二叉搜索树，又称二叉排序树，它是一棵空树或者时具有如下性质的一棵二叉树：

1.若它的左子树不为空，则左子树上所有节点的值都小于根结点；

2.若它的右子树不为空，则右子树上所有节点的值都大于根结点；

3.它的左右子树也分别为二叉搜索树。

如下图所示：

可以发现它的中序遍历结果是：0,1,2,3,4,5,6,7,8,9；是有序的。

二叉搜索树主要包括了结点的递归插入和非递归插入，递归删除和非递归删除，查找以及中序遍历这四个函数。

其中插入和删除的主体部分是查找，查找效率代表了二叉搜索树中各个操作的性能。对有N个结点的二叉排序树，若每个元素查找的概率相等，则二叉搜索树平均查找长度是结点在二叉搜索树的深度的函数，即结点越深，则比较次数越多。

具体实现代码如下：

#pragma once
#include <iostream>
using namespace std;
template <class K,class V>
struct BSTreeNode
{
	BSTreeNode(const K& key,const V& value)
	: _key(key),_value(value),_pLeft(NULL),_pRight(NULL),_pParent(NULL)
	{}
	BSTreeNode<K,V>* _pLeft;
	BSTreeNode<K,V>* _pRight;
	BSTreeNode<K,V>* _pParent;
	K _key;
	V _value;
};

template <class K,class V>
class BSTree
{
	typedef BSTreeNode<K,V> Node;
	typedef Node* pNode;
public:
	BSTree()
		: _pRoot(NULL)
	{}

	bool Insert_N(const K& key,const V& value)//非递归插入
	{
		if (NULL == _pRoot)
		{
			_pRoot = new Node(key,value);
			return true;
		}
		pNode pCur = _pRoot;
		pNode pParent = NULL;
		while (pCur)
		{
			pParent = pCur;
			if (key < pCur->_key)
				pCur = pCur->_pLeft;
			else
				pCur = pCur->_pRight;
		}
		pCur = new Node(key,value);
		if (key < pParent->_key)
			pParent->_pLeft = pCur;
		else if (key > pParent->_key)
			pParent->_pRight = pCur;
		else
			return false;
	  pCur->_pParent=pParent;
		return true;
	}

	bool Insert(const K& key,const V& value)//递归插入
	{
		return _Insert(_pRoot,key,value);
	}

	void InOrder()//中序遍历
	{
		_InOrder(_pRoot);
	}

	bool Delete_N(const K& key)//非递归删除
	{
		if (_pRoot == NULL)
			return false;

		pNode pDel = _pRoot;
		pNode pParent = NULL;
		while (pDel)
		{
			if (key < pDel->_key)
				pDel = pDel->_pLeft;
			else if (key > pDel->_key)
				pDel = pDel->_pRight;
			else
			{
				pParent = pDel->_pParent;
				if (pDel->_pLeft == NULL)//只有右子树
				{
					if (_pRoot == pDel)
						_pRoot = _pRoot->_pRight;
					else
					{
						if (pDel == pParent->_pLeft)
							pParent->_pLeft = pDel->_pRight;
						else
							pParent->_pRight = pDel->_pRight;
					}
					if (pDel->_pRight)
						pDel->_pRight->_pParent = pParent;
					delete pDel;
					pDel = NULL;
				}
				else if (pDel->_pRight == NULL)//只有左子树
				{
					if (_pRoot == pDel)
						_pRoot = _pRoot->_pLeft;
					else
					{
						if (pDel == pParent->_pRight)
							pParent->_pRight = pDel->_pLeft;
						else
							pParent->_pLeft = pDel->_pLeft;
					}
					if (pDel->_pLeft)
						pDel->_pLeft->_pParent = pParent;
					delete pDel;
					pDel = NULL;
				}
				else
				{
					pNode firstOfIn = pDel->_pRight;
					while (firstOfIn->_pLeft)
						firstOfIn = firstOfIn->_pLeft;
					pDel->_key = firstOfIn->_key;
					pDel->_value = firstOfIn->_value;

					pNode pParent = firstOfIn->_pParent;
					if (firstOfIn == pDel->_pRight)
					{
						pParent->_pRight = firstOfIn->_pRight;
						if (firstOfIn->_pRight)
							firstOfIn->_pRight->_pParent = pParent;
					}
					else
					{
						pParent->_pLeft = firstOfIn->_pLeft;
						if (firstOfIn->_pLeft)
							firstOfIn->_pLeft->_pParent = pParent;
					}
					delete firstOfIn;
					firstOfIn = NULL;
				}
				return true;
			}
		}
		return false;
	}

	bool Delete(K key)//递归删除
	{
		return _Delete(_pRoot,key);
	}

	pNode Find(K key)//查找结点
	{
		return _Find(_pRoot,key);
	}
private:
	bool _Insert(pNode& pRoot,const K& key,const V& value)
	{
		if (NULL == pRoot)
		{
			pRoot = new Node(key,value);
			return true;
		}
		
		if (key < pRoot->_key)
			return _Insert(pRoot->_pLeft,value);
		else if (key > pRoot->_key)
			return _Insert(pRoot->_pRight,value);
		else
			return false;
	}


	bool _Delete(pNode& pRoot,K key)
	{
		if (NULL == pRoot)
			return false;
		if (key < pRoot->_key)
			return _Delete(pRoot->_pLeft,key);
		else if (key> pRoot->_key)
			return _Delete(pRoot->_pRight,key);
		else
		{
			if (NULL == pRoot->_pLeft && NULL == pRoot->_pRight)
			{
				delete pRoot;
				pRoot = NULL;
				return true;
			}
			else if (NULL == pRoot->_pLeft)
			{
				pNode pDel = pRoot;
				pRoot = pRoot->_pRight;
				delete pDel;
				pDel = NULL;
				return true;
			}
			else if (NULL == pRoot->_pRight)
			{
				pNode pDel = pRoot;
				pRoot = pRoot->_pLeft;
				delete pDel;
				pDel = NULL;
				return true;
			}
			else
			{
				pNode firstOfIn = pRoot->_pRight;
				while (firstOfIn->_pLeft)
					firstOfIn = firstOfIn->_pLeft;

				pRoot->_key = firstOfIn->_key;
				pRoot->_value = firstOfIn->_value;
				return _Delete(pRoot->_pRight,firstOfIn->_key);
			}
		}
	}


	pNode _Find(pNode pRoot,K key)
	{
		if (NULL == pRoot)
			return NULL;


		if (key == pRoot->_key)
			return pRoot;
		else if (key < pRoot->_key)
			return _Find(pRoot->_pLeft,key);
		else
			return _Find(pRoot->_pRight,key);
	}


	void _InOrder(pNode pRoot)
	{
		if (pRoot)
		{
			_InOrder(pRoot->_pLeft);
			cout << "<" << pRoot->_key << "," << pRoot->_value << ">" << endl;
			_InOrder(pRoot->_pRight);
		}
	}
private:
	pNode _pRoot;
}

void Test()
{
	int arr[] = { 5,9 };
	BSTree<int,int> bt;
	for (int i = 0; i < sizeof(arr) / sizeof(arr[0]); i++)
		bt.Insert_N(arr[i],arr[i]);
	bt.InOrder();
	cout << endl;
	bt.Delete_N(4);
	bt.InOrder();
}