c++逆天改命进阶--RedBlackTree

1.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。

2.红黑树的性质

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

思考：为什么满足上面的性质，红黑树就能保证：其最长路径中节点个数不会超过最短路径节点个数的两倍？

3.红黑树的实现

REBBLACKTree.h

#pragma once
#include 
using namespace std;

enum Color
{
	BLACK,
	RED
};
template<class K, class V>
struct RBTreeNode
{
	RBTreeNode<K, V>* _left;
	RBTreeNode<K, V>* _right;
	RBTreeNode<K, V>* _parent;
	pair<K, V> _kv;
	Color _col;
	RBTreeNode(const pair<K,V>& kv)
		:_left(nullptr)
		,_right(nullptr)
		,_parent(nullptr)
		,_kv(kv)
		,_col(RED)
	{}
};

template<class K,class V>
class RBTree
{
	typedef RBTreeNode<K, V> Node;
public:
	RBTree()
		:_root(nullptr)
	{}
	void _Destory(Node* root)
	{
		if (root == nullptr)
		{
			return;
		}
		_Destory(root->_left);
		_Destory(root->_right);
		delete root;
	}
	~RBTree()
	{
		_Destory(_root);
		_root = nullptr;
	}
	Node* Find(const K& key)
	{
		Node* cur = _root;
		while (cur)
		{
			if (cur->_kv.first > key)
			{
				cur = cur->_left;
			}
			else if (cur->_kv.first < key)
			{
				cur = cur->_right;
			}
			else
			{
				return cur;
			}
		}
		return nullptr;
	}
	pair<Node*, bool> Insert(const pair<K,V>& kv)
	{
		if (_root == nullptr)
		{
			_root = new Node(kv);
			_root->_col = BLACK;
			return make_pair(_root, true);
        }
		Node* cur = _root;
		Node* parent = nullptr;
		while (cur)
		{
			if (cur->_kv.first > kv.first)
			{
				parent = cur;
				cur = cur->_left;
			}
			else if (cur->_kv.first < kv.first)
			{
				parent = cur;
				cur = cur->_right;
			}
			else
			{
				return make_pair(cur, false);
			}
		}
		Node* newNode = new Node(kv);
		newNode->_col = RED;
		//为什么我们要将新插入的节点的颜色设置为红色
		//如果我们设置为黑色，则该路径黑色节点数量相比于其他路径的黑色节点数量多了一个
		//总不可能插入一个节点就对所有路径进行更改
		//如果我们插入红色，有可能会出现连续红色节点，我们针对连续红色节点进行下面的处理

		if (newNode->_kv.first > parent->_kv.first)
		{
			parent->_right = newNode;
			newNode->_parent = parent;
		}
		else
		{
			parent->_left = newNode;
			newNode->_parent = parent;
		}
		cur = newNode;
		//当我们插入了新节点之后，可能我们破坏了红黑树的性质
		//如果父亲是黑色不用处理，如果是红色需要处理（出现了连续的红色节点）

		while (parent && parent->_col == RED)
		{
			Node* grandfather = parent->_parent;
			if (parent == grandfather->_left)
			{
				Node* uncle = grandfather->_right;
				if (uncle && uncle->_col == RED)//叔叔存在且为红
				{
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;
					cur = grandfather;
					parent = cur->_parent;
				}
				else//叔叔存在且为黑 或者 叔叔不存在
				{
					if (cur == parent->_left)//单旋
					{
						RotateR(grandfather);
						grandfather->_col = RED;
						parent->_col = BLACK;
					}
					else
					{
						RotateL(parent);
						RotateR(grandfather);
						grandfather->_col = RED;
						cur->_col = BLACK;
					}
					break;
				}
			}
			else//同上
			{
				Node* uncle = grandfather->_left;
				if (uncle && uncle->_col == RED)//叔叔存在且为红
				{
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;
					cur = grandfather;
					parent = cur->_parent;
				}
				else
				{
					if (cur == parent->_left)
					{
						RotateR(parent);
						RotateL(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						RotateL(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					break;
				}
			}
		}
		_root->_col = BLACK;
		return make_pair(newNode, true);

