二叉搜索树的操作集

04-树7 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("
");
    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
", X);
        else {
            printf("%d is found
", Tmp->Data);
            if (Tmp==MinP) printf("%d is the smallest key
", Tmp->Data);
            if (Tmp==MaxP) printf("%d is the largest key
", Tmp->Data);
        }
    }
    scanf("%d", &N);
    for( i=0; i<N; i++ ) {
        scanf("%d", &X);
        BST = Delete(BST, X);
    }
    printf("Inorder:"); InorderTraversal(BST); printf("
");

    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

 1 BinTree Insert( BinTree BST, ElementType X ){
 2     if(!BST) {
 3     BST=(BinTree)malloc(sizeof(struct TNode)); BST->Data=X; BST->Left=BST->Right=NULL;
 4     }else if(X<BST->Data) BST->Left=Insert(BST->Left,X);
 5      else if(X>BST->Data) BST->Right=Insert(BST->Right,X);
 6      return BST;
 7 }
 8 BinTree Delete( BinTree BST, ElementType X ){
 9     BinTree temp;
10     if(!BST) printf("Not Found
");
11     else {
12     if(X<BST->Data) BST->Left=Delete(BST->Left,X);
13     else if(X>BST->Data) BST->Right=Delete(BST->Right,X);
14     else{
15         if(BST->Left&&BST->Right){
16         BinTree temp=FindMin(BST->Right);
17         BST->Data=temp->Data;
18         BST->Right=Delete(BST->Right,BST->Data);
19         }
20         else{ temp=BST;
21             if(!BST->Left) BST=BST->Right;
22             else BST=BST->Left;
23             free(temp);
24         }
25         
26     }
27     }
28     return BST;
29 }
30 Position Find(BinTree BST, ElementType X) {  
31     while (BST && (X != BST->Data)) {  
32         if (X < BST->Data)  
33             BST = BST->Left;  
34         else  
35             BST = BST->Right;  
36     }  
37     return BST;  
38 }  
39   
40 Position FindMin(BinTree BST) {  
41     if (BST) {  
42         while (BST->Left)  
43             BST = BST->Left;  
44     }  
45     return BST;  
46 }  
47   
48 Position FindMax(BinTree BST) {  
49     if (BST) {  
50         while (BST->Right)  
51             BST = BST->Right;  
52     }  
53     return BST;  
54 }

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