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at302_redblack_tree.py
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#!/usr/bin/env python
# -*- encoding: utf-8 -*-
# 红黑树
"""
Topic: sample
Desc : 红黑树
红黑树是满足下面红黑性质的二叉搜索树：
1，每个结点或者是红色的，或者是黑色的
2，根结点黑色
3，每个叶子结点（None）是黑色的
4，如果一个结点是红色的，则它的两个子结点都是黑色的
5，对每个结点，从该结点到其所有后代叶结点的简单路径上，均包含相同数目的黑色结点。
一个有n个内部结点的红黑树的高度最多为2lg(n+1)
"""
from .at301_bisearch_tree import treeMinimum, inOrderWalk
__author__ = 'Xiong Neng'
class RBTree():
COLOR_RED = 0
COLOR_BLACK = 1
def __init__(self, root=None):
self.root = root
self.nil = RBNode('', RBTree.COLOR_BLACK)
if root is None:
self.root = self.nil
class RBNode():
"""节点元素定义"""
def __init__(self, key, color=RBTree.COLOR_RED, p=None, left=None, right=None):
self.key = key
self.color = color
self.p = p
self.left = left
self.right = right
def leftRotate(T, x):
"""
左旋：
假设x的右孩子为y，且不为None，以x到y的链作为支轴，
使y成为该子树新的根结点，x成为y的左孩子，y的左孩子成为x的右孩子
"""
y = x.right
x.right = y.left
if y.left != T.nil:
y.left.p = x
y.p = x.p
if x.p == T.nil:
T.root = y
elif x == x.p.left:
x.p.left = y
else:
x.p.right = y
y.left = x
x.p = y
def rightRotate(T, x):
y = x.left
x.left = y.right
if y.right != T.nil:
y.right.p = x
y.p = x.p
if x.p == T.nil:
T.root = y
elif x == x.p.left:
x.p.left = y
else:
x.p.right = y
y.right = x
x.p = y
def rbTreeInsert(T, z):
"""
红黑树的插入算法
"""
RED = RBTree.COLOR_RED
y = T.nil
x = T.root
while x != T.nil:
y = x
if z.key < x.key:
x = x.left
else:
x = x.right
z.p = y
if y == T.nil:
T.root = z
elif z.key < y.key:
y.left = z
else:
y.right = z
z.left = T.nil
z.right = T.nil
z.color = RED
rbInsertFixup(T, z)
def rbInsertFixup(T, z):
"""给结点重新着色，将其保持为红黑树"""
RED = RBTree.COLOR_RED
BLACK = RBTree.COLOR_BLACK
while z.p.color == RED:
if z.p == z.p.p.left:
y = z.p.p.right
if y.color == RED:
z.p.color = BLACK
y.color = BLACK
z.p.p.color = RED
z = z.p.p
else:
if z == z.p.right:
z = z.p
leftRotate(T, z)
z.p.color = BLACK
z.p.p.color = RED
rightRotate(T, z.p.p)
elif z.p == z.p.p.right:
y = z.p.p.left
if y.color == RED:
z.p.color = BLACK
y.color = BLACK
z.p.p.color = RED
z = z.p.p
else:
if z == z.p.left:
z = z.p
rightRotate(T, z)
z.p.color = BLACK
z.p.p.color = RED
leftRotate(T, z.p.p)
T.root.color = BLACK
def rbTransplant(T, u, v):
"""红黑树中子树的替换算法"""
if u.p == T.nil:
T.root = v
elif u == u.p.left:
u.p.left = v
else:
u.p.right = v
v.p = u.p
def rbTreeDelete(T, z):
"""红黑树删除算法"""
BLACK = RBTree.COLOR_BLACK
y = z
yOriginalColor = y.color
if z.left == T.nil:
x = z.right
rbTransplant(T, z, z.right)
elif z.right == T.nil:
x = z.left
rbTransplant(T, z, z.left)
else:
y = treeMinimum(z.right)
yOriginalColor = y.color
x = y.right
if y.p == z:
x.p = y
else:
rbTransplant(T, y, y.right)
y.right = z.right
y.right.p = y
rbTransplant(T, z, y)
y.left = z.left
y.left.p = y
y.color = z.color
if yOriginalColor == BLACK:
rbDeleteFixup(T, x)
def rbDeleteFixup(T, x):
"""红黑树删除时的调整算法"""
RED = RBTree.COLOR_RED
BLACK = RBTree.COLOR_BLACK
while x != T.root and x.color == BLACK:
if x == x.p.left:
w = x.p.right
if w.color == RED:
w.color = BLACK
x.p.color = RED
leftRotate(T, x.p)
w = x.p.right
if w.left.color == BLACK and w.right.color == BLACK:
w.color = RED
x = x.p
else:
if w.right.color == BLACK:
w.left.color = BLACK
w.color = RED
rightRotate(T, w)
w = x.p.right
w.color = x.p.color
x.p.color = BLACK
w.right.color = BLACK
leftRotate(T, x.p)
x = T.root
elif x == x.p.right:
w = x.p.left
if w.color == RED:
w.color = BLACK
x.p.color = RED
rightRotate(T, x.p)
w = x.p.left
if w.left.color == BLACK and w.right.color == BLACK:
w.color = RED
x = x.p
else:
if w.left.color == BLACK:
w.right.color = BLACK
w.color = RED
leftRotate(T, w)
w = x.p.left
w.color = x.p.color
x.p.color = BLACK
w.left.color = BLACK
rightRotate(T, x.p)
x = T.root
x.color = BLACK
def inOrderRBWalk(tree):
"""中序遍历二叉搜索树，从小到大输出元素"""
inOrderRBWalkNode(tree.root, tree.nil)
print('')
def inOrderRBWalkNode(node, ni):
"""中序遍历二叉搜索树，从小到大输出元素"""
if node and node != ni:
inOrderRBWalkNode(node.left, ni)
print(node.key),
inOrderRBWalkNode(node.right, ni)
if __name__ == '__main__':
ss = [4, 23, 65, 22, 12, 3, 7, 1, 256, 34, 27]
tree = RBTree()
for i in ss:
rbTreeInsert(tree, RBNode(i))
inOrderRBWalk(tree)
n = RBNode(26)
rbTreeInsert(tree, n)
inOrderRBWalk(tree)
rbTreeDelete(tree, n)
inOrderRBWalk(tree)