers as you want ！！！
+    * clearly see how the loss decreasing
+Easy to expand:
+    * more activation functions
+    * more loss functions
+    * more optimization method
+
+Author: Stephen Lee
+Github : https://github.com/RiptideBo
+Date: 2017.11.23
+
+'''
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def sigmoid(x):
+    return 1 / (1 + np.exp(-1 * x))
+
+class DenseLayer():
+    '''
+    Layers of BP neural network
+    '''
+    def __init__(self,units,activation=None,learning_rate=None,is_input_layer=False):
+        '''
+        common connected layer of bp network
+        :param units: numbers of neural units
+        :param activation: activation function
+        :param learning_rate: learning rate for paras
+        :param is_input_layer: whether it is input layer or not
+        '''
+        self.units = units
+        self.weight = None
+        self.bias = None
+        self.activation = activation
+        if learning_rate is None:
+            learning_rate = 0.3
+        self.learn_rate = learning_rate
+        self.is_input_layer = is_input_layer
+
+    def initializer(self,back_units):
+        self.weight = np.asmatrix(np.random.normal(0,0.5,(self.units,back_units)))
+        self.bias = np.asmatrix(np.random.normal(0,0.5,self.units)).T
+        if self.activation is None:
+            self.activation = sigmoid
+
+    def cal_gradient(self):
+        if self.activation == sigmoid:
+            gradient_mat = np.dot(self.output ,(1- self.output).T)
+            gradient_activation = np.diag(np.diag(gradient_mat))
+        else:
+            gradient_activation = 1
+        return gradient_activation
+
+    def forward_propagation(self,xdata):
+        self.xdata = xdata
+        if self.is_input_layer:
+            # input layer
+            self.wx_plus_b = xdata
+            self.output = xdata
+            return xdata
+        else:
+            self.wx_plus_b = np.dot(self.weight,self.xdata) - self.bias
+            self.output = self.activation(self.wx_plus_b)
+            return self.output
+
+    def back_propagation(self,gradient):
+
+        gradient_activation = self.cal_gradient() # i * i 维
+        gradient = np.asmatrix(np.dot(gradient.T,gradient_activation))
+
+        self._gradient_weight = np.asmatrix(self.xdata)
+        self._gradient_bias = -1
+        self._gradient_x = self.weight
+
+        self.gradient_weight = np.dot(gradient.T,self._gradient_weight.T)
+        self.gradient_bias = gradient * self._gradient_bias
+        self.gradient = np.dot(gradient,self._gradient_x).T
+        # ----------------------upgrade
+        # -----------the Negative gradient direction --------
+        self.weight = self.weight - self.learn_rate * self.gradient_weight
+        self.bias = self.bias - self.learn_rate * self.gradient_bias.T
+
+        return self.gradient
+
+
+class BPNN():
+    '''
+    Back Propagation Neural Network model
+    '''
+    def __init__(self):
+        self.layers = []
+        self.train_mse = []
+        self.fig_loss = plt.figure()
+        self.ax_loss = self.fig_loss.add_subplot(1,1,1)
+
+    def add_layer(self,layer):
+        self.layers.append(layer)
+
+    def build(self):
+        for i,layer in enumerate(self.layers[:]):
+            if i < 1:
+                layer.is_input_layer = True
+            else:
+                layer.initializer(self.layers[i-1].units)
+
+    def summary(self):
+        for i,layer in enumerate(self.layers[:]):
+            print('------- layer %d -------'%i)
+            print('weight.shape ',np.shape(layer.weight))
+            print('bias.shape ',np.shape(layer.bias))
+
+    def train(self,xdata,ydata,train_round,accuracy):
+        self.train_round = train_round
+        self.accuracy = accuracy
+
+        self.ax_loss.hlines(self.accuracy, 0, self.train_round * 1.1)
+
+        x_shape = np.shape(xdata)
+        for round_i in range(train_round):
+            all_loss = 0
+            for row in range(x_shape[0]):
+                _xdata = np.asmatrix(xdata[row,:]).T
+                _ydata = np.asmatrix(ydata[row,:]).T
+
+                # forward propagation
+                for layer in self.layers:
+                    _xdata = layer.forward_propagation(_xdata)
+
+                loss, gradient = self.cal_loss(_ydata, _xdata)
+                all_loss = all_loss + loss
+
+                # back propagation
+                # the input_layer does not upgrade
+                for layer in self.layers[:0:-1]:
+                    gradient = layer.back_propagation(gradient)
+
+            mse = all_loss/x_shape[0]
+            self.train_mse.append(mse)
+
+            self.plot_loss()
+
+            if mse < self.accuracy:
+                print('----达到精度----')
+                return mse
+
+    def cal_loss(self,ydata,ydata_):
+        self.loss = np.sum(np.power((ydata - ydata_),2))
+        self.loss_gradient = 2 * (ydata_ - ydata)
+        # vector (shape is the same as _ydata.shape)
+        return self.loss,self.loss_gradient
+
+    def plot_loss(self):
+        if self.ax_loss.lines:
+            self.ax_loss.lines.remove(self.ax_loss.lines[0])
+        self.ax_loss.plot(self.train_mse, 'r-')
+        plt.ion()
+        plt.show()
+        plt.pause(0.1)
+
+
+
+
+def example():
+
+    x = np.random.randn(10,10)
+    y = np.asarray([[0.8,0.4],[0.4,0.3],[0.34,0.45],[0.67,0.32],
+                    [0.88,0.67],[0.78,0.77],[0.55,0.66],[0.55,0.43],[0.54,0.1],
+                    [0.1,0.5]])
+
+    model = BPNN()
+    model.add_layer(DenseLayer(10))
+    model.add_layer(DenseLayer(20))
+    model.add_layer(DenseLayer(30))
+    model.add_layer(DenseLayer(2))
+
+    model.build()
+
+    model.summary()
+
+    model.train(xdata=x,ydata=y,train_round=100,accuracy=0.01)
+
+if __name__ == '__main__':
+    example()

