• 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InsertX插入二叉搜索树BST并返回结果树的根结点指针;
    • 函数DeleteX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

    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 )
    {
        BinTree p;
    
        if ( !BST )
        {
            printf("Not Found
    ");
            return BST;
        }
    
        if ( BST->Data > X)
        {
            BST->Left = Delete( BST->Left, X);
        }
        else if ( BST->Data < X)
        {
            BST->Right = Delete( BST->Right, X);
        }
        else
        {
            if ( BST->Right && BST->Left )
            {
                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;
    }
    
    Position Find( BinTree BST, ElementType X )
    {
        if ( !BST )
        {
            return NULL;
        }
    
        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 )
        {
            while ( BST->Left )
            {
                BST = BST->Left;
            }
        }
        return BST;
    }
    Position FindMax( BinTree BST )
    {
        if ( BST )
        {
            while ( BST->Right )
            {
                BST = BST->Right;
            }
        }
        return BST;
    }
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  • 原文地址:https://www.cnblogs.com/wanghao-boke/p/11681448.html
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