本篇文章主要介绍AVL树的四种旋转方法。

首先，右单旋：

插入节点位于根节点的左子节点的左子树。

void _RotateR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;

		parent->_left = subLR;
		if (subLR)
			subLR->_parent = parent;

		subL->_right = parent;
		Node* pparent = parent->_parent;
		subL->_parent = pparent;
		parent->_parent = subL;

		if (pparent == NULL)
			_root = subL;
		else
		{
			if (parent = pparent->_left)
				pparent->_left = subL;
			else
				pparent->_right = subL;
		}
		parent->_bf = subL->_bf = 0;
	}

左单旋：

插入节点位于根节点的右子节点的右子树。

void  _RotateL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;

		//处理节点
		parent->_right = subRL;
		if (subRL)
			subRL->_parent = parent;

		subR->_left = parent;
		Node* pparent = parent->_parent;
		subR->_parent = pparent;
		parent->_parent = subR;

		if (parent == _root)
			_root = subR;
		else
		{
			if (pparent->_left == parent)
				pparent->_left = subR;
			else
				pparent->_right = subR;
		}
		parent->_bf = subR->_bf = 0;
	}

左右双旋：

插入节点位于根节点的左子节点的右子树。

void _RotateLR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;
		int bf = subLR->_bf;

		_RotateL(subL);
		_RotateR(parent);

		if (bf == 1)
			subL->_bf = -1;
		if (bf == -1)
			parent->_bf = 1;

	}

右左双旋：

插入节点位于根节点的右子节点的左子树。

void _RotateRL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;
		int bf = subRL->_bf;

		_RotateR(subR);
		_RotateL(parent);

		if (bf == 1)
			parent->_bf = -1;
		else if (bf == -1)
			subR->_bf = 1;
	}

接下来是AVL树的代码：

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

template <class K,class V>
struct AVLTreeNode
{
	AVLTreeNode(const K& key,const V& value)
	:_left(NULL)
	, _right(NULL)
	,_parent(NULL)
	, _key(key)
	, _value(value)
	, _bf(0)
	{}


	AVLTreeNode<K, V>* _left;
	AVLTreeNode<K, V>* _right;
	AVLTreeNode<K, V>* _parent;
	K _key;
	V _value;
	int _bf;
};

template<class K,class V>
class AVLTree
{
	typedef AVLTreeNode<K, V> Node;

public:
	AVLTree()
		:_root(NULL)
	{}



	bool Insert(const K& key,const  V& value)
	{
		if (_root == NULL)
		{
			_root = new Node(key, value);
			return true;
		}

		//找插入位置
		Node* cur = _root;
		Node* parent = NULL;
		while (cur)
		{
			if (key < cur->_key)
			{
				parent = cur;
				cur = cur->_left;
			}
			else if (key > cur->_key)
			{
				parent = cur;
				cur = cur->_right;
			}
			else
				return false;
		}


		//插入
		cur = new Node(key, value);
		if (key < parent->_key)
			parent->_left = cur;
		else
			parent->_right = cur;

		cur->_parent = parent;


		//更新双亲的平衡因子
		while (parent)
		{
			if (parent->_left == cur)
				parent->_bf--;
			else
				parent->_bf++;


			if (parent->_bf == 0)
				break;
			else if (parent->_bf == 1 || parent->_bf == -1)
			{
				cur = parent;
				parent = cur->_parent;
			}
			else
			{
				if (parent->_bf == 2)
				{
					if (cur->_bf == 1)
						_RotateL(parent);
					else
						_RotateRL(parent);
				}
				else
				{
					if (cur->_bf == -1)
						_RotateR(parent);
					else
						_RotateLR(parent);
				}
				break;
			}
		}
		return true;
	}


	void InOreder()
	{
		return _InOrder(_root);
	}


	bool IsBalance()
	{
		return _IsBalance(_root);
	}


private:
	bool _IsBalance(Node* root)
	{
		if (_root == NULL)
			return true;

		int LeftHight = _Hight(_root->_left);
		int RightHight = _Hight(_root->_right);

        if (abs(LeftHight - RightHight) >= 2)
			return false;

		return _IsBalance(_root->_left) && _IsBalance(_root->_right);
	}  


	int _Hight(Node* _root)
	{
		if (_root == NULL)
			return 0;
		int LeftHight = _Hight(_root->_left)+1;
		int RightHight = _Hight(_root->_right)+1;
		return LeftHight > RightHight ? LeftHight+1 : RightHight+1;
	}


	void  _RotateL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;

		//处理节点
		parent->_right = subRL;
		if (subRL)
			subRL->_parent = parent;

		subR->_left = parent;
		Node* pparent = parent->_parent;
		subR->_parent = pparent;
		parent->_parent = subR;

		if (parent == _root)
			_root = subR;
		else
		{
			if (pparent->_left == parent)
				pparent->_left = subR;
			else
				pparent->_right = subR;
		}
		parent->_bf = subR->_bf = 0;
	}



	void _RotateR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;

		parent->_left = subLR;
		if (subLR)
			subLR->_parent = parent;

		subL->_right = parent;
		Node* pparent = parent->_parent;
		subL->_parent = pparent;
		parent->_parent = subL;

		if (pparent == NULL)
			_root = subL;
		else
		{
			if (parent = pparent->_left)
				pparent->_left = subL;
			else
				pparent->_right = subL;
		}
		parent->_bf = subL->_bf = 0;
	}




	void _RotateRL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;
		int bf = subRL->_bf;

		_RotateR(subR);
		_RotateL(parent);

		if (bf == 1)
			parent->_bf = -1;
		else if (bf == -1)
			subR->_bf = 1;
	}



	void _RotateLR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;
		int bf = subLR->_bf;

		_RotateL(subL);
		_RotateR(parent);

		if (bf == 1)
			subL->_bf = -1;
		if (bf == -1)
			parent->_bf = 1;

	}


	void _InOrder(Node* _root)
	{
		if (_root)
		{
			_InOrder(_root->_left);
			cout << " " << _root->_key << " " << _root->_value << endl;
			_InOrder(_root->_right);
		}
	}

private:
	Node* _root;

};


void TestAVLTree()
{
	int array[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };
	AVLTree<int, int> t;
	for (int i = 0; i < sizeof(array) / sizeof(array[0]); i++)
	{
		t.Insert(i, array[i]);
	}

	t.InOreder();
	if (t.IsBalance())
		cout << "平衡" << endl;
	else
		cout << "不平衡" << endl;
	    

}