浙江大学数据结构04-树7 二叉搜索树的操作集

题目

本题要求实现给定二叉搜索树的5种常用操作。

函数接口定义：

BinTree Insert( BinTree BST, ElementType X );
BinTree Delete( BinTree BST, ElementType X );
Position Find( BinTree BST, ElementType X );
Position FindMin( BinTree BST );
Position FindMax( BinTree BST );

其中BinTree结构定义如下：

typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
    ElementType Data;
    BinTree Left;
    BinTree Right;
};

要求

函数Insert将X插入二叉搜索树BST并返回结果树的根结点指针；
函数Delete将X从二叉搜索树BST中删除，并返回结果树的根结点指针；如果X不在树中，则打印一行Not Found并返回原树的根结点指针；
函数Find在二叉搜索树BST中找到X，返回该结点的指针；如果找不到则返回空指针；
函数FindMin返回二叉搜索树BST中最小元结点的指针；
函数FindMax返回二叉搜索树BST中最大元结点的指针。

解法

#include <stdio.h>
#include <stdlib.h>

typedef int ElementType;
typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
    ElementType Data;
    BinTree Left;
    BinTree Right;
};

void PreorderTraversal( BinTree BT ); /* 先序遍历，由裁判实现，细节不表 */
void InorderTraversal( BinTree BT );  /* 中序遍历，由裁判实现，细节不表 */

BinTree Insert( BinTree BST, ElementType X );
BinTree Delete( BinTree BST, ElementType X );
Position Find( BinTree BST, ElementType X );
Position FindMin( BinTree BST );
Position FindMax( BinTree BST );


void PreorderTraversal( BinTree  BST)
{
	if(BST)
	{
		printf("%d ",BST->Data);
		PreorderTraversal(BST->Left);
		PreorderTraversal(BST->Right);	
	}	
} 

void  InorderTraversal(BinTree BST)
{
	if(BST)
	{
		InorderTraversal(BST->Left);
		printf("%d ",BST->Data);
		InorderTraversal(BST->Right);	
	}
			
}
int main()
{
    BinTree BST, MinP, MaxP, Tmp;
    ElementType X;
    int N, i;

    BST = NULL;
    scanf("%d", &N);
    for ( i=0; i<N; i++ ) {
        scanf("%d", &X);
        BST = Insert(BST, X);
    }
    printf("Preorder:"); PreorderTraversal(BST); printf("\n");
    MinP = FindMin(BST);
    MaxP = FindMax(BST);
    scanf("%d", &N);
    for( i=0; i<N; i++ ) {
        scanf("%d", &X);
        Tmp = Find(BST, X);
        if (Tmp == NULL) printf("%d is not found\n", X);
        else {
            printf("%d is found\n", Tmp->Data);
            if (Tmp==MinP) printf("%d is the smallest key\n", Tmp->Data);
            if (Tmp==MaxP) printf("%d is the largest key\n", Tmp->Data);
        }
    }
    scanf("%d", &N);
    for( i=0; i<N; i++ ) {
        scanf("%d", &X);
        BST = Delete(BST, X);
    }
    printf("Inorder:"); InorderTraversal(BST); printf("\n");

    return 0;
}
/* 你的代码将被嵌在这里 */

BinTree Insert(BinTree BST ,ElementType X)
{
    if(BST == NULL)
    {
        BST = (BinTree)malloc(sizeof(struct TNode));
        BST->Left = NULL;
        BST->Right = NULL;
        BST->Data = X;
    }
    if(X < BST->Data)
    	BST->Left = Insert(BST->Left,X);
    else if(X > BST->Data)
    	BST->Right = Insert(BST->Right,X);
	return BST;
}

Position FindMin( BinTree BST )
{
	if(BST)
		while(BST->Left)
			BST = BST->Left;
	return BST; 
}

Position FindMax( BinTree BST )
{
	if(!BST)
		return NULL;
	while(BST->Right)
		BST = BST->Right;
	return BST; 
}

Position Find( BinTree BST, ElementType X )
{
	if(!BST)
		return NULL;
	else
		if(X < BST->Data)
			return  Find(BST->Left,X);
		else if(X > BST->Data)
			 return Find(BST->Right,X);
		else 
			return BST;
	return NULL; 
	
}
BinTree Delete( BinTree BST, ElementType X )
{
	if(!BST)
	{	printf("Not Found\n");
		return NULL;
		}
	if(X < BST->Data)
			BST->Left = Delete(BST->Left,X);
	else if(X > BST->Data)
			BST->Right = Delete(BST->Right,X);
	else
		if(BST->Left && BST->Right)
			{
				BST->Data = FindMin(BST->Right)->Data;
				BST->Right = Delete(BST->Right,BST->Data);
			}
			else
			{
				BinTree temp = BST;
				BST = BST->Left ? BST->Left :BST->Right;
				free(temp);	
			}
	return BST;		
}