C++进阶之AVL树

2.旋转

2.3.1旋转的原则

1.保持搜索树的原则

2.让旋转的树从不平衡变平衡，会降低这棵树的高度

2.3.2右单旋

本质就是将a这颗子树上升一层来解决平衡因子过大的问题

void RotateR(Node* parent)
{
	Node* subL = parent->_left;
	Node* subLR = subL->_right;
	if (subLR)
	{
		subLR->_parent = parent;
	}
	parent->_left = subLR;
	subL->_right = parent;

	Node* pParent = parent->_parent;

	parent->_parent = subL;

	if (parent == _root)
	{
		_root = subL;
		_root->_parent = nullptr;
	}
	else
	{
		if (pParent->_left == parent)
		{
			pParent->_left = subL;
		}
		else
		{
			pParent->_right = subL;
		}

		subL->_parent = pParent;
	}

	subL->_bf = 0;
	parent->_bf = 0;
}

2.3.3左单旋

原理同上，但是编写时要注意平衡因子的更新和parent节点的更新

void RotateL(Node* parent)
{
	Node* subR = parent->_right;
	Node* subRL = subR->_left;
	parent->_right = subRL;
	if (subRL)
	{
		subRL->_parent = parent;
	}

	Node* pParent = parent->_parent;
	subR->_left = parent;
	parent->_parent = subR;
	if (pParent == nullptr)
	{
		_root = subR;
		subR->_parent = nullptr;
	}
	else
	{
		if (parent == pParent->_left)
		{
			pParent->_left = subR;
		}
		else
		{
			pParent->_right = subR;
		}
		subR->_parent = pParent;
	}
	parent->_bf = subR->_bf = 0;
}

2.3.4左右双旋

左右双旋就是不是纯粹的一边高，这个时候如果进行纯粹的单旋转就会出现下图的情况，注意不要看上标

此时最好的办法就是先在5这个左节点先进行单旋，让其变成纯粹的一边高，然后在进行正常的单旋

//左右双旋转
void RotateLR(Node* parent)
{
	RotateL(parent->_left);
	RotateR(parent);
}

旋转代码参考上面

注意：还有很多细节，比如平衡因子的更新之类的重点没有提到，不代表可以忽略！！！

注意：还有很多细节，比如平衡因子的更新之类的重点没有提到，不代表可以忽略！！！

注意：还有很多细节，比如平衡因子的更新之类的重点没有提到，不代表可以忽略！！！

详细的参考代码部分

#pragma once
#include<iostream>
#include<assert.h>
using namespace std;

template<class K,class V>
struct AVLTreeNode
{
	pair<K, V> _kv;
	AVLTreeNode<K, V>* _left;
	AVLTreeNode<K, V>* _right;
	AVLTreeNode<K, V>* _parent;

	int _bf;
	AVLTreeNode(const pair<K,V>& kv)
		:_kv(kv),
		_right(nullptr),
		_left(nullptr),
		_parent(nullptr),
		_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* parent = nullptr;
		Node* cur = _root;
		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;
			}
		}

		cur = new Node(kv);
		if (parent->_kv.first < kv.first)
		{
			parent->_right = cur;
		}
		else
		{
			parent->_left = cur;
		}
		cur->_parent = parent;
		//控制平衡
		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)
			{
				//旋转

				if (parent->_bf == -2 && cur->_bf == -1)
				{
					RotateR(parent);
				}
				else if (parent->_bf == 2 && cur->_bf == 1)
				{
					RotateL(parent);
				}
				else if (parent->_bf == -2 && cur->_bf == 1)
				{
					RotateLR(parent);
				}
				else if (parent->_bf == 2 && cur->_bf == -1)
				{
					RotateRL(parent);
				}
				else
				{
					assert(false);
				}
				break;
			}
			else
			{
				//这一行代码的含义是理论上不应该执行到这个地方，如果真的执行到了应该主动触发报错
				assert(false);
			}
		}

		return true;

	}
	//右旋
	void RotateR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;
		if (subLR)
		{
			subLR->_parent = parent;
		}
		parent->_left = subLR;
		subL->_right = parent;

		Node* pParent = parent->_parent;

		parent->_parent = subL;

		if (parent == _root)
		{
			_root = subL;
			_root->_parent = nullptr;
		}
		else
		{
			if (pParent->_left == parent)
			{
				pParent->_left = subL;
			}
			else
			{
				pParent->_right = subL;
			}

			subL->_parent = pParent;
		}

		subL->_bf = 0;
		parent->_bf = 0;
	}

	//左旋
	void RotateL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;
		parent->_right = subRL;
		if (subRL)
		{
			subRL->_parent = parent;
		}

		Node* pParent = parent->_parent;
		subR->_left = parent;
		parent->_parent = subR;
		if (pParent == nullptr)
		{
			_root = subR;
			subR->_parent = nullptr;
		}
		else
		{
			if (parent == pParent->_left)
			{
				pParent->_left = subR;
			}
			else
			{
				pParent->_right = subR;
			}
			subR->_parent = pParent;
		}
		parent->_bf = subR->_bf = 0;
	}

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

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

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

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

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

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

	//中序遍历
	void InOrder()
	{
		_InOrder(_root);
		cout << endl;
	}

	bool IsBalanceTree()
	{
		return _IsBalanceTree(_root);
	}

	int Size()
	{
		return _Size(_root);
	}
private:
	void _InOrder(Node* root)
	{
		if (root == nullptr)
		{
			return;
		}

		_InOrder(root->_left);
		cout << root->_kv.first << ":" << root->_kv.second << endl;
		_InOrder(root->_right);
	}

	//高度差计算
	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;
	}
	//平衡检查
	bool _IsBalanceTree(Node* root)
	{
		if (root == nullptr)
			return true;
		int leftHeight = _Height(root->_left);
		int rightHeight = _Height(root->_right);
		int diff = leftHeight - rightHeight;
		//abs是绝对值的计算
		if (abs(diff) >= 2)
		{
			cout << root->_kv.first << "高度异常" << endl;
			return false;
		}
		if (root->_bf != diff)
		{
			cout << root->_kv.first << "数据异常" << endl;
			return false;
		}
		return _IsBalanceTree(root->_left) && _IsBalanceTree(root->_right);
	}

	int _Size(Node* root)
	{
		if (root == nullptr)
		{
			return 0;
		}
		return _Size(root->_left) + _Size(root->_right) + 1;
	}
private:
	Node* _root = nullptr;
};