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

#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);
void InorderTraversal(BinTree BT);

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

BinTree Insert(BinTree BST, ElementType X);
BinTree Delete(BinTree BST, ElementType X);

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); 
    printf("%d %d
",MinP->Data,MaxP->Data);
     
    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
",X);
            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("InorderTraver:");
    InorderTraversal(BST);
    
    return 0;
}

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

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

Position FindMin(BinTree BST) {
    if (BST) {
        while (BST->Left != NULL) {
            BST = BST->Left;
        }
    }
    return BST;
}
Position FindMax(BinTree BST) {
    if (BST) {
        while (BST->Right != NULL) {
            BST = BST->Right;
        }
    }
    return BST;
}
Position Find(BinTree BST, ElementType X) {
    if (!BST)
        return NULL;
    if (X < BST->Data) {
        return Find(BST->Left, X);
    }
    else if (X > BST->Data) {
        return Find(BST->Right, X);
    }
    else
        return BST;
}

BinTree Delete(BinTree BST, ElementType X){
    BinTree p;
    if(!BST){
        printf("Not Found
");
        return BST;
    }
    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){
            p = FindMax(BST->Left);
            BST->Data = p->Data;
            BST->Left = Delete(BST->Left,BST->Data);
           }else{
            p = BST;
            if(!BST->Left) BST = BST->Right;
            else if(!BST->Right) BST = BST->Left;
            free(p);
        }
    } 
    return BST;
}

void InorderTraversal(BinTree BT){
    if(BT){
        InorderTraversal(BT->Left);
        printf("%d ",BT->Data);
        InorderTraversal(BT->Right);
    }
    else return;
}