【C++】AVL树的模拟实现

AVLTree.h

#pragma once
template<class K,class V>
struct AVLTreeNode
{
	struct AVLTreeNode<K, V>* _left;
	struct AVLTreeNode<K, V>* _right;
	struct AVLTreeNode<K, V>* _parent;
	pair<K, V> _kv;
	int _bf;
	AVLTreeNode(const pair<K,V>& kv)
		:_left(nullptr)
		,_right(nullptr)
		,_parent(nullptr)
		,_kv(kv)
		,_bf(0)
	{ }
};

template<class K,class V>
class AVLTree
{
	typedef AVLTreeNode<K, V> Node;
public:
	bool insert(const pair<K, V>& kv)
	{
		if (_root == nullptr)
		{
			_root = new Node(kv);
			return true;
		}
		Node* cur = _root;
		Node* parent = nullptr;
		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;
			}
		}
		//记得创建新节点给值
		cur = new Node(kv);
		if (parent->_kv.first<kv.first)
		{
			parent->_right = cur;
		}
		else
		{
			parent->_left = cur;
		}
		cur->_parent = parent;
		while (parent)
		{
			if (cur == parent->_left)
			{
				parent->_bf--;
			}
			else 
			{
				parent->_bf++;
			}
			if (parent->_bf == 0)
			{
				break;
			}
			else if (parent->_bf == 1|| parent->_bf == -1)
			{
				cur = parent;
				parent = parent->_parent;
			}
			else if(parent->_bf==2|| parent->_bf == -2)
			{
				if (parent->_bf == 2&&cur->_bf == 1)
				{
					RotateL(parent);
				}
				else if (parent->_bf == -2&&cur->_bf == -1)
				{
					RotateR(parent);
				}
				else if (parent->_bf == -2&&cur->_bf == 1)
				{
					RotateLR(parent);
				}
				else if (parent->_bf == 2&&cur->_bf == -1)
				{
					RotateRL(parent);
				}
				break;
				//旋转之后要出循环！
			}
			else
			{
				assert(false);
			}
		}
		return true;
	}
	void RotateL(Node* parent)
	{
		Node* cur = parent->_right;
		Node* curleft = cur->_left;
		parent->_right = curleft;
		if (curleft)
			curleft->_parent = parent;
		cur->_left = parent;
		Node* ppnode = parent->_parent;
		parent->_parent = cur;
		if (ppnode == nullptr)
		{
			_root = cur;
			cur->_parent = nullptr;
		}
		else
		{
			if (ppnode->_left == parent)
			{
				ppnode->_left = cur;
			}
			else
			{
				ppnode->_right = cur;
			}
			cur->_parent = ppnode;
		}
		cur->_bf = parent->_bf = 0;
	}
	void RotateR(Node* parent)
	{
		Node* cur = parent->_left;
		Node* curright = cur->_right;
		parent->_left = curright;
		if (curright)
			curright->_parent = parent;
		cur->_right = parent;
		Node* ppnode = parent->_parent;
		parent->_parent = cur;
		if (ppnode == nullptr)
		{
			_root = cur;
			cur->_parent = nullptr;
		}
		else
		{
			if (ppnode->_left == parent)
			{
				ppnode->_left = cur;
			}
			else
			{
				ppnode->_right = cur;
			}
			cur->_parent = ppnode;
		}
		cur->_bf = parent->_bf = 0;
	}
	void RotateLR(Node* parent)
	{
		Node* cur = parent->_left;
		Node* curright = cur->_right;
		int bf = curright->_bf;
		RotateL(parent->_left);
		RotateR(parent);
		if (bf == 0)
		{
			cur->_bf = 0;
			parent->_bf = 0;
			curright->_bf = 0;
		}
		else if (bf == 1)
		{
			cur->_bf = -1;
			parent->_bf = 0;
			curright->_bf = 0;
		}
		else if (bf == -1)
		{
			cur->_bf = 0;
			parent->_bf = 1;
			curright->_bf = 0;
		}
		else
		{
			assert(false);
		}
	}
	void RotateRL(Node* parent)
	{
		Node* cur = parent->_right;
		Node* curleft = cur->_left;
		int bf = curleft->_bf;
		RotateR(parent->_right);
		RotateL(parent);
		if (bf == 0)
		{
			cur->_bf = 0;
			parent->_bf = 0;
			curleft->_bf = 0;
		}
		else if (bf == 1)
		{
			cur->_bf = 0;
			parent->_bf = -1;
			curleft->_bf = 0;
		}
		else if (bf == -1)
		{
			cur->_bf = 1;
			parent->_bf = 0;
			curleft->_bf = 0;
		}
		else
		{
			assert(false);
		}
	}
	int Height()
	{
		return _Height(_root);
	}
	bool Isbalance()
	{
		return _Isbalance(_root);
	}
private: 
	bool _Isbalance(Node* root)
	{
		if (root == nullptr)
		{
			return true;
		}
		int leftHeight = _Height(root->_left);
		int rightHeight = _Height(root->_right);
		if ((rightHeight - leftHeight) != root->_bf)
		{
			cout << "平衡因子出异常了：" << root->_kv.first << " " << root->_bf << endl;
			cout << rightHeight - leftHeight << endl;
			return false;
		}
		return abs(rightHeight - leftHeight) < 2
			&& _Isbalance(root->_left)
			&& _Isbalance(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;
	}
	Node* _root = nullptr;
};

test.cpp

#include <iostream>
#include <assert.h>
#include <stdlib.h>
#include <vector>
using namespace std;
#include "AVLTree.h"
int main()
{
	const int N = 10000000;
	vector<int> v;
	v.reserve(N);
	srand(time(0));
	for (int i = 0; i < N; i++)
	{
		v.push_back(i);
	}
	AVLTree<int, int> t;
	for (auto e : v)
	{
		t.insert(make_pair(e, e));
	}
	cout << t.Isbalance() << endl;
	cout << t.Height() << endl;
	return 0;
}
//int main()
//{
//	//int a[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };
//	int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
//	AVLTree<int, int> t;
//	for (auto e : a)
//	{
//		t.insert(make_pair(e, e));
//		cout << "Insert:" << e << "->" << t.Isbalance() << endl;
//	}
//
//	return 0;
//}