【C++篇】红黑树

文章目录

准备

博主:大大怪先森(记得关注哦!）
编程环境：vs2013
所示代码：码源

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前言

本文将讲解红黑树的相关知识！！！

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提示：以下是本篇文章正文内容，下面案例可供参考

一、红黑树的概念

红黑树，是一种二叉搜索树，但在每个结点上增加一个存储位表示结点的颜色，可以是Red或Black。 通过对任何一条从根到叶子的路径上各个结点着色方式的限制，红黑树确保没有一条路径会比其他路径长出俩倍，因而是接近平衡的。

二、红黑树的性质

1. 每个结点不是红色就是黑色
2. 根节点是黑色的
3. 如果一个节点是红色的，则它的两个孩子结点是黑色的
4. 对于每个结点，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
5. 每个叶子结点都是黑色的(此处的叶子结点指的是空结点)

三、红黑树插入操作

1.旋转图解

2.代码实现

代码如下（示例）：

#define _CRT_SECURE_NO_WARNINGS 1
#pragma once
#include
#include
#include
using namespace std;
enum Colour
{
	RED,
	BLACK
};

template<class K,class V>
struct RBTreeNode
{
	RBTreeNode<K,V>* _left;
	RBTreeNode<K,V>* _right;
	RBTreeNode<K,V>* _parent;

	pair<K, V> _kv;

	Colour _col;

	RBTreeNode(const pair<K,V>&kv)
		:_left(nullptr)
		, _right(nullptr)
		, _parent(nullptr)
		, _kv(kv)
		, _col(RED)
	{}
};

template<class K,class V>
struct RBTree
{
	typedef RBTreeNode<K, V> Node;
public:
	RBTree()
		:_root(nullptr)
	{}
	bool Insert(const pair<K, V>& kv)
	{
		if (_root == nullptr)
		{
			_root = new Node(kv);
			_root->_col = BLACK;
			return true;
		}

		Node* parent = nullptr;
		Node* cur = _root;
		while (cur)
		{
			if (cur->_kv.first < kv.first)
			{
				parent = cur;
				cur = cur->_right;
			}
			else if (cur->_kv.first > kv.first)
			{
				parent = cur;
				cur = cur->_left;
			}
			else
			{
				return false;
			}
		}

		cur = new Node(kv);
		cur->_col = RED; // 新增节点
		if (parent->_kv.first < kv.first)
		{
			parent->_right = cur;
			cur->_parent = parent;
		}
		else
		{
			parent->_left = cur;
			cur->_parent = parent;
		}

		//控制平衡
		while (parent && parent->_col == RED)
		{
			Node* grandfather = parent->_parent;
			if (parent == grandfather->_left)
			{
				Node* uncle = grandfather->_right;
				//1.uncle存在且为红
				if (uncle && uncle->_col == RED)
				{
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;
					cur = grandfather;
					parent = cur->_parent;
				}
				else//2 + 3的情况uncle不存在//存在且为黑
				{
					if (cur == parent->_left)
					{
						//       g
						//    p
						// c
						//右单旋
						RotateR(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						//双旋
						RotateL(parent);
						RotateR(grandfather);
						cur->_col = RED;
						grandfather->_col = BLACK;
					}
					break;
				}
			}
			else//parent == grandparent->_right
			{
				Node* uncle = grandfather->_left;
				if (uncle && uncle->_col == RED)
				{
					// 变色+继续向上处理
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;

					cur = grandfather;
					parent = cur->_parent;
				}
				else // 2 + 3、uncle不存在/ 存在且为黑
				{
					//  g    
					//     p
					//        c

					//  g
					//     p
					//  c
					if (cur == parent->_right)
					{
						RotateL(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						RotateR(parent);
						RotateL(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}

					break;
				}
			}
			_root->_col = BLACK;
		}
	}
	void RotateR(Node* parent)
	{
		Node* SubL = parent->_left;
		Node* SubLR = SubL->_right;

		parent->_left = SubLR;
		if (SubLR)
		{
			SubLR->_parent = parent;
		}
		Node* parentParent = parent->_parent;
		SubL->_right = parent;
		parent->_parent = SubL;
		if (parent == _root)
		{
			_root = SubL;
			_root->_parent = nullptr;
		}
		else
		{
			if (parentParent->_left == parent)
			{
				parentParent->_left = SubL;
			}
			else
			{
				parentParent->_right = SubL;
			}
			SubL->_parent = parentParent;
		}
	}
	void RotateL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;

		parent->_right = subRL;
		if (subRL)
		{
			subRL->_parent = parent;
		}

		Node* parentParent = parent->_parent;
		subR->_left = parent;
		parent->_parent = subR;

		if (_root == parent)
		{
			_root = subR;
			subR->_parent = nullptr;
		}
		else
		{
			if (parentParent->_left == parent)
				parentParent->_left = subR;
			else
				parentParent->_right = subR;
			subR->_parent = parentParent;
		}
	}
	void InOrder()
	{
		_InOrder(_root);
	}

	void _InOrder(Node* root)
	{
		if (root == NULL)
			return;

		_InOrder(root->_left);
		cout << root->_kv.first << ":" << root->_kv.second << endl;
		_InOrder(root->_right);
	}

	bool IsBalance()
	{
		if (_root && _root->_col == RED)
		{
			cout << "根节点不是黑色" << endl;
			return false;
		}

		// 最左路径黑色节点数量做基准值
		int banchmark = 0;
		Node* left = _root;
		while (left)
		{
			if (left->_col == BLACK)
				++banchmark;

			left = left->_left;
		}

		int blackNum = 0;
		return _IsBalance(_root, banchmark, blackNum);
	}

	bool _IsBalance(Node* root, int banchmark, int blackNum)
	{
		if (root == nullptr)
		{
			if (banchmark != blackNum)
			{
				cout << "存在路径黑色节点的数量不相等" << endl;
				return false;
			}

			return true;
		}

		if (root->_col == RED && root->_parent->_col == RED)
		{
			cout << "出现连续红色节点" << endl;
			return false;
		}

		if (root->_col == BLACK)
		{
			++blackNum;
		}

		return _IsBalance(root->_left, banchmark, blackNum)
			&& _IsBalance(root->_right, banchmark, blackNum);
	}
	int Height()
	{
		return _Height(_root);
	}

	int _Height(Node* root)
	{
		if (root == NULL)
			return 0;
		int leftHeight = _Height(root->_left);
		int rightHeight = _Height(root->_right);
		return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;
	}
private:
	Node* _root;
};

四、红黑树的插入

红黑树的删除本节不做讲解，有兴趣的同学可参考：《算法导论》或者《STL源码剖析》

五、红黑树和AVL的比较

红黑树和AVL树都是高效的平衡二叉树，增删改查的时间复杂度都是O(log2 ^ n )，红黑树不追求绝对平衡，其只需保证最长路径不超过最短路径的2倍，相对而言，降低了插入和旋转的次数，所以在经常进行增删的结构中性能比AVL树更优，而且红黑树实现比较简单，所以实际运用中红黑树更多。

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总结

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