【数据结构】二叉搜索树

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。

   //BSTree.h
   
   #pragma once 
   
   template<class K,class V>
   struct BSTreeNode
   {
   	BSTreeNode(const K& key,const V& value)
   		:_key(key)
   		,_value(value)
   		,_left(NULL)
   		,_right(NULL)
   	{}
   
   	K _key;
   	V _value;
   	BSTreeNode<K,V>* _left;
   	BSTreeNode<K,V>* _right;
   };
   
   template<class K,class V>
   class BSTree
   {
   	typedef BSTreeNode<K,V> Node;
   public:
   	BSTree()
   		:_root(NULL)
   	{}
   	bool Insert(const K& key,const V& value)
   	{
   		if(_root == NULL)
   		{
   			_root = new Node(key,value);
   		}
   		Node* cur = _root;
   		Node* parent  = NULL;
   		while(cur)
   		{
   			if(cur->_key < key)
   			{
   				parent = cur;
   				cur = cur->_right;
   			}
   			else if(cur->_key > key)
   			{
   				parent = cur;
   				cur = cur->_left;
   			}
   			else
   				return false;
   		}
   		cur =  new Node(key,value);
   		if(parent->_key < key)
   		{
   			parent->_right = cur;
   		}
   		else
   		{
   			parent->_left = cur;
   		}
   		return true;
   	}
   
   	Node* Find(const K& key)
   	{
   		Node* cur = _root;
   		while(cur)
   		{
   			if(cur->_key < key)
   				cur =  cur->_right;
   			else if(cur->_key > key)
   				cur = cur->_left;
   			else
   			{
   				cout<<cur->_key<<":"<<cur->_value<<endl;
   				return cur;
   			}
   		}
   		return NULL;
   	}
   
   	bool Remove(const K& key)
   	{
   		if(_root == NULL)
   		{
   			return false;
   		}
   		Node* cur =  _root;
   		Node* parent = NULL;
   		//找到要删除的节点
   		while(cur)
   		{
   			if(cur->_key > key)
   			{
   				parent = cur;
   				cur = cur->_left;
   			}
   			else if(cur->_key < key)
   			{
   				parent = cur;
   				cur =  cur->_right;
   			}
   			else
   			{
   				break;
   			}
   		}
   		Node* del = NULL;
   		//1.要删除节点的左孩子或者右孩子为空
   		if(cur->_left == NULL)
   		{
   			del = cur;
   			if(parent->_left == cur)
   			{
   				parent->_left = cur->_right;
   			}
   			else
   			{
   				parent->_right = cur->_right;
   			}
   			delete del;
   		}
   		//删除节点的右孩子为空
   		else if(cur->_right == NULL) 
   		{
   			del = cur;
   			if(parent->_left == cur)
   			{
   				parent->_left = cur->_left;
   			}
   			else
   			{
   				parent->_right = cur->_left;
   			}
   			delete del;
   		}
   		// //找以该节点为根节点的左边（最大的）最右的孩子代替它，然后删除
   		else		//要删除节点的左右孩子都不为空
   		{
   			parent = cur;
   			//找以该节点为根节点的右边（最小的）最左的孩子代替它，然后删除
   			Node* subLeft = cur->_right;
   			while(subLeft->_left)
   			{
   				parent = subLeft;
   				subLeft =  subLeft->_left;
   			}
   			cur->_key = subLeft->_key;
   			cur->_value = subLeft->_value;
   
   			if(parent->_left == subLeft)
   				parent->_left = subLeft->_right;
   			else
   				parent->_right = subLeft->_right;
   			delete subLeft;
   		}
   		return false;
   	}
   
   	//递归插入
   	bool InsertR(const K& key,const V& value)
   	{
   		return _InsertR(_root,key,value);
   	}
   	//递归删除
   	bool RemoveR(const K& key)
   	{
   		return _RemoveR(_root,key);	
   	}
   	//递归查找
   	Node* FindR(const K& key)
   	{
   		return _FindR(_root,key);
   	}
   
   	void InOrder()
   	{
   		_InOrder(_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)
   		{
   			return _InsertR(root->_left,key,value);
   		}
   		else if(root->_key < key)
   		{
   			return _InsertR(root->_right,key,value);
   		}
   		else
   		{
   			return false;			
   		}
   	}
   	//递归的删除一个节点
   	bool _RemoveR(Node*& root,const 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* subLeft = root->_right;
   				while(subLeft->_left)
   				{
   					subLeft = subLeft->_left;
   				}
   				swap(root->_key,subLeft->_key);
   				swap(root->_value,subLeft->_value);
   				return _RemoveR(root->_right,key);
   			}
   			delete del;
   		}
   		return true;
   	}
   
   	Node* _FindR(Node*& root,const K& key)
   	{
   		if(_root == NULL)
   		{
   			return NULL;
   		}
   		if(root->_key > key)
   		{
   			_FindR(root->_left,key);
   		}
   		else if(root->_key < key)
   		{
   			_FindR(root->_right,key);
   		}
   		else
   		{
   			cout<<root->_key<<":"<<root->_value<<endl;
   			return root;
   		}
   		return NULL;
   	}
   
   	void _InOrder(Node* root)
   	{
   		if(root == NULL)
   		{
   			return;
   		}
   		_InOrder(root->_left);
   		cout<<root->_key<<" ";
   		_InOrder(root->_right);	
   	}
   protected:
   	Node* _root;
   };
   
   //测试迭代
   void TestTree()
   {
   	BSTree<int ,int> bst;
   	int a[] = {5,3,7,1,4,6,8,0,2,9};
   	for(size_t i = 0; i < sizeof(a)/sizeof(a[0]); i++)
   	{
   		bst.Insert(a[i],i);
   	}
   	bst.InOrder();
   	BSTreeNode<int,int>* ret = bst.Find(6);
   	bst.Remove(9);
   	bst.InOrder();
   	bst.Remove(7);
   	bst.InOrder();
   	bst.Remove(5);
   	bst.InOrder();
   	bst.Remove(3);
   	bst.InOrder();
   }
   
   //测试递归
   void TestTreeR()
   {
   	BSTree<int ,int> bst1;
   	int a1[] = {5,3,7,1,4,6,8,0,2,9};
   	for(size_t i = 0; i < sizeof(a1)/sizeof(a1[0]); i++)
   	{
   		bst1.InsertR(a1[i],i);
   	}
   	bst1.InOrder();
   	BSTreeNode<int,int>* ret1 = bst1.FindR(6);
   	bst1.RemoveR(9);
   	bst1.InOrder();
   	bst1.RemoveR(5);
   	bst1.InOrder();
   	bst1.RemoveR(3);
   	bst1.InOrder();
   	bst1.RemoveR(7);
   	bst1.InOrder();
   	bst1.RemoveR(8);
   	bst1.InOrder();
   	bst1.RemoveR(2);
   	bst1.InOrder();
   	bst1.RemoveR(6);
   	bst1.InOrder();
   }

   
   

   //Test.cpp
   
   #include<iostream>
   using namespace std;
   #include"BSTree.h"
   
   int main()
   {
   	//TestTree();
   	TestTreeR();
   	getchar();
   	return 0;
   }