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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。

最长路径≤最短路径×2

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 (不存在连续的红色节点)
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 (每条路径都存在相同数量的黑色节点)
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，不是传统的叶子节点)

2.红黑树的几种情况

2.1 情况一：cur为红，p为红，g为黑，u存在且为红(p为parent，g为grandfather，u为uncle)

太过复杂

2.2 情况二：cur为红，p为红，g为黑，u不存在/u存在且为黑(p为parent，g为grandfather，u为uncle)

2.3 情况三：cur为红，p为红，g为黑，u不存在/u存在且为黑(p为parent，g为grandfather，u为uncle)双旋情况

3.红黑树的底层

#pragma once
#include<iostream>
#include<vector>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>
class RBTree
{typedef RBTreeNode<K, V> Node;
public: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; // 新增节点给红色if (parent->_kv.first < kv.first){parent->_right = cur;}else{parent->_left = cur;}cur->_parent = parent;// parent的颜色是黑色也结束while (parent && parent->_col == RED){// 关键看叔叔Node* grandfather = parent->_parent;if (parent == grandfather->_left){Node* uncle = grandfather->_right;// 叔叔存在且为红，-》变色即可if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandfather->_col = RED;// 继续往上处理cur = grandfather;parent = cur->_parent;}else // 叔叔不存在，或者存在且为黑{if (cur == parent->_left){//     g  //   p   u// c //单旋RotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{//      g  //   p     u//      c //双旋RotateL(parent);RotateR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}else{Node* uncle = grandfather->_left;// 叔叔存在且为红，-》变色即可if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandfather->_col = RED;// 继续往上处理cur = grandfather;parent = cur->_parent;}else // 叔叔不存在，或者存在且为黑{// 情况二：叔叔不存在或者存在且为黑// 旋转+变色//      g//   u     p//            c//单旋if (cur == parent->_right){RotateL(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{//		g//   u     p//      c//双旋RotateR(parent);RotateL(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}}_root->_col = BLACK;return true;}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 (parent == _root){_root = subL;_root->_parent = nullptr;}else{if (ppNode->_left == parent){ppNode->_left = subL;}else{ppNode->_right = subL;}subL->_parent = ppNode;}}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 (parent == _root){_root = subR;_root->_parent = nullptr;}else{if (ppNode->_right == parent){ppNode->_right = subR;}else{ppNode->_left = subR;}subR->_parent = ppNode;}}void InOrder(){_InOrder(_root);cout << endl;}bool IsBalance(){if (_root->_col == RED){return false;}int refNum = 0;Node* cur = _root;while (cur){if (cur->_col == BLACK){++refNum;}cur = cur->_left;}return Check(_root, 0, refNum);}private:bool Check(Node* root, int blackNum, const int refNum){if (root == nullptr){//cout << blackNum << endl;if (refNum != blackNum){cout << "存在黑色节点的数量不相等的路径" << endl;return false;}return true;}if (root->_col == RED && root->_parent->_col == RED){cout << root->_kv.first << "存在连续的红色节点" << endl;return false;}if (root->_col == BLACK){blackNum++;}return Check(root->_left, blackNum, refNum)&& Check(root->_right, blackNum, refNum);}void _InOrder(Node* root){if (root == nullptr){return;}_InOrder(root->_left);cout << root->_kv.first << ":" << root->_kv.second << ":" << (root->_col == RED ? "RED" : "BLACK") << endl;_InOrder(root->_right);}private:Node* _root = nullptr;//size_t _size = 0;
};void TestRBTree1()
{//int a[] = { 8, 3, 1, 10, 6, 4, 7, 14, 13 };int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14,8, 3, 1, 10, 6, 4, 7, 14, 13 };RBTree<int, int> t1;for (auto e : a){// 1、先看是插入谁导致出现的问题// 2、打条件断点，画出插入前的树// 3、单步跟踪，对比图一一分析细节原因t1.Insert({ e,e });cout << "Insert:" << e << "->" << t1.IsBalance() << endl;}t1.InOrder();cout << t1.IsBalance() << endl;
}