红黑树
Posted wanglelelihuanhuan
tags:
篇首语：本文由小常识网(cha138.com)小编为大家整理，主要介绍了红黑树相关的知识，希望对你有一定的参考价值。
红黑树介绍：
红黑树是一棵二叉搜索树，它在每个节点上增加了一个存储位来表示节点的颜色，可以是Red或Black。通过对任何一条从根到叶子简单路径上的颜色来约束，红黑树保证最长路径不超过最短路径的两倍，因而近似于平衡。 红黑树和我们以前学过的AVL树类似，都是在进行插入和删除操作时通过特定操作保持二叉查找树的平衡，从而获得较高的查找性能。红黑树和AVL树的区别在于它使用颜色来标识结点的高度，它所追求的是局部平衡而不是AVL树中的非常严格的平衡。 红黑树是满足下面红黑性质的二叉搜索树：
- 每个节点，不是红色就是黑色的
- 根节点是黑色的
- 如果一个节点是红色的，则它的两个子节点是黑色的(没有连续的红节点)
- 对每个节点，从该节点到其所有后代叶节点的简单路径上，均包含相同数目的黑色节点。（每条路径的黑色节点的数量相等）
- 每个叶子节点都是黑色的（这里的叶子节点是指的NIL节点（空节点））
解析：cur、parent都为红，违反性质3；若把parent改为黑，符合性质3，但是左边少了一个黑节点，违反性质4；所
5、cur为红，parent为红，grandfather为黑，uncle不存在/uncle为黑，parent为grandfather的左孩子，cur为parent的右孩子，则针对parent做左单旋转；相反，parent为grandfather的右孩子，cur为parent的左孩子，则针对parent做右单旋转，则转换成了情况4
红黑树左单旋转和右单旋转同AVL树左单旋转和右单旋转一样，详见http://blog.csdn.net/wanglelelihuanhuan/article/details/51863275
RBTree.h
#pragma once
enum Color
RED,
BLACK,
;
template<class K, class V>
struct RBTreeNode
K _key;
V _value;
RBTreeNode<K, V>* _left;
RBTreeNode<K, V>* _right;
RBTreeNode<K, V>* _parent;
Color _color;
RBTreeNode<K, V>(const K& key, const V& value)
: _key(key)
, _value(value)
, _left(NULL)
, _right(NULL)
, _parent(NULL)
, _color(RED)
;
template<class K, class V>
class RBTree
typedef RBTreeNode<K, V> Node;
public:
RBTree()
:_root(NULL)
public:
bool Insert(const K& key, const V& value)
if (_root == NULL)
_root = new Node(key, value);
_root->_color = BLACK;
return true;
//先插入节点
Node* cur = _root;
Node* parent = NULL;
while (cur)
if (cur->_key > key)
parent = cur;
cur = cur->_left;
else if (cur->_key < key)
parent = cur;
cur = cur->_right;
else
return false;
cur = new Node(key, value);
if (parent->_key > key)
parent->_left = cur;
cur->_parent = parent;
else
parent->_right = cur;
cur->_parent = parent;
//再调颜色
while (cur != _root && parent->_color == RED)
Node* grandfather = parent->_parent;
if (grandfather->_left == parent)
//第一种情况，uncle存在且为红，进行变色处理
Node* uncle = grandfather->_right;
if (uncle && uncle->_color == RED)
parent->_color = uncle->_color = BLACK;
grandfather->_color = RED;
//然后把grandfather当成cur，继续向上调整。
cur = grandfather;
parent = cur->_parent;
else // uncle不存在/uncle存在为黑
//第三种情况,左右双旋 '<'-->'/'-->'/\\'
if (cur == parent->_right)
RotateL(parent);
swap(parent, cur);
grandfather->_color = RED;
parent->_color = BLACK;
RotateR(grandfather);
break;
else //grandfather->_right == parent
Node* uncle = grandfather->_left;
if (uncle && uncle->_color == RED)
parent->_color = uncle->_color = BLACK;
grandfather->_color = RED;
cur = grandfather;
parent = cur->_parent;
else
//右左双旋 '>'-->'\\'-->'/\\'
if (cur == parent->_left)
RotateR(parent);
swap(parent, cur);
grandfather->_color = RED;
parent->_color = BLACK;
RotateL(grandfather);
break;
_root->_color = BLACK;
return true;
void InOrder()
if (_root == NULL)
return;
_InOrder(_root);
cout << endl;
bool IsBalance()
if (_root == NULL || (_root && _root->_color == RED))
return false;
//统计最左路径中黑色节点个数
int k = 0;
Node* cur = _root;
while (cur)
if (cur->_color == BLACK)
++k;
cur = cur->_left;
int count = 0;
return _IsBalance(_root, k, count);
public:
void _InOrder(Node* root)
if (root == NULL)
return;
_InOrder(root->_left);
cout << root->_key << " ";
_InOrder(root->_right);
bool _IsBalance(Node* root, const int k, int count)
if (root->_color == RED && root->_parent->_color == RED)
return false;
if (root->_color == BLACK)
++count;
if (root->_left == NULL&&root->_right == NULL)
if (k != count)
cout << "黑色节点个数不相等" << root->_key << endl;
return false;
else
cout << "平衡" << endl;
return true;
return _IsBalance(root->_left, k, count);
return _IsBalance(root->_right, k, count);
void RotateL(Node* parent)
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
subRL->_parent = parent;
subR->_left = parent;
Node* ppNode = parent->_parent;
parent->_parent = subR;
if (ppNode == NULL)
_root = subR;
subR->_parent = NULL;
else
if (ppNode->_left == parent)
ppNode->_left = subR;
else
ppNode->_right = subR;
subR->_parent = ppNode;
void RotateR(Node* parent)
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
subLR->_parent = parent;
subL->_right = parent;
Node* ppNode = parent->_parent;
parent->_parent = subL;
if (ppNode == NULL)
_root = subL;
subL->_parent = NULL;
else
if (ppNode->_left == parent)
ppNode->_left = subL;
else
ppNode->_right = subL;
subL->_parent = ppNode;
protected:
Node* _root;
;
void TestInsert()
int arr[] = 16, 3, 7 ;
RBTree<int, int> rb;
for (int i = 0; i < sizeof(arr) / sizeof(arr[0]); ++i)
rb.Insert(arr[i], i);
cout << arr[i] << endl;
cout << "IsBalance " << rb.IsBalance() << endl;
cout << "IsBalance " << rb.IsBalance() << endl;
rb.InOrder();
Test.cpp
#include<iostream>
using namespace std;
#include"RBTree.h"
int main()
TestInsert();
return 0;
红黑树和AVL树的比较
红黑树和AVL树都是高效的平衡二叉树，增删查改的时间复杂度都是O(lg(N)) 红黑树的不追求完全平衡，保证最长路径不超过最短路径的2倍，相对而言，降低了旋转的要求，所以性能跟AVL树差不多，但是红黑树实现更简单，所以实际运用中红黑树更多。以上是关于红黑树的主要内容，如果未能解决你的问题，请参考以下文章