04-树7 二叉搜索树的操作集（30 point(s)） 【Tree】

04-树7 二叉搜索树的操作集（30 point(s)）

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

思路

先序遍历 是 根 左 右

中序遍历 是 左 根 右

插入就是 如果目标比当前的结点大 就往右 递归 比当前结点小 往左递归

碰到 NULL 就插入

然后删除

如果左右子树都存在

那么就找右子树的最小结点来替代当前结点

如果右子数不存在 直接把左子树接过来

如果左子树不存在 直接把右子数接过来

AC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("\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 */
void PreorderTraversal( BinTree BT )
{
    if (BT == NULL)
        return;
    printf(" %d", BT->Data);
    PreorderTraversal( BT->Left);
    PreorderTraversal( BT->Right);
}

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

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

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

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

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

BinTree Delete( BinTree BST, ElementType X )
{
    BinTree temp;
    if (BST == NULL)
        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)
            {
                temp = FindMin(BST->Right);
                BST->Data = temp->Data;
                BST->Right = Delete(BST->Right, temp->Data);
            }
            else
            {
                temp = BST;
                if (BST->Left == NULL)
                    BST = BST->Right;
                else if (BST->Right == NULL)
                    BST = BST->Left;
                free(temp);
            }
        }
    }
    return BST;
}