# 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```

```BinTree Insert(BinTree BST, ElementType X) {
if (!BST) {
BST = (BinTree)malloc(sizeof(struct TNode));
BST->Data = X;
BST->Left = NULL;
BST->Right = NULL;
}
else if (BST->Data > X) {
BST->Left = Insert(BST->Left, X);
}
else if (BST->Data < X) {
BST->Right = Insert(BST->Right, X);
}
return BST;
}

BinTree Delete(BinTree BST, ElementType X) {
if (!BST) {
}
else if (BST->Data > X) {
BST->Left = Delete(BST->Left, X);
}
else if (BST->Data < X) {
BST->Right = Delete(BST->Right, X);
}
else if (BST->Left != NULL && BST->Right == NULL) {
BinTree tmp = BST;
BST = BST->Left;
free(tmp);
}
else if (BST->Left == NULL && BST->Right != NULL) {
BinTree tmp = BST;
BST = BST->Right;
free(tmp);
}
else if (BST->Left == NULL && BST->Right == NULL) {
free(BST);
BST = NULL;
}
else {
Position tmp = FindMin(BST->Right);
BST->Data = tmp->Data;
BST->Right = Delete(BST->Right, BST->Data);
}
return BST;
}

Position Find(BinTree BST, ElementType X) {
if (!BST) {
return NULL;
}
else if (BST->Data > X) {
return Find(BST->Left, X);
}
else if (BST->Data < X) {
return Find(BST->Right, X);
}
else {
return BST;
}
}

Position FindMin(BinTree BST)
{
if (!BST)
{
return NULL;
}
else if (BST->Left != NULL) {
return FindMin(BST->Left);
}
else {
return BST;
}
}

Position FindMax(BinTree BST)
{
if (!BST) {
return NULL;
}
else if (BST->Right != NULL) {
return FindMax(BST->Right);
}
else {
return BST;
}
}```

```#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;
}

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

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

BinTree Insert(BinTree BST, ElementType X) {
if (!BST) {
BST = (BinTree)malloc(sizeof(struct TNode));
BST->Data = X;
BST->Left = NULL;
BST->Right = NULL;
}
else if (BST->Data > X) {
BST->Left = Insert(BST->Left, X);
}
else if (BST->Data < X) {
BST->Right = Insert(BST->Right, X);
}
return BST;
}

BinTree Delete(BinTree BST, ElementType X) {
if (!BST) {
}
else if (BST->Data > X) {
BST->Left = Delete(BST->Left, X);
}
else if (BST->Data < X) {
BST->Right = Delete(BST->Right, X);
}
else if (BST->Left != NULL && BST->Right == NULL) {
BinTree tmp = BST;
BST = BST->Left;
free(tmp);
}
else if (BST->Left == NULL && BST->Right != NULL) {
BinTree tmp = BST;
BST = BST->Right;
free(tmp);
}
else if (BST->Left == NULL && BST->Right == NULL) {
free(BST);
BST = NULL;
}
else {
Position tmp = FindMin(BST->Right);
BST->Data = tmp->Data;
BST->Right = Delete(BST->Right, BST->Data);
}
return BST;
}

Position Find(BinTree BST, ElementType X) {
if (!BST) {
return NULL;
}
else if (BST->Data > X) {
return Find(BST->Left, X);
}
else if (BST->Data < X) {
return Find(BST->Right, X);
}
else {
return BST;
}
}

Position FindMin(BinTree BST)
{
if (!BST)
{
return NULL;
}
else if (BST->Left != NULL) {
return FindMin(BST->Left);
}
else {
return BST;
}
}

Position FindMax(BinTree BST)
{
if (!BST) {
return NULL;
}
else if (BST->Right != NULL) {
return FindMax(BST->Right);
}
else {
return BST;
}
}```

04-树7 二叉搜索树的操作集 (30分)

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