学步园

 二叉查找树（Binary Search Tree），或者是一棵空树，或者是具有下列性质的二叉树： 若它的左子树不空，则左子树上所有结点的值均小于它的根结点的值； 若它的右子树不空，则右子树上所有结点的值均大于它的根结点的值

头文件SearchTree.h

#ifndef SEARCHTREE_H
#define SEARCHTREE_H
typedef int Element;
typedef struct Node{
	Element data;
	struct Node* Left;
	struct Node* Right;
}SearchNode,*SearchTree,*Position;
void MakeEmpty(SearchTree T);
bool IsEmpty(SearchTree T);
bool Find(Element x,SearchTree T);
Position FindMin(SearchTree T);
Position FindMax(SearchTree T);
Position Insert(Element x,SearchTree &T);
Position Delete(Element x,SearchTree T);
void InOrderTraverse(SearchTree T);
#endif //SEARCHTREE_H

实现文件SearchTree.cpp

#include "SearchTree.h"
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
void MakeEmpty(SearchTree T) //清空二叉树
{
	if(T)
	{
		MakeEmpty(T->Left);
		MakeEmpty(T->Right);
		free(T);
	}
}
bool IsEmpty(SearchTree T) //判断二叉树是否为空
{
	if(T == NULL)
		return true;
	else
		return false;
}
bool Find(Element x,SearchTree T)  //查找x是否在树中存在
{
	if(T == NULL)
		return false;
	else if(x < T->data)
		return Find(x,T->Left);
	else if(x > T->data)
		return Find(x,T->Right);
	return true;
}
Position FindMin(SearchTree T) //查找最小数
{
	if(T == NULL)
		return NULL;
	else if(T->Left == NULL)
		return T;
	else 
		return FindMin(T->Left);
}
Position FindMax(SearchTree T) //查找最大数
{
	if(T == NULL)
		return NULL;
	while(T->Right != NULL)
		T = T->Right;
	return T;
}
Position Insert(Element x,SearchTree &T) //向二叉树中插入数据
{
	if(T == NULL)
	{
		T = (SearchTree)malloc(sizeof(SearchNode));
		if(!T)
		{
			printf("内存分配失败\n");
			exit(1);
		}
		T->data = x;
		T->Left = T->Right = NULL;
	}
	else
	{
		if(x < T->data)
			T->Left = Insert(x,T->Left);
		else if( x > T->data)
			T->Right = Insert(x,T->Right);
	}
	return T;
}
Position Delete(Element x,SearchTree T) //删除元素为x的节点
{
	SearchTree temp = NULL;
	SearchTree tp = NULL;
	if(T == NULL)
		return NULL;
	else if(x < T->data)
		T->Left = Delete(x,T->Left);
	else if(x > T->data)
		T->Right = Delete(x,T->Right);
	else if(T->Left && T->Right)
	{
		temp = FindMin(T->Right);
		T->data = temp->data;
		T->Right = Delete(temp->data,T->Right);
	}
	else
	{
		tp = T;
		if(T->Left == NULL)
			T = T->Right;
		if(T->Right == NULL)
			T = T->Left;
		free(tp);
	}
	return T;
}
void InOrderTraverse(SearchTree T) //前序遍历
{
	if(T)
	{
		printf("%d ",T->data);
		InOrderTraverse(T->Left);
		InOrderTraverse(T->Right);
	}
}

测试文件main.cpp

#include "SearchTree.h"
#include <stdio.h>
int main()
{
	SearchTree T = NULL;
	printf("please enter the element\n");
	int ch;
	while(scanf_s("%d",&ch) != EOF)
		Insert(ch,T);
	printf("集合中的内容为:\n");
	InOrderTraverse(T);
	printf("\n");
	printf("请输入要查找的数据\n");
	scanf_s("%d",&ch);
	if(Find(ch,T))
		printf("在集合中找到元素:%d\n",ch);
	else
		printf("在集合中没有找到元素:%d\n",ch);
	printf("集合中的最小元素为:%d\n",FindMin(T)->data);
	printf("集合中的最大元素为:%d\n",FindMax(T)->data);
	printf("请输入要删除的元素\n");
	int word;
	scanf_s("%d",&word);
	Delete(word,T);
	printf("删除后集合的元素为:\n");
	InOrderTraverse(T);
	return 0;
}