一、基本概念

二叉查找树算是树里面比较常用而且重要的一类，二叉查找树相对于二叉树的不同之处在于，查找树中的每个节点X，它的左子树中的所有关键字要小于X的关键字值，而X的右子树中所有关键字的值大于X的关键字值。这种结构让二叉树按照一定的顺序排序，实现和搜索都会比较简单。

二叉查找树的平均深度为O（log N）。

二、二叉查找树的实现

BSTree.h

#pragma once
#include<iostream>
using namespace std;
typedef int ElementType;
struct BSTreeNode;
typedef BSTreeNode *ptrTree;
typedef ptrTree BSTree;
BSTree createBsTree(ElementType e);
ptrTree findX(ElementType e, BSTree t);
ptrTree findMin(BSTree t);
ptrTree findMax(BSTree t);
BSTree insertX(ElementType e, BSTree t);
BSTree deleteX(ElementType e, BSTree t);
void disposeTree(BSTree t);
struct BSTreeNode
{
	ElementType element;
	ptrTree left;
	ptrTree right;
};

BSTree.cpp

#include "stdafx.h"
#include "BSTree.h"
BSTree createBsTree(ElementType e)
{
	BSTree bst = (BSTree)malloc(sizeof(struct BSTreeNode));
	if (bst==nullptr)
	{
		return nullptr;
	}
	bst->element = e;
	bst->left = nullptr;
	bst->right = nullptr;
	return bst;
}
ptrTree findX(ElementType e, BSTree t)
{
	if (t==nullptr)
	{
		return nullptr;
	}
	if (e>t->element)
	{
		return findX(e, t->right);
	}
	else if(e<t->element)
	{
		return findX(e, t->left);
	}
	return t;
}
ptrTree findMin(BSTree t)
{
	if (t==nullptr)
	{
		return nullptr;
	}
	if (t->left==nullptr)
	{
		return t;
	}
	else
	{
		return findMin(t->left);
	}
}
ptrTree findMax(BSTree t)
{
	if (t==nullptr)
	{
		return nullptr;
	}
	if (t->right==nullptr)
	{
		return t;
	}
	else
	{
		return findMax(t->right);
	}
}
BSTree insertX(ElementType e, BSTree t)
{
	if (t == nullptr)
	{
		t = createBsTree(e);
	}
	else if (e > t->element)
	{
		t->right = insertX(e, t->right);
	}
	else if(e < t->element)
	{
		t->left = insertX(e, t->left);
	}
	return t;
}
BSTree deleteX(ElementType e, BSTree t)
{
	if (t==nullptr)
	{
		return nullptr;
	}
	ptrTree tmp;
	if (e>t->element)
	{
		t->right = deleteX(e, t->right);
	}
	else if(e<t->element)
	{
		t->left = deleteX(e, t->left);
	}
	else if (t->left&&t->right)
	{
		tmp = findMin(t->right);
		t->element = tmp->element;
		t->right = deleteX(tmp->element, t->right);
		//tmp = deleteX(tmp->element, tmp);
	}
	else
	{
		tmp = t;
		if (t->right==nullptr)
		{
			t = t->left;
		}
		else
		{
			t = t -> right;
		}
		free(tmp);
	}
	return t;
}
void disposeTree(BSTree t)
{
	if (t==nullptr)
	{
		return;
	}
	disposeTree(t->left);
	disposeTree(t->right);
	free(t);
}

main.cpp（测试）

#include "stdafx.h"
#include "BSTree.h"
#include<vld.h>
int _tmain(int argc, _TCHAR* argv[])
{
	BSTree bst = createBsTree(6);
	bst = insertX(2, bst);
	bst = insertX(8, bst);
	bst = insertX(1, bst);
	bst = insertX(3, bst);
	bst = insertX(4, bst);
	ptrTree ptrx = findX(3, bst);
	cout << "findX: " << ptrx->element << endl;
	ptrTree pmin = findMin(bst);
	cout << "findMin: " << pmin->element << endl;
	ptrTree pmax = findMax(bst);
	cout << "findMax: " << pmax->element << endl;
	bst = deleteX(2, bst);
	bst = deleteX(3, bst);
	disposeTree(bst);
	return 0;
}