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

提交测试代码：

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

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

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

Position FindMin(BinTree BST)
{
    if (!BST)
    {
        return NULL;
    }
    else if (BST->Left != NULL) {
        return FindMin(BST->Left);
    }
    else {
        return BST;
    }
}

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

提测结果：

完整自测代码：

#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;
}

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

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

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

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

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

Position FindMin(BinTree BST)
{
    if (!BST)
    {
        return NULL;
    }
    else if (BST->Left != NULL) {
        return FindMin(BST->Left);
    }
    else {
        return BST;
    }
}

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