	}
	void RotateL(Node* parent)//左单旋
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;
		Node* parentParent = parent->_parent;
		parent->_right = subRL;
		if (subRL)//subRL为空就不用给subRL找父母了
		{
			subRL->_parent = parent;
		}
		parent->_parent = subR;
		subR->_left = parent;
		if (parent == _root)//如果parent是根节点，把根节点改为subR，_root的父母置为nullptr
		{
			_root = subR;
			_root->_parent = nullptr;
		}
		else//parent不是根节点
		{
			//判断parent是parentParent的左还是右
			if (parentParent->_left == parent)
			{
				parentParent->_left = subR;
			}
			else
			{
				parentParent->_right = subR;
			}
			subR->_parent = parentParent;
		}
	}

	void RotateR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;
		Node* parentParent = parent->_parent;
		parent->_left = subLR;
		if (subLR)
		{
			subLR->_parent = parent;
		}
		parent->_parent = subL;
		subL->_right = parent;
		if (parent == _root)
		{
			_root = subL;
			_root->_parent = nullptr;
		}
		else
		{
			if (parent == parentParent->_left)
			{
				parentParent->_left = subL;
			}
			else
			{
				parentParent->_right = subL;
			}
			subL->_parent = parentParent;
		}
	}
	bool _CheckBalance(Node* root, int blackNum, int count)
	{
		if (root == nullptr)//走到空了说明要开始比较黑色节点数量
		{
			if (count != blackNum)
			{
				cout << "黑色节点数量不相等" << endl;
				return false;
			}
			return true;
		}
		if (root->_col == RED && root->_parent->_col == RED)
		{
			cout << "存在连续的红色节点" << endl;
			return false;
		}
		if (root->_col == BLACK)
			count++;
		return _CheckBalance(root->_left, blackNum, count)
			&& _CheckBalance(root->_right, blackNum, count);
	}
	bool CheckBalance()
	{
		if (_root == nullptr)//空树认为平衡
			return true;
		if (_root->_col == RED)//根节点颜色为红则不平衡
			return false;

		//通过每条路径的黑色节点数量是否全部相等来判断,且不能有连续的红色节点

		//我们先记录最左路径黑色节点的数量作为参考值
		//在依次遍历其他路径，每遍历一条路径，就将其黑色节点数量与参考值比较
		//如果遇到不相等的就不平衡

		int blackNum = 0;
		Node* cur = _root;
		while (cur)
		{
			if (cur->_col == BLACK)
				blackNum++;
			cur = cur->_left;
		}
		int count = 0;
		return _CheckBalance(_root, blackNum, count);
	
	}
	void _InOrder(Node* root)
	{
		if (root == nullptr)
			return;
		_InOrder(root->_left);
		cout << root->_kv.first << ":" << root->_kv.second << " ";
		_InOrder(root->_right);
	}
	void InOrder()
	{
		_InOrder(_root);
		cout << endl;
	}

private:
	Node* _root;
};

test.cpp

#include "RedBlackTree.h"
#include 
void TestRBTree()
{
	//int a[] = {16,3,7,11,9,26,18,14,15};
	//int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16,14 };
    int a[] = { 13,8,17,1,11,15,25,6,22,27 };
	RBTree<int,int> t;
	for (auto e : a)
	{
		t.Insert(make_pair(e, e));
	}
	t.InOrder();
	int ret = t.CheckBalance();
	cout << ret << endl;
	srand(time(0));
	int i = 100000000;
	while (i--)
	{
		int e = rand();
		t.Insert(make_pair(e, e));
	}
	cout << t.CheckBalance() << endl;

}
int main()
{
	TestRBTree();
	return 0;
}

4.关于红黑树插入的细节