二叉搜索树

Posted 2022-11-30 ZDF0414

二叉搜索树的性质：
（1）每个节点都有一个作为搜索依据的关键码（key），所有节点的关键码互不相同。
（2）左子树上所有节点的关键码（key）都小于根节点的关键码（key）。
（3）右子树上所有节点的关键码（key）都大于根节点的关键码（key）。
（4）左右子树都是二叉搜索树。
          
缺陷：在特殊情况下，会退化成单链表的形式，若还以搜索树来看待问题，效率就会很低.
如：在二叉搜索树中插入0、1、2、3、4
        

#pragma once
#include<iostream>
template<class K,class V>
struct TreeNode

	TreeNode<K, V>*  _left;
	TreeNode<K, V>* _right;
	K _key;
	V _value;
	TreeNode<K, V>(const K&key, const V&value)
		: _left(NULL)
		, _right(NULL)
		, _key(key)
		, _value(value)
	
;
template<class K,class V>
class BSTree

	typedef TreeNode<K, V> Node;
public:
	BSTree()
		:_root(NULL)
	
	bool Insert(const K&key, const V&value)
	
		if (_root == NULL)
		
			_root = new Node(key, value);
			return true;
		
		Node*parent = NULL;
		Node*cur = _root;
		while (cur)
		
			if (cur->_key < key)
			
				parent = cur;
				cur = cur->_right;
			
			else if (cur->_key>key)
			
				parent = cur;
				cur = cur->_left;
			
			else
				return false;
		
		if (parent->_key < key)
			parent->_right = new Node(key, value);
		else
			parent->_left = new Node(key, value);
	
	bool InsertR(const K&key, const V&value)
	
		return _InsertR(_root, key, value);
	
	Node* Find(const K&key)
	
		if (_root == NULL)
			return NULL;
		Node* ret = _root;
		while (ret)
		
			if (ret->_key > key)
				ret = ret->_left;
			else if (ret->_key < key)
				ret = ret->_right;
			else
				return ret;
		
		return NULL;
	
	void Remove(K key)
	
		if (_root == NULL)
			return ;
		Node*parent = NULL;
		Node* del = _root;
        //1、找到要删除结点的位置
		while (del)
		
			if (del->_key < key)
			
				parent = del;
				del = del->_right;
			
			else if (del->_key>key)
			
				parent = del;
				del = del->_left;
			
			else
				break;
		
		if (del)
		
			//2、要删除的结点的左结点为空
			if (del->_left == NULL)
			
				if (del == _root)
				
					_root = del->_right;
				
				else if (del == parent->_left)
				
					parent->_left = del->_right;
				
				else
				
					parent->_right = del->_right;
				
				delete del;
				del = NULL;
			
			//3、要删除的结点的右结点为空
			else if (del->_right == NULL)
			
				if (del == _root)
				
					_root = del->_left;
				
				else if (del == parent->_left)
				
					parent->_left = del->_left;
				
				else
				
					parent->_right = del->_left;
				
				delete del;
			
			//4、要删除的结点的左右都不为空
			else
			
				Node* curR = del->_right;
				Node*parent = del;
				while (curR->_left)
				
					parent = curR;
					curR = curR->_left;//找到删除节点右子树中最左边的结点
				
				swap(del->_key, curR->_key);
				swap(del->_value, curR->_value);

				if (parent->_left == curR)
					parent->_left = curR->_right;
				else
					parent->_right = curR->_right;
				delete curR;
				curR = NULL;
		
				
			
		
	
	void RemoveR(K key)
	
		_RemoveR(_root, key);
		//cout << endl;
	
	void InSort()
	
		_InSort(_root);
		cout << endl;
	
protected:
	bool _InsertR(Node* &root,const K&key, const V&value)
	
		if (root == NULL)
		
			root = new Node(key, value);
			return true;
		
		if (root->_key < key)
			_InsertR(root->_right, key, value);
		else if (root->_key>key)
			_InsertR(root->_left, key, value);
		return false;
	
	void _InSort(Node*root)
	
		if (root == NULL)
			return;
		_InSort(root->_left);
		cout << root->_key << " ";
		_InSort(root->_right);
	
	bool _RemoveR(Node* &root, K key)
	
		if (root == NULL)
			return false;
		if (root->_key < key)
			_RemoveR(root->_right, key);
		else if (root->_key > key)
			_RemoveR(root->_left, key);
		else
		
			Node*del = root;
			if (root->_left == NULL)
				root = root->_right;
			else if (root->_right == NULL)
				root = root->_left;
			else
			
				Node*curR = root->_right;
				Node*curRL = curR->_left;
				Node*parent = root;
				while (curRL)
				
					parent = curRL;
					curRL = curRL->_left;
				
				swap(root->_key, curRL->_key);
				if (parent->_left == curRL)
					parent->_left = curRL->_right;
				else
					parent->_right = curRL->_left;
				del = curRL;
			
			delete del;
			del = NULL;
		
	
private:
	Node* _root;
;

要解决此问题，即引入了平衡二叉树（AVL树），即根据结点的平衡因子对树进行调节。