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：

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

#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);Position FindMin(BinTree BST);
Position FindMax(BinTree BST);
Position Find(BinTree BST,ElementType X);BinTree Insert(BinTree BST, ElementType X);
BinTree Delete(BinTree BST, ElementType X);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",X);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("InorderTraver:");InorderTraversal(BST);return 0;
}BinTree Insert(BinTree BST, ElementType X){if(!BST){BST = (BinTree)malloc(sizeof(struct TNode));BST->Left = NULL;BST->Right = NULL;BST->Data = X;}else if(X > BST->Data){BST->Right = Insert(BST->Right,X);}else if(X < BST->Data){BST->Left = Insert(BST->Left,X);}return BST;
}void PreorderTraversal(BinTree BT){if(BT){printf("%d ",BT->Data);PreorderTraversal(BT->Left);PreorderTraversal(BT->Right);}else return;
}Position FindMin(BinTree BST) {if (BST) {while (BST->Left != NULL) {BST = BST->Left;}}return BST;
}
Position FindMax(BinTree BST) {if (BST) {while (BST->Right != NULL) {BST = BST->Right;}}return BST;
}
Position Find(BinTree BST, ElementType X) {if (!BST)return NULL;if (X < BST->Data) {return Find(BST->Left, X);}else if (X > BST->Data) {return Find(BST->Right, X);}elsereturn BST;
}BinTree Delete(BinTree BST, ElementType X){BinTree p;if(!BST){printf("Not Found\n");return BST;}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){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;
}void InorderTraversal(BinTree BT){if(BT){InorderTraversal(BT->Left);printf("%d ",BT->Data);InorderTraversal(BT->Right);}else return;
}