diff --git a/data_structures/binary tree/AVLtree.py b/data_structures/binary tree/AVLtree.py new file mode 100644 index 000000000..cb27004b6 --- /dev/null +++ b/data_structures/binary tree/AVLtree.py @@ -0,0 +1,255 @@ +# -*- coding: utf-8 -*- +''' +An auto-balanced binary tree! +''' +import math +import random +class my_queue: + def __init__(self): + self.data = [] + self.head = 0 + self.tail = 0 + def isEmpty(self): + return self.head == self.tail + def push(self,data): + self.data.append(data) + self.tail = self.tail + 1 + def pop(self): + ret = self.data[self.head] + self.head = self.head + 1 + return ret + def count(self): + return self.tail - self.head + def print(self): + print(self.data) + print("**************") + print(self.data[self.head:self.tail]) + +class my_node: + def __init__(self,data): + self.data = data + self.left = None + self.right = None + self.height = 1 + def getdata(self): + return self.data + def getleft(self): + return self.left + def getright(self): + return self.right + def getheight(self): + return self.height + def setdata(self,data): + self.data = data + return + def setleft(self,node): + self.left = node + return + def setright(self,node): + self.right = node + return + def setheight(self,height): + self.height = height + return + +def getheight(node): + if node is None: + return 0 + return node.getheight() + +def my_max(a,b): + if a > b: + return a + return b + + + +def leftrotation(node): + ''' + A B + / \ / \ + B C Bl A + / \ --> / / \ + Bl Br UB Br C + / + UB + + UB = unbalanced node + ''' + print("left rotation node:",node.getdata()) + ret = node.getleft() + node.setleft(ret.getright()) + ret.setright(node) + h1 = my_max(getheight(node.getright()),getheight(node.getleft())) + 1 + node.setheight(h1) + h2 = my_max(getheight(ret.getright()),getheight(ret.getleft())) + 1 + ret.setheight(h2) + return ret + +def rightrotation(node): + ''' + a mirror symmetry rotation of the leftrotation + ''' + print("right rotation node:",node.getdata()) + ret = node.getright() + node.setright(ret.getleft()) + ret.setleft(node) + h1 = my_max(getheight(node.getright()),getheight(node.getleft())) + 1 + node.setheight(h1) + h2 = my_max(getheight(ret.getright()),getheight(ret.getleft())) + 1 + ret.setheight(h2) + return ret + +def rlrotation(node): + ''' + A A Br + / \ / \ / \ + B C RR Br C LR B A + / \ --> / \ --> / / \ + Bl Br B UB Bl UB C + \ / + UB Bl + RR = rightrotation LR = leftrotation + ''' + node.setleft(rightrotation(node.getleft())) + return leftrotation(node) + +def lrrotation(node): + node.setright(leftrotation(node.getright())) + return rightrotation(node) + + +def insert_node(node,data): + if node is None: + return my_node(data) + if data < node.getdata(): + node.setleft(insert_node(node.getleft(),data)) + if getheight(node.getleft()) - getheight(node.getright()) == 2: #an unbalance detected + if data < node.getleft().getdata(): #new node is the left child of the left child + node = leftrotation(node) + else: + node = rlrotation(node) #new node is the right child of the left child + else: + node.setright(insert_node(node.getright(),data)) + if getheight(node.getright()) - getheight(node.getleft()) == 2: + if data < node.getright().getdata(): + node = lrrotation(node) + else: + node = rightrotation(node) + h1 = my_max(getheight(node.getright()),getheight(node.getleft())) + 1 + node.setheight(h1) + return node + +def getRightMost(root): + while root.getright() is not None: + root = root.getright() + return root.getdata() +def getLeftMost(root): + while root.getleft() is not None: + root = root.getleft() + return root.getdata() + +def del_node(root,data): + if root.getdata() == data: + if root.getleft() is not None and root.getright() is not None: + temp_data = getLeftMost(root.getright()) + root.setdata(temp_data) + root.setright(del_node(root.getright(),temp_data)) + elif root.getleft() is not None: + root = root.getleft() + else: + root = root.getright() + elif root.getdata() > data: + if root.getleft() is None: + print("No such data") + return root + else: + root.setleft(del_node(root.getleft(),data)) + elif root.getdata() < data: + if root.getright() is None: + return root + else: + root.setright(del_node(root.getright(),data)) + if root is None: + return root + if getheight(root.getright()) - getheight(root.getleft()) == 2: + if getheight(root.getright().getright()) > getheight(root.getright().getleft()): + root = rightrotation(root) + else: + root = lrrotation(root) + elif getheight(root.getright()) - getheight(root.getleft()) == -2: + if getheight(root.getleft().getleft()) > getheight(root.getleft().getright()): + root = leftrotation(root) + else: + root = rlrotation(root) + height = my_max(getheight(root.getright()),getheight(root.getleft())) + 1 + root.setheight(height) + return root + +class AVLtree: + def __init__(self): + self.root = None + def getheight(self): +# print("yyy") + return getheight(self.root) + def insert(self,data): + print("insert:"+str(data)) + self.root = insert_node(self.root,data) + + def del_node(self,data): + print("delete:"+str(data)) + if self.root is None: + print("Tree is empty!") + return + self.root = del_node(self.root,data) + def traversale(self): #a level traversale, gives a more intuitive look on the tree + q = my_queue() + q.push(self.root) + layer = self.getheight() + if layer == 0: + return + cnt = 0 + while not q.isEmpty(): + node = q.pop() + space = " "*int(math.pow(2,layer-1)) + print(space,end = "") + if node is None: + print("*",end = "") + q.push(None) + q.push(None) + else: + print(node.getdata(),end = "") + q.push(node.getleft()) + q.push(node.getright()) + print(space,end = "") + cnt = cnt + 1 + for i in range(100): + if cnt == math.pow(2,i) - 1: + layer = layer -1 + if layer == 0: + print() + print("*************************************") + return + print() + break + print() + print("*************************************") + return + + def test(self): + getheight(None) + print("****") + self.getheight() +if __name__ == "__main__": + t = AVLtree() + t.traversale() + l = list(range(10)) + random.shuffle(l) + for i in l: + t.insert(i) + t.traversale() + + random.shuffle(l) + for i in l: + t.del_node(i) + t.traversale()