neural_network/convolution_neural_network.py

@@ -0,0 +1,306 @@
+#-*- 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
+    - - - - - -- - - - - - - - - - - - - - - - - - - - - - -
+          '''
+from __future__ import print_function
+
+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
+    '''

neural_network/perceptron.py

@@ -0,0 +1,124 @@
+'''
+
+	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
+
+'''
+from __future__ import print_function
+
+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 training(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(raw_input('value: ')))
+    network.sort(sample)

project_euler/Problem 01/sol1.py

@@ -0,0 +1,17 @@
+'''
+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.
+'''
+from __future__ import print_function
+try:
+    raw_input          # Python 2
+except NameError:
+    raw_input = input  # Python 3
+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)

project_euler/Problem 01/sol2.py

@@ -0,0 +1,20 @@
+'''
+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.
+'''
+from __future__ import print_function
+try:
+    raw_input          # Python 2
+except NameError:
+    raw_input = input  # Python 3
+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)

project_euler/Problem 01/sol3.py

@@ -0,0 +1,50 @@
+from __future__ import print_function
+
+'''
+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.
+'''
+
+try:
+    raw_input          # Python 2
+except NameError:
+    raw_input = input  # Python 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);

project_euler/Problem 01/sol4.py

@@ -0,0 +1,30 @@
+def mulitples(limit):
+    xmulti = []
+    zmulti = []
+    z = 3
+    x = 5
+    temp = 1
+    while True:
+        result = z * temp
+        if (result < limit):
+            zmulti.append(result)
+            temp += 1
+        else:
+            temp = 1
+            break
+    while True:
+        result = x * temp
+        if (result < limit):
+            xmulti.append(result)
+            temp += 1
+        else:
+            break
+    collection = list(set(xmulti+zmulti))
+    return (sum(collection))
+    
+    
+        
+        
+        
+    
+print (mulitples(1000))

project_euler/Problem 02/sol1.py

@@ -0,0 +1,26 @@
+'''
+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.
+'''
+from __future__ import print_function
+
+try:
+    raw_input          # Python 2
+except NameError:
+    raw_input = input  # Python 3
+
+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)

