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04-树7 二叉搜索树的操作集 (30分)

发表于: 2017-05-15   作者:chcnsn   来源:转载   浏览:
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摘要: 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:BinTreeInsert(BinTreeBST,ElementTypeX); BinTreeDelete(BinTreeBST,ElementTypeX); PositionFind(BinTreeBST,ElementTypeX); PositionFindMin(BinTreeBST); P
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("\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
//二叉搜索树的操作集


#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);

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);
    //printf("%d %d\n", 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\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;
}

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->Right = Insert(BST->Right, X);
    else if(X < BST->Data) BST->Left = Insert(BST->Left, X);
    return BST;
}


BinTree Delete(BinTree BST, ElementType X) {
    Position Tmp;
    //没找到;
    if(!BST) { printf("Not Found\n"); return BST; }
    if(X < BST->Data) BST->Left = Delete(BST->Left, X);
    if(X > BST->Data) BST->Right = Delete(BST->Right, X);
    if(X == BST->Data) {
        if(BST->Left && BST->Right) {
            Tmp = FindMin(BST->Right);
            BST->Data = Tmp->Data;
            BST->Right = Delete(BST->Right, BST->Data);
        }
        else {
            Tmp = BST;
            //包括了左右都空及一个空的情况;
            if(!BST->Left)
                BST = BST->Right;
            else if(!BST->Right)
                BST = BST->Left;
            free(Tmp);
        }
    }
    return BST;
}

Position Find(BinTree BST, ElementType X) {
    /*
    if(!BST) return BST;
    if(X == BST->Data) return BST;
    else if(X > BST->Data) return Find(BST->Right, X);
    else return Find(BST->Left, X);
    */
    //尾递归,改为递归实现
    while(BST) {
        if(X == BST->Data) break;
        else if(X > BST->Data) BST = BST->Right;
        else if(X < BST->Data) BST = BST ->Left;
    }
    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;
}


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

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

04-树7 二叉搜索树的操作集 (30分)

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