# 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)

### 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 );
``````

``````typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
ElementType Data;
BinTree Left;
BinTree Right;
};
``````
• 函数`Insert``X`插入二叉搜索树`BST`并返回结果树的根结点指针；
• 函数`Delete``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);
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
10 is found
10 is the largest key
0 is found
0 is the smallest key
5 is 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);
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(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)