project_euler/Problem 02/sol2.py

@@ -0,0 +1,12 @@
+def fib(n):
+    a, b, s = 0, 1, 0
+    while b < n:
+        if b % 2 == 0 and b < n: s += b
+        a, b = b, a+b
+    ls.append(s)
+
+T = int(input().strip())
+ls = []
+for _ in range(T):
+    fib(int(input().strip()))
+print(ls, sep = '\n')

project_euler/Problem 02/sol3.py

@@ -0,0 +1,20 @@
+'''
+Problem:
+Each new term in the Fibonacci sequence is generated by adding the previous two terms. 
+                0,1,1,2,3,5,8,13,21,34,55,89,..
+Every third term from 0 is even So using this I have written a simple code
+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.
+'''
+"""Python 3"""
+n = int(raw_input())
+a=0
+b=2
+count=0
+while 4*b+a<n:
+    c=4*b+a
+    a=b
+    b=c
+    count=count+a
+print(count+b)
+   

project_euler/Problem 03/sol1.py

@@ -0,0 +1,39 @@
+'''
+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.
+'''
+from __future__ import print_function, division
+
+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
+
+maxNumber = 0
+n=int(raw_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)):
+                    maxNumber = n/i
+                    break
+                elif(isprime(i)):
+                    maxNumber = i
+        print(maxNumber)

project_euler/Problem 03/sol2.py

@@ -0,0 +1,17 @@
+'''
+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.
+'''
+from __future__ import print_function
+n=int(raw_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)

project_euler/Problem 04/sol1.py

@@ -0,0 +1,29 @@
+'''
+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.
+'''
+from __future__ import print_function
+limit = int(raw_input("limit? "))
+
+# fetchs the next number
+for number in range(limit-1,10000,-1):
+
+    # converts number into string.
+    strNumber = str(number)
+
+    # checks whether 'strNumber' is a palindrome.
+    if(strNumber == strNumber[::-1]):
+
+        divisor = 999
+
+        # if 'number' is a product of two 3-digit numbers
+        # then number is the answer otherwise fetch next number.
+        while(divisor != 99): 
+            
+            if((number % divisor == 0) and (len(str(number / divisor)) == 3)):
+
+                print(number)
+                exit(0)
+
+            divisor -=1

project_euler/Problem 04/sol2.py

@@ -0,0 +1,19 @@
+'''
+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.
+'''
+from __future__ import print_function
+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(raw_input())
+for i in arr[::-1]:
+    if(i<n):
+        print(i)
+        exit(0)

project_euler/Problem 05/sol1.py

@@ -0,0 +1,21 @@
+'''
+Problem:
+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?
+'''
+from __future__ import print_function
+
+n = int(raw_input())
+i = 0
+while 1:
+    i+=n*(n-1)
+    nfound=0
+    for j in range(2,n):
+        if (i%j != 0):
+            nfound=1
+            break
+    if(nfound==0):
+        if(i==0):
+            i=1
+        print(i)
+        break

project_euler/Problem 05/sol2.py

@@ -0,0 +1,20 @@
+#!/bin/python3
+'''
+Problem:
+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?
+'''
+
+""" Euclidean GCD Algorithm """
+def gcd(x,y):
+    return x if y==0 else gcd(y,x%y)
+
+""" Using the property lcm*gcd of two numbers = product of them """
+def lcm(x,y):
+    return (x*y)//gcd(x,y)
+
+n = int(raw_input())
+g=1
+for i in range(1,n+1):
+    g=lcm(g,i)
+print(g)

project_euler/Problem 06/sol1.py

@@ -0,0 +1,20 @@
+# -*- coding: utf-8 -*-
+'''
+Problem:
+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.
+'''
+from __future__ import print_function
+
+suma = 0
+sumb = 0
+n = int(raw_input())
+for i in range(1,n+1):
+    suma += i**2
+    sumb += i
+sum = sumb**2 - suma
+print(sum)

project_euler/Problem 06/sol2.py

@@ -0,0 +1,16 @@
+# -*- coding: utf-8 -*-
+'''
+Problem:
+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.
+'''
+from __future__ import print_function
+n = int(raw_input())
+suma = n*(n+1)/2
+suma **= 2
+sumb = n*(n+1)*(2*n+1)/6
+print(suma-sumb)

