C++实现AVL树的基本操作指南

template<class K, class V>
struct AVLTreeNode 
{
	AVLTreeNode<K, V>* _left; //左孩子
	AVLTreeNode<K, V>* _right; //右孩子
	AVLTreeNode<K, V>* _parent; //父亲结点
	 
	pair<K, V> _Kv; //键值
	int _bf; //平衡因子

	//构造函数
	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:
	AVLTree() 
		:_root(nullptr)
	{}

private:
	Node* _root;
};

bool Insert(const pair<K, V> &kv) 
	{
		if (!_root) _root = new Node(kv); //初始根节点

		Node* cur = _root;
		Node* parent = _root;
		while (cur) 
		{
			K key = cur->_Kv.first;
			if (key > kv.first) //比根结点的key值小，
			{
				parent = cur;
				cur = cur->_left;
			}
			else if(key < kv.first)//比根结点的key值大，
			{
				parent = cur;
				cur = cur->_right;
			}
			else 
			{
				return false;  //插入失败
			}
		}
		
		//开始插入
		cur = new Node(kv);
		Node* newNode = cur;
		if (parent->_Kv.first > newNode->_Kv.first) //新插入的结点key值比根节点小就插入到左子树
		{
			parent->_left = newNode;
			newNode->_parent = parent;
		}
		else		//新插入的结点key值比根节点大就插入到右子树
		{
			parent->_right = newNode;
			newNode->_parent = parent;
		}
	}

//更新祖先路径的所以结点的平衡因子
		/* 
			总结五种情况：
				1、新增结点出现在父结点的左边，平衡因子减减
				2、新增结点出现在父结点的右边，平衡因子加加
				3、父亲的平衡因子为0就不再调整
				4、父亲结点的平衡因子为1或者-1继续调整
				5、父亲结点的平衡因子为2或者-2那就旋转
				
		*/
	while (parent) 
	{
		if (parent->_left == cur) parent->_bf--;   //1、
		if (parent->_right == cur) parent++;	   //2、
		if (parent->_bf == 0) break; 			  //3、
		if (parent->_bf == -1 || parent->_bf == 1)//4、 
		{
			cur = parent;
			parent = parent->_parent;
		}
		if (parent->_bf == -2 || parent->_bf == 2) //5、
		{
			//旋转
			if (parent->_bf == -2) 
			{
				if (cur->_bf == -1) RotateR(parent); //左边高，右单旋
				else RotateLR(parent); //左右双旋
			}
			else //右 parent->_bf == 2
			{
				if (cur->_bf == 1) RotateL(parent);//右边高左单旋转
				else RotateRL(parent); //右左双旋
			}

			break;
		}
	}

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

	parent->_left = subLR; 
	if (subLR) subLR->_parent = parent;  //防止subLR为nullptr

	subL->_right = parent;
	Node* parent_parent = parent->_p	arent; //指针备份
	parent->_parent = subL;
	if (_root == parent) //如果parent就是树的根 
	{
		_root = subL;  //subL取代parent
		_root->_parent = nullptr;
	}
	else  //如果parent并不是树的根
	{
		if (parent_parent->_left == parent) parent->_left = subL;
		else parent_parent->_right = subL;

		subL->_parent = parent_parent; //subL去做parent_parent的孩子
	}
	//调节平衡因子
	subL->_bf = parent->_bf = 0;
}

//左单旋
void RotateL(Node* parent) 
{
	Node* subR = parent->_right;
	Node* subRL = subR->_left;
	
	parent->_right = subRL;
	if (subRL) subRL->_parent = parent;
	
	subR->_left = parent;
	Node* parent_parent = parent->_parent;
	parent->_parent = subR;
	
	if (_root == parent) 
	{
		_root = subR;
		_root->_parent = nullptr;
	}
	else  
	{
		if (parent_parent->_left == parent) parent_parent->_left = subR;
		else parent_parent->_right = subR;

		subR->_parent = parent_parent;
	}
	subR->_bf = parent->_bf = 0;
}

//左右旋转
	void RotateLR(Node* parent) 
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;
		int bf = subLR->_bf;

		RotateL(parent->_left);
		RotateR(parent);
		if (bf == -1)  //h > 0，新增结点在b
		{
			parent->_bf = 1;
			subLR->_bf = 0;
			subL->_bf = 0;
		}
		else if (bf == 1) //h > 0，新增结点在c
		{
			subL->_bf = -1;
			subLR->_bf = 0;
			parent->_bf = 0;
		}
		else if(bf == 0) //h = 0
		{
			parent->_bf = 0;
			subLR->_bf = 0;
			subL->_bf = 0;
		}
		
	}

	//右左旋转
	void RotateRL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;
		int bf = subRL->_bf;

		RotateR(parent->_right);
		RotateL(parent);
		if (bf == -1)  //h > 0，新增结点在b
		{
			parent->_bf = 0;
			subR->_bf = 1;
			subRL->_bf = 0;
		}
		else if (bf == 1) //h > 0，新增结点在c
		{
			parent->_bf = -1;
			subR->_bf = 0;
			subRL->_bf = 0;
		}
		else if (bf == 0)//h = 0
		{
			subR->_bf = 0;
			subRL->_bf = 0;
			parent->_bf = 0;
		}

	}

Node* Find(const K& key) 
{
	Node* cur = _root;
	while (cur) 
	{
		if (key > cur->_Kv.first) cur = cur->_right; //左子树
		else if (key < cur->_Kv.first) cur = cur->_left; //右子树
		else return cur;
	}
}

int height(Node* root) //求高度
{
	return !root ? 0 
		   : max(height(root->_left), 
			 height(root->_right)) + 1;
}

void _Inorder(Node* root)//中序遍历 
{
	if (!root) return;
	_Inorder(root->_left);
	printf("%d : %d\n",root->_Kv.first, root->_Kv.second);
	_Inorder(root->_right);
}

//判断是不是平衡二叉树
bool IsAVLTree() 
{
	return _IsAVLTree(_root);
}

bool _IsAVLTree(Node* root)
{
	if (!root) return true;
	int left = height(root->_left);
	int right = height(root->_right);
	//检查平衡因子	
	if (right - left != root->_bf)
	{
		printf("错误的平衡因子 %d :%d\n", root->_Kv.first, root->_Kv.second);
		return false;
	}
	return (abs(right - left) < 2)
		&& _IsAVLTree(root->_left)
		&& _IsAVLTree(root->_right);
}

//析构函数
~AVLTree()
{
	Destroy(_root);
	_root = nullptr;
}

void Destroy(Node *root)//后序销毁结点
{
	if (!root) return;
	Destroy(root->_left);
	Destroy(root->_right);
	delete root;
}

Node* copy(Node* cp)
{
	if (!cp) return nullptr;

	Node* newnode = new Node(cp->_Kv);
	newnode->_left = copy(cp->_left);
	newnode->_right = copy(cp->_right);
	return newnode;
}

//拷贝构造
AVLTree(const AVLTree<K, V>& job)
{
	if(&job != this)
	_root = copy(job._root);
}

void operator=(AVLTree<K, V> tmp)
{
	if (&tmp != this)
	swap(tmp._root, this->_root);
}

V& operator[](const K& key)
{
	return (Insert(make_pair(key, V())).first)->_Kv.second;
}