平衡因子=右子树个数-左子树

#define _CRT_SECURE_NO_WARNINGS 1
#include<iostream>
#include<stdlib.h>

using namespace std;
template<class K,class V>
struct AVLTreeNode
{
	K _key;
	V _value;
	AVLTreeNode<K, V> *_left;
	AVLTreeNode<K, V> *_right;
	AVLTreeNode<K, V> *_parent;
	int _bf;//平衡因子，只能是-1，0，1

	AVLTreeNode(const K&key, const V&value)
		:_key(key)
		, _value(value)
		, _left(NULL)
		, _right(NULL)
		, _parent(NULL)
		, _bf(0)
	{}
};
template<class K, class V>
class AVLTree
{
	typedef AVLTreeNode<K, V> Node;
public:
	AVLTree()
		:_root(NULL)
	{}
	~AVLTree()
	{
		_destroy(_root);
	}
public:
	bool Insert(const K&key, const V&value)//插入
	{
		if (_root == NULL)
		{
			_root = new Node(key, value);
		}
		Node*parent = NULL;
		Node*cur = _root;
		while (cur)
		{
			if (cur->_key > key)
			{
				parent = cur;
				cur = cur->_left;
			}
			else if (cur->_key < key)
			{
				parent = cur;
				cur = cur->_right;
			}
			else
				return false;
		}
		cur = new Node(key, value);
		if (parent->_key>key)
		{
			parent->_left = cur;
			cur->_parent = parent;
		}
		else
		{
			parent->_right = cur;
			cur->_parent = parent;
		}

		bool IsRotate = false;

		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
			{
				IsRotate = true;
				if (parent->_bf == 2)
				{
					if (cur->_bf == 1)
					{
						//left  
						_RotateL(parent);
					}
					else
					{
						//right left  
						_RotateRL(parent);
					}
				}
				else if (parent->_bf == -2)
				{
					if (cur->_bf == -1)
					{
						//right  
						_RotateR(parent);
					}
					else
					{
						//left right  
						_RotateLR(parent);
					}
				}
				break;
			}
		}
		if (IsRotate)
		{
			Node *ppNode = parent->_parent;
			if (ppNode == NULL)
			{
				_root = parent;
			}
			else
			{
				if (ppNode->_key < parent->_key)
				{
					ppNode->_right = parent;
				}
				else
				{
					ppNode->_left = parent;
				}
			}
		}
		return true;
	}
	bool IsBalanceTree()//判断是否是平衡二叉树
	{
		return _IsBalance(_root);
	}
	void InOrder()//前序遍历
	{
		_InOrder(_root);
		cout << endl;
	}
protected:
	bool _IsBalance(Node *root)
	{
		return true;
	}
	int _Height(Node *root)//求高
	{
		if (root == NULL)
			return 0;
		int leftlen = _Height(root->_left);
		int rightlen = _Height(root->_right);
		return leftlen > rightlen ? leftlen + 1 : rightlen + 1;
	}
	void _RotateL(Node*& parent)//左单旋
	{
		Node *subR = parent->_right;
		Node *subRL = subR->_left;
		parent->_right = subRL;
		if (subRL != NULL)
		{
			subRL->_parent = parent;
		}
		subR->_left = parent;
		subR->_parent = parent->_parent;
		parent->_parent = subR;
		parent->_bf = 0;
		subR->_bf = 0;
		parent = subR;
	}
	void _RotateR(Node*& parent)//右单旋
	{
		Node*subL = parent->_left;
		Node*subLR = subL->_right;
		parent->_left = subLR;
		if (subLR != NULL)
		{
			subLR->_parent = parent;
		}
		subL->_right = parent;
		subL->_parent = parent->_parent;
		parent->_parent = subL;
		subL->_bf = 0;
		parent->_bf = 0;
		parent = subL;
	}
	void _RotateLR_R(Node*& parent)//左右旋转(递归)
	{
		_RotateL(parent->_right);
		_RotateR(parent);
	}
	void _RotateRL_R(Node*& parent)//右左旋转(递归)
	{
		_RotateR(parent->_left);
		_RotateL(parent);
	}
	void _RotateLR(Node*& parent)	//左右旋转(非递归)
	{
		Node *subL = parent->_left;
		Node *subLR = subL->_right;
		subL->_right = subLR->_left;
		if (subLR->_left != NULL)
		{
			subLR->_left->_parent = subL;
		}
		subLR->_left = subL;
		subL->_parent = subLR;
		//调整平衡因子，右树减去左树
		if (subLR->_bf == 0 || subLR->_bf == 1)
		{
			subL->_bf = 0;
		}
		else
		{
			subL->_bf = 1;
		}
		parent->_left = subLR->_right;
		if (subLR->_right != NULL)
		{
			subLR->_right->_parent = parent;
		}
		subLR->_right = parent;
		subLR->_parent = parent->_parent;
		parent->_parent = subLR;
		//调整平衡因子，右树减去左树
		if (subLR->_bf == 0 || subLR->_bf == 1)
		{
			parent->_bf = 0;
		}
		else
		{
			parent->_bf = 1;
		}
		parent = subLR;
		subLR->_bf = 0;
	}
	void _RotateRL(Node*& parent)//右左旋转(非递归)
	{
		Node *subR = parent->_right;
		Node *subRL = subR->_left;
		subR->_left = subRL->_right;

		if (subRL->_right != NULL)
		{
			subRL->_right->_parent = subR;
		}
		subRL->_right = subR;
		subR->_parent = subRL;

		if (subRL->_bf == 0 || subRL->_bf == 1)
		{
			subR->_bf = 0;
		}
		else
		{
			subR->_bf = 1;
		}

		parent->_right = subRL->_left;

		if (subRL->_left != NULL)
		{
			subRL->_left->_parent = parent;
		}
		subRL->_left = parent;
		subRL->_parent = parent->_parent;
		parent->_parent = subRL;
		if (subRL->_bf == 0 || subRL->_bf == -1)
		{
			parent->_bf = 0;
		}
		else
		{
			parent->_bf = -1;
		}
		parent = subRL;
		subRL->_bf = 0;
	}
	void _InOrder(Node *root)
	{
		if (root == NULL)
		{
			return;
		}
		_InOrder(root->_left);
		cout << root->_key << " ";
		_InOrder(root->_right);
	}
	void _destroy(Node *root)
	{
		if (root)
		{
			_destroy(root->_left);
			_destroy(root->_right);
			delete root;
			root = NULL;
		}
	}
private:
	Node *_root;
};
void test()
{
	AVLTree<int, int> AVLtree;
	int a[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };
	for (int i = 0; i < sizeof(a) / sizeof(a[0]); i++)
	{
		AVLtree.Insert(a[i], a[i]);
	}
	AVLtree.InOrder();
	AVLtree.IsBalanceTree();
}
int main()
{
	test();
	system("pause");
	return 0;
}