PTA 数据结构与算法题目集（中文）6-12 二叉搜索树的操作集

6-12 二叉搜索树的操作集（30 分）

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;
};

• 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。

裁判测试程序样例：

#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 );

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 */

输入样例：

10
5 8 6 2 4 1 0 10 9 7
5
6 3 10 0 5
5
5 7 0 10 3

输出样例：

Preorder: 5 2 1 0 4 8 6 7 10 9
6 is found
3 is not found
10 is found
10 is the largest key
0 is found
0 is the smallest key
5 is found
Not Found
Inorder: 1 2 4 6 8 9

作者: 陈越

单位: 浙江大学

时间限制: 400 ms

内存限制: 64 MB

代码长度限制: 16 KB

BinTree Insert( BinTree BST, ElementType X )
{
    if(BST == NULL)
    {
        BST = (struct TNode*)malloc(sizeof(struct TNode));
        BST->Data = X;
        BST->Left = BST->Right = NULL;
        return BST;
    }
    else if(BST->Data>X)
    {
        BST->Left = Insert(BST->Left,X);
    }
    else
    {
        BST->Right = Insert(BST->Right,X);
    }
    return BST;
}
BinTree Delete( BinTree BST, ElementType X )
{
    if(BST == NULL)
    {
        printf("Not Found\n");
        return BST;
    }
    if(BST->Data == X)
    {
        if(BST->Left==NULL&&BST->Right==NULL)
        {
            free(BST);
            return NULL;
        }
        else if(BST->Left!=NULL)
        {
            BinTree p,q;
            p = BST;
            q = p->Left;
            if(q->Right == NULL)
            {
                BST->Data = q->Data;
                p->Left = q->Left;
                free(q);
                return BST;
            }
            while(q->Right)
            {
                p = q;
                q = q->Right;
            }
            BST->Data = q->Data;
            p->Right = NULL;
            if(q->Left!=NULL)
            {
                p->Right = q->Left;
                free(q);
            }
        }
        else
        {
            BinTree p,q;
            p = BST;
            q = p->Right;
            if(q->Left == NULL)
            {
                BST->Data = q->Data;
                p->Right = q->Right;
                free(q);
                return BST;
            }
            while(q->Left)
            {
                p = q;
                q = q->Left;
            }
            BST->Data = q->Data;
            p->Left = NULL;
            if(q->Right!=NULL)
            {
                p->Left = q->Right;
                free(q);
            }
        }
        return BST;
    }
    if(BST->Data>X)BST->Left = Delete(BST->Left,X);
    else BST->Right = Delete(BST->Right,X);
    return BST;
}
Position Find( BinTree BST, ElementType X )
{
    if(BST == NULL)return BST;
    if(BST->Data == X)
    {
        return BST;
    }
    return BST->Data>X?Find(BST->Left,X):Find(BST->Right,X);
}
Position FindMin( BinTree BST )
{
    if(BST==NULL)return NULL;
    while(BST->Left)BST = BST->Left;
    return BST;
}
Position FindMax( BinTree BST )
{
    if(BST==NULL)return NULL;
    while(BST->Right)BST = BST->Right;
    return BST;
}