04-树7 二叉搜索树的操作集 (30分)

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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：

105 8 6 2 4 1 0 10 9 756 3 10 0 555 7 0 10 3

输出样例：

Preorder: 5 2 1 0 4 8 6 7 10 96 is found3 is not found10 is found10 is the largest key0 is found0 is the smallest key5 is foundNot FoundInorder: 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);    }}

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