数据结构---04-树7 二叉搜索树的操作集（30 分）

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("\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

思路：按照要求写函数；（写树的基本练习，很棒！）

代码如下：

#include<cstdio>#include<cstdlib>#include<iostream>using namespace std;typedef int ElementType;typedef struct TNode* Position;typedef Position BinTree;struct TNode{ElementType Data;BinTree Left;BinTree Right;};BinTree Insert(BinTree BST,ElementType X);//构建树 BinTree Delete(BinTree BST,ElementType X);//删除元素 Position Find(BinTree BST,ElementType X);//查找某一元素 Position FindMin(BinTree BST);Position FindMax(BinTree BST);void PreorderTravesal(BinTree BT){// 前序遍历 (格式写法一)if(!BT) return ;printf(" %d",BT->Data);PreorderTravesal(BT->Left);PreorderTravesal(BT->Right);} void InorderTraversal(BinTree BT){//中顺遍历     if (!BT) return;          PreorderTravesal(BT->Left);      printf(" %d", BT->Data);      PreorderTravesal(BT->Right);  }  void InorderTravesal(BinTree BT){//后续遍历 (格式写法二)if(BT){InorderTravesal(BT->Left);printf(" %d",BT->Data);InorderTravesal(BT->Right);}}int main(){BinTree BST,MinP,MaxP,Tmp;ElementType X;int N,i;BST=NULL;cin>>N;for(i=0;i<N;i++){cin>>X;BST=Insert(BST,X);}printf("Preorder:");PreorderTravesal(BST);printf("\n");MinP=FindMin(BST);MaxP=FindMax(BST);cin>>N;for(i=0;i<N;i++){cin>>X;Tmp=Find(BST,X);if(Tmp==NULL) printf("%d id 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);}} cin>>N;for(i=0;i<N;i++){cin>>X;BST=Delete(BST,X);}printf("Inorder:");InorderTravesal(BST);printf("\n");return 0;}BinTree Insert(BinTree BST,ElementType X){ //构建树，每次构建，(原则：大于父截点的放在左边，小于父截点的放在右边。),便于查找 if(!BST){BST=(BinTree)malloc(sizeof(struct TNode));//BST=new struct TNode;BST->Data=X;BST->Left=NULL;BST->Right=NULL; }else if(X<BST->Data)BST->Left=Insert(BST->Left,X);else if(X>BST->Data)BST->Right=Insert(BST->Right,X); return BST;}BinTree Delete(BinTree BST,ElementType X){//删除元素 Position Tmp;if(!BST)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){Tmp=FindMax(BST->Left);BST->Data=Tmp->Data;BST->Left=Delete(BST->Left,Tmp->Data);}else{Tmp=BST;if(!BST->Left)BST=BST->Right;elseBST=BST->Left;free(Tmp); }} return BST;}Position Find(BinTree BST,ElementType X){//查找某一元素 while(BST&&(X!=BST->Data)){if(X<BST->Data)BST=BST->Left;elseBST=BST->Right;}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;}