mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 09:10:16 +00:00
256 lines
7.4 KiB
Python
256 lines
7.4 KiB
Python
# -*- 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):
|
|
r'''
|
|
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):
|
|
r'''
|
|
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()
|