C++:AVL树 - 技术栈

文章目录

- 一、AVL树的概念
- 二、AVL树的实现
- - - 1、AVL树的节点
    - [2、 AVL的插入的过程](#2、 AVL的插入的过程)
    - 3、平衡因子的更新
- 三、旋转
- 四、AVL树平衡检测
- 五、AVL树查找

一、AVL树的概念

二、AVL树的实现

1、AVL树的节点

key,vaule的二叉搜索树，需要用三叉链，多定义的父亲指针用来更新平衡因子

cpp 复制代码

template<class K,class V>
struct AVLTreeNode
{
	pair<k, v> _kv;
	AVLTreeNode* _left;
	AVLTreeNode* _right;
	AVLTreeNode* _parent;
	int _bf;//banlance factor平衡因子
	AVLTreeNode(const pair<K, V>& kv)
		:_kv(kv)
		, _left(nullptr)
		, _right(nullptr)
		, _parent(nullptr)
		, _bf(0)
	{}
};

2、 AVL的插入的过程

3、平衡因子的更新

cpp 复制代码

	bool Insert(const pair<K,V>& kv)
	{
		if (_root == nullptr)
		{
			_root = new Node(kv);
			return true;
		}
		Node* parent = nullptr;
		Node* cur = _root;
		while (cur)
		{
			if (cur->_kv.first > kv.first)
			{
				parent = cur;
				cur = cur->_left;
			}
			else if (cur->_kv.first < kv.first)
			{
				parent = cur;
				cur = cur->_right;
			}
			else
				return false;
		}
		cur = new Node(kv);
		cur->_parent = parent;
		if (parent->_kv.first > kv.first)
		{
			parent->_left = cur;
		}
		else
		{
			parent->_right = cur;
		}

		//更新平衡因子
		while (parent)
		{
			if (parent->_left == cur)
			{
				--parent->_bf;
			}
			else
			{
				++parent->_bf;
			}

			if (parent->_bf == 0)
			{
				//平衡后结束
				break;
			}
			else if (parent->_bf == -1 || parent->_bf == 1)
			{
				//不平衡继续向上更新
				cur = parent;
				parent = parent->_parent;
			}
			else if (parent->_bf == -2 || parent->_bf == 2)
			{
				//高度差大于1，进行旋转

				//右单旋，左边高
				if (parent->_bf == -2 && cur->_bf == -1)
					RotateR(parent);
				else if (parent->_bf == 2 && cur->_bf == 1)//纯粹的右边高，进行左单旋
					RotateL(parent);
				else if (parent->_bf == -2 && cur->_bf == 1)//进行左右双旋
				{
					RotateLR(parent);
				}
				else if (parent->_bf == 2 && cur->_bf == -1)//进行右左双旋
				{
					RotateRL(parent);
				}
				else
				{
					assert(false);
				}


				break;

			}
			else
			{
				assert(false);
			}
		}

		return true;
	}

三、旋转

1、持搜索树的规则

2、让旋转的树从不满⾜变平衡，其次降低旋转树的⾼度

旋转总共分为四种，左单旋/右单旋/左右双旋/右左双旋。

1、右单旋

左边的高度大于右边时右旋转

cpp 复制代码

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

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

2、左单旋

右边高进行左单旋

cpp 复制代码

//左单旋
void RotateL(Node* parent)
{
	Node* subR = parent->_right;
	Node* subRL = subR->_left;
	Node* ppNode = parent->_parent;

	parent->_right = subRL;
	subR->_left = parent;
	if (subRL)
		subRL->_parent = parent;
	parent->_parent = subR;
	subR->_parent = ppNode;

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

}

3、右左双旋

cpp 复制代码

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

	RotateL(parent->_left);
	RotateR(parent);

	if (bf == -1)
	{
		subL->_bf = 0;
		parent->_bf = 1;
		subLR->_bf = 0;
	}
	else if (bf == 1)
	{
		subL->_bf = -1;
		parent->_bf = 0;
		subLR->_bf = 0;
	}
	else if (bf == 0)
	{
		subL->_bf = 0;
		parent->_bf = 0;
		subLR->_bf = 0;
	}
	else
	{
		assert(false);
	}
}

4、右左双旋

cpp 复制代码

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

		RotateR(parent->_right);
		RotateL(parent);

		if (bf == 1)
		{
			subR->_bf = 0;
			parent->_bf = -1;
			subRL->_bf = 0;
		}
		else if (bf == -1)
		{
			subR->_bf = 1;
			parent->_bf = 0;
			subRL->_bf = 0;
		}
		else if (bf == 0)
		{
			subR->_bf = 0;
			parent->_bf = 0;
			subRL->_bf = 0;
		}
		else
		{
			assert(false);
		}
	}

四、AVL树平衡检测

cpp 复制代码

bool IsBalanceTree()
{
	return _IsBalanceTree(_root) != -1;
}

	int _IsBalanceTree(Node* root)
	{
		if (root == nullptr)
			return 0;
		int left = _IsBalanceTree(root->_left);
		if (left == -1)
			return -1;
		int right = _IsBalanceTree(root->_right);
		if (right == -1)
			return -1;

		int dif = right - left;
		if (abs(dif) >= 2)
		{
			cout << root->_kv.first << "高度异常" << endl;
			return -1;
		}

		if (dif != root->_bf)
		{
			cout << root->_kv.first << "平衡因子异常" << endl;
			return - 1;
		}
		return abs(left - right) < 2 ? max(left, right) + 1 : -1;
	}

五、AVL树查找

cpp 复制代码

	Node* Find(const K& key)
	{
		Node* cur = _root;

		while (cur)
		{
			if (cur->_kv.first > key)
			{
				cur = cur->_left;
			}
			else if (cur->_kv.first < key)
			{
				cur = cur->_right;
			}
			else
				return cur;
		}
		return nullptr;
	}