二叉查找树

.h文件：

/*二叉查找（排序）树*/

struct BTreeNode
{
	ElemType data;
	BTreeNode *left;
	BTreeNode *right;
};

//#define FLAG

#ifdef FLAG
//二叉排序树的查找(递归)
int Find(BTreeNode *BST,ElemType &item)
{
	if(BST == NULL)
		return 0;
	if(item.key == BST->data.key)
	{
		item = BST->data;
		return 1;
	}
	else if(item.key < BST->data.key)
		return Find(BST->left,item);
	else if(item.key > BST->data.key)
		return Find(BST->right,item);
}

//二叉查找树的插入(假设不允许具有相同值的结点存在)(递归)
void Insert(BTreeNode* &BST,const ElemType &item)
{
	if(BST == NULL)
	{
		BTreeNode *p = new BTreeNode;
		p->data = item;
		p->left = p->right = NULL;
		BST = p;
	}
	else if(item.key < BST->data.key)
		Insert(BST->left,item);
	else if(item.key > BST->data.key)
		Insert(BST->right,item);
}

#endif

#ifndef FLAG

//二叉排序树的查找(非递归)
int Find(BTreeNode *BST,ElemType &item)
{
	while(BST != NULL)
	{
		if(item.key == BST->data.key)
		{
			item = BST->data;
			return 1;
		}
		else if(item.key < BST->data.key)
			BST = BST->left;
		else if(item.key > BST->data.key)
			BST = BST->right;
	}
	return 0;
}

//二叉查找树的插入(假设不允许具有相同值的结点存在)(非递归)
void Insert(BTreeNode* &BST,const ElemType &item)
{
	BTreeNode *t = BST;   //指向当前待比较的结点
	BTreeNode *parent = NULL;  //指向t结点的双亲节点
	while(t != NULL)
	{
		parent = t;
		if(item.key < t->data.key)
			t = t->left;
		else
			t= t->right;
	}
	BTreeNode *p = new BTreeNode;
	p->data = item;
	p->left = p->right = NULL;
	if(parent == NULL)
		BST = p;
	else if(item.key < parent->data.key)
		parent->left = p;
	else if(item.key > parent->data.key)
		parent->right = p;
}

#endif

//二叉排序树的更新(不可使用非递归的方法)
int Update(BTreeNode* &BST,const ElemType &item)
{
	if(BST == NULL)
		return 0;
	if(item.key == BST->data.key)
	{
		BST->data = item;
		return 1;
	}
	else if(item.key < BST->data.key)
		return Update(BST->left,item);
	else if(item.key > BST->data.key)
		return Update(BST->right,item);
}

//二叉查找树的生成
void CreateBSTree(BTreeNode* &BST,ElemType a[],int n)
{
	BST = NULL;
	for(int i = 0; i < n; i++)
		Insert(BST,a[i]);
}

//中序遍历
void InOrder(BTreeNode* BST)  
{  
    if(BST != NULL)  
    {  
        InOrder(BST->left);  
		cout<<"("<<BST->data.key<<","<<BST->data.rest<<") ";
        InOrder(BST->right);  
    }  
}  

//二叉查找树的删除
int Delete(BTreeNode* &BST,const ElemType &item)
{
	BTreeNode *t = BST;  //指向待比较的结点
	BTreeNode *s = NULL;  //指向t的双亲结点，从根结点开始比较
	while(t != NULL)
	{
		if(item.key == t->data.key)
			break;
		else if(item.key < t->data.key)
		{
			s = t;
			t = t->left;
		}
		else if(item.key > t->data.key)
		{
			s = t;
			t = t->right;
		}
	}
	if(t == NULL)
		return 0;
	/*分三种情况删除已查找到的t结点*/
	//t结点为叶子节点
	if(t->left == NULL && t->right == NULL)
	{
		if(t == BST)
			BST = NULL;
		else if(t == s->left)
			s->left = NULL;
		else if(t == s->right)
			s->right = NULL;
		delete t;
	}
	//t结点为单分支结点
	else if(t->left == NULL || t->right == NULL)
	{
		//t结点为根结点
		if(t == BST)
		{
			if(t->left == NULL)
				BST = t->right;
			else if(t->right == NULL)
				BST = t->left;
		}
		else  //t结点不是根结点，分四种情况
		{
			if(t == s->left && t->left != NULL)
				s->left = t->left;
			else if(t == s->left && t->right != NULL)
				s->left = t->right;
			else if(t == s->right && t->left != NULL)
				s->right = t->left;
			else if(t == s->right && t->right != NULL)
				s->right = t->right;
		}
		delete t;
	}
	//t结点为双分支结点
	else if(t->left != NULL && t->right != NULL)
	{
		BTreeNode *p = t;  //p初始指向t结点
		BTreeNode *q = t->left;  //q初始指向p结点的左子树
		//查找t结点的中序后继结点，查找结束后q结点为t结点的中序后继结点，p结点为q结点的双亲结点
		while(q->right != NULL)
		{
			p = q;
			q = q->right;
		}
		t->data = q->data;
		//删除右子树为空的q结点，使得它的右子树链接到它所在的链接位置
		if(p == t)
			t->left = q->left;
		else
			p->right = q->left;
		delete q;
	}
	return 1;
}

.cpp文件：

/*二叉查找树应用举例*/

#include <iostream>

using namespace std;

typedef struct student
{
	int key;  //整型学号域作为关键字域
	int rest;  //其他整型域
}ElemType;

#include "BSTree.h"

int main()
{
	ElemType a[8];
	for(int i = 0; i < 8; i++)
	{
		cin>>a[i].key>>a[i].rest;
	}
	BTreeNode *bst = NULL;
	ElemType x = {28};
	ElemType y = {20,37};
	CreateBSTree(bst,a,8);
	cout<<"中序遍历："<<endl;
	InOrder(bst);
	cout<<endl;
	if(Find(bst,x))
		cout<<"查找成功！得到的x为：("<<x.key <<","<<x.rest<<")"<<endl;
	if(Update(bst,y))
	{
		cout<<"更新成功:"<<endl;
		InOrder(bst);
	}
	cout<<endl;
	Delete(bst,x);
	Delete(bst,y);
	cout<<"删除关键字为28和20的元素后的中序遍历为："<<endl;
	InOrder(bst);
	cout<<endl;
	return 0;
}

/*
输入：
30 50 20 70 25 80 23 40 28 50 15 90 60 12 48 60
*/