C++基础（12.红黑树实现）

代码实现：

RBTree.h：

#pragma onceenum Colour
{RED,BLACK
};template<class K, class V>
struct RBTreeNode
{// 这里更新控制平衡也要加入parent指针pair<K, V> _kv;RBTreeNode<K, V>* _left;RBTreeNode<K, V>* _right;RBTreeNode<K, V>* _parent;Colour _col;RBTreeNode(const pair<K, V>& kv):_kv(kv), _left(nullptr), _right(nullptr), _parent(nullptr){}
};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;if (parent->_kv.first < kv.first){parent->_right = cur;}else{parent->_left = cur;}// 链接父亲cur->_parent = parent;// 父亲是红色，出现连续的红色节点，需要处理while (parent && parent->_col == RED){Node* grandfather = parent->_parent;if (parent == grandfather->_left){//   g// p   uNode* uncle = grandfather->_right;if (uncle && uncle->_col == RED){// 变色parent->_col = uncle->_col = BLACK;grandfather->_col = RED;// 继续往上处理cur = grandfather;parent = cur->_parent;}else{if (cur == parent->_left){//     g//   p    u// cRotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{//      g//   p    u//     cRotateL(parent);RotateR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}else{//   g// u   pNode* 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//       cif (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;return true;}// 旋转代码的实现跟AVL树是⼀样的，只是不需要更新平衡因⼦void RotateR(Node * parent){Node* subL = parent->_left;Node* subLR = subL->_right;parent->_left = subLR;if (subLR)subLR->_parent = parent;Node* pParent = parent->_parent;subL->_right = parent;parent->_parent = subL;if (parent == _root){_root = subL;subL->_parent = nullptr;}else{if (pParent->_left == parent){pParent->_left = subL;}else{pParent->_right = subL;}subL->_parent = pParent;}}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 (parentParent == nullptr){_root = subR;subR->_parent = nullptr;}else{if (parent == parentParent->_left){parentParent->_left = subR;}else{parentParent->_right = subR;}subR->_parent = parentParent;}}void InOrder(){_InOrder(_root);cout << endl;}int Height(){return _Height(_root);}int Size(){return _Size(_root);}Node* Find(const K& key){Node* cur = _root;while (cur){if (cur->_kv.first < key){cur = cur->_right;}else if (cur->_kv.first > key){cur = cur->_left;}else{return cur;}}return nullptr;}bool IsBalance(){if (_root == nullptr)return true;if (_root->_col == RED)return false;// 参考值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){// 前序遍历走到空时，意味着一条路径走完了//cout << blackNum << endl;if (refNum != blackNum){cout << "存在黑色结点的数量不相等的路径" << endl;return false;}return true;}// 检查孩子不太方便，因为孩子有两个，且不一定存在，反过来检查父亲就方便多了if (root->_col == RED && root->_parent->_col == RED){cout << root->_kv.first << "存在连续的红色结点" << 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 << endl;_InOrder(root->_right);}int _Height(Node* root){if (root == nullptr)return 0;int leftHeight = _Height(root->_left);int rightHeight = _Height(root->_right);return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;}int _Size(Node* root){if (root == nullptr)return 0;return _Size(root->_left) + _Size(root->_right) + 1;}private:Node* _root = nullptr;
};

Test.cpp：

#define _CRT_SECURE_NO_WARNINGS 1#include<iostream>
using namespace std;#include"RBTree.h"void TestRBTree1()
{RBTree<int, int> t;// 常规的测试用例//int a[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };// 特殊的带有双旋场景的测试用例int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };for (auto e : a){t.Insert({ e, e });}t.InOrder();cout << t.IsBalance() << endl;
}int main()
{TestRBTree1();return 0;
}