C++红黑树详解-代码

#pragma once
#include<iostream>
using namespace std;

// 枚举红黑树的颜色
enum Colour
{
	RED,
	BLACK
};

// 按Key/Value的模式实现
template<class K,class V>
struct RBTreeNode
{
	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
			{
				// 不冗余,插入失败
				return false;
			}
		}
        
		cur = new Node(kv);
		// 如果是非空树,插入红色节点
		cur->_col = RED;
		if (parent->_kv.first < kv.first)
		{
			parent->_right = cur;
		}
		else if (parent->_kv.first > kv.first)
		{
			parent->_left = cur;
		}
		// 链接父亲节点
		cur->_parent = parent;

		// parent是红色,出现了连续的红色节点,需要向上调整
		// 调整之后cur是根,cur的parent是nullptr
		while (parent&&parent->_col == RED)
		{
			Node* grandfather = parent->_parent;
			if (grandfather->_left == parent)
			{
				 //   g
			    // p     u
				Node* uncle = grandfather->_right;
				if (uncle && uncle->_col == RED)
				{
					// 变色是为了处理连续的红节点,保证黑节点的数量不变,
					// 向上继续调整是因为grandfather的节点可能是黑节点就结束,
					// 可能是红节点就继续向上处理
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;

					// 继续向上处理
					cur = grandfather;
					parent = cur->_parent;
				}
				else
				{
					// uncle不存在或uncle存在且为黑
					//   g
				   // p     u
				  // c
				  // 右单旋
					if (cur == parent->_left)
					{
						RotateR(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						// 双旋
						//   g
				        // p   u
				          // c
						RotateL(parent);
						RotateR(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}
					break;
				}
			}
			else
			{
				 //   g
			    // u     p
				Node* uncle = grandfather->_left;
				if (uncle && uncle->_col == RED)
				{
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;

					// 继续向上更新
					cur = grandfather;
					parent = cur->_parent;
				}
				else
				{
					// uncle不存在或者存在且是黑
					//    g
				    // u     p
				   //          c
				   // 左单旋
					if (parent->_right == cur)
					{
						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;
				}
			}
			
		}

		// 无论如何结束之后根都是黑色的
		_root->_col = BLACK;

		return true;
	}


	// 右单旋,旋转点是parent
	void RotateR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;

		parent->_left = subLR;
		// b可能为空树
		if (subLR != nullptr)
			subLR->_parent = parent;

		// 记录parent的parent
		Node* pParent = parent->_parent;

		subL->_right = parent;
		parent->_parent = subL;

		// 1. 10是这棵树的总根
		if (parent == _root)
		{
			_root = subL;
			subL->_parent = nullptr;
		}
		else
		{
			// 2. 10是这棵树的局部根
			// pParent左可能是parent,右也可能是parent
			if (pParent->_left == parent)
			{
				pParent->_left = subL;
			}
			else
			{
				pParent->_right = subL;
			}
			subL->_parent = pParent;
		}
	}

	// 左单旋,旋转点是parent
	void RotateL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;

		parent->_right = subRL;
		// b不是空树
		if (subRL)
			subRL->_parent = parent;

		// 记录父亲节点的父亲节点
		Node* pParent = parent->_parent;

		subR->_left = parent;
		parent->_parent = subR;

		// 1. 10是这棵树的总根
		if (_root == parent)
		{
			_root = subR;
			subR->_parent = nullptr;
		}
		else
		{
			// 2. 10是这棵树的局部根
			if (pParent->_left == parent)
			{
				pParent->_left = subR;
			}
			else
			{
				pParent->_right = subR;
			}
			subR->_parent = pParent;
		}
	}

	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()
	{
		// 根节点是空
		if (_root == nullptr)
			return true;
		// 根节点非空且是红色
		if (_root->_col == RED)
			return false;

	    // 算出一条路径上黑色节点的个数作为参考值
		Node* cur = _root;
		// 参考值
		int blacknum = 0;
		while (cur)
		{
			if (cur->_col == BLACK)
			{
				++blacknum;
			}
			// 就走最左边的一条路径
			cur = cur->_left;
		}

		return Check(_root,0,blacknum);
	}
     
private:
	bool Check(Node* root, int blacknum, const int refnum)
	{
		// refnum参考值
		if (root == nullptr)
		{
			// 当前路径走完了
			if (blacknum != refnum)
			{
				cout << "存在黑色节点的数量不相等的路径" << endl;
				return false;
			}
			return true;
		}

		// 规则3
		if (root->_col == RED && root->_parent->_col == RED)
		{
			cout << "存在连续两个红节点" << 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 << 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;
};

#define _CRT_SECURE_NO_WARNINGS

#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;
}