project_euler/Problem 07/sol1.py

@@ -0,0 +1,30 @@
+'''
+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 __future__ import print_function
+from math import sqrt
+def isprime(n):
+    if (n==2):
+        return True
+    elif (n%2==0):
+        return False
+    else:
+        sq = int(sqrt(n))+1
+        for i in range(3,sq,2):
+            if(n%i==0):
+                return False
+    return True
+n = int(raw_input())
+i=0
+j=1
+while(i!=n and j<3):
+    j+=1
+    if (isprime(j)):
+        i+=1
+while(i!=n):
+    j+=2
+    if(isprime(j)):
+        i+=1
+print(j)

project_euler/Problem 07/sol2.py

@@ -0,0 +1,16 @@
+# 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?
+def isprime(number):
+	for i in range(2,int(number**0.5)+1):
+		if number%i==0:
+			return False
+	return True
+n = int(raw_input('Enter The N\'th Prime Number You Want To Get: ')) # Ask For The N'th Prime Number Wanted
+primes = []
+num = 2
+while len(primes) < n:
+	if isprime(num):
+		primes.append(num)
+		num += 1
+	else:
+		num += 1
+print(primes[len(primes) - 1])

project_euler/Problem 08/sol1.py

@@ -0,0 +1,15 @@
+import sys
+def main():
+    LargestProduct = -sys.maxsize-1
+    number=raw_input().strip()
+    for i in range(len(number)-13):
+        product=1
+        for j in range(13):
+            product *= int(number[i+j])
+        if product > LargestProduct:
+            LargestProduct = product
+    print(LargestProduct)
+
+
+if __name__ == '__main__':
+    main()

project_euler/Problem 09/sol1.py

@@ -0,0 +1,15 @@
+from __future__ import print_function
+# Program to find the product of a,b,c which are Pythagorean Triplet that satisfice the following:
+# 1. a < b < c
+# 2. a**2 + b**2 = c**2
+# 3. a + b + c = 1000
+
+print("Please Wait...")
+for a in range(300):
+    for b in range(400):
+        for c in range(500):
+            if(a < b < c):
+                if((a**2) + (b**2) == (c**2)):
+                    if((a+b+c) == 1000):
+                        print(("Product of",a,"*",b,"*",c,"=",(a*b*c)))
+                        break

project_euler/Problem 09/sol2.py

@@ -0,0 +1,18 @@
+"""A Pythagorean triplet is a set of three natural numbers, for which,
+a^2+b^2=c^2
+Given N, Check if there exists any Pythagorean triplet for which a+b+c=N
+Find maximum possible value of product of a,b,c among all such Pythagorean triplets, If there is no such Pythagorean triplet print -1."""
+#!/bin/python3
+
+product=-1
+d=0
+N = int(raw_input())
+for a in range(1,N//3):
+    """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c """
+    b=(N*N-2*a*N)//(2*N-2*a)
+    c=N-a-b
+    if c*c==(a*a+b*b):
+        d=(a*b*c)
+        if d>=product:
+            product=d
+print(product)

project_euler/Problem 10/sol1.py

@@ -0,0 +1,38 @@
+from __future__ import print_function
+from math import sqrt
+
+try:
+	xrange			#Python 2
+except NameError:
+	xrange = range	#Python 3
+
+def is_prime(n):
+	for i in xrange(2, int(sqrt(n))+1):
+		if n%i == 0:
+			return False
+
+	return True
+
+def sum_of_primes(n):
+	if n > 2:
+		sumOfPrimes = 2
+	else:
+		return 0
+
+	for i in xrange(3, n, 2):
+		if is_prime(i):
+			sumOfPrimes += i
+
+	return sumOfPrimes
+
+if __name__ == '__main__':
+	import sys
+
+	if len(sys.argv) == 1:
+		print(sum_of_primes(2000000))
+	else:
+		try:
+			n = int(sys.argv[1])
+			print(sum_of_primes(n))
+		except ValueError:
+			print('Invalid entry - please enter a number.')