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("\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

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