6-1 二叉搜索樹的操做集（30 分）

本題要求實現給定二叉搜索樹的5種經常使用操做。

函數接口定義：

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結構定義以下：

typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
    ElementType Data;
    BinTree Left;
    BinTree Right;
};

• 函數Insert將X插入二叉搜索樹BST並返回結果樹的根結點指針；
• 函數Delete將X從二叉搜索樹BST中刪除，並返回結果樹的根結點指針；若是X不在樹中，則打印一行Not Found並返回原樹的根結點指針；
• 函數Find在二叉搜索樹BST中找到X，返回該結點的指針；若是找不到則返回空指針；
• 函數FindMin返回二叉搜索樹BST中最小元結點的指針；
• 函數FindMax返回二叉搜索樹BST中最大元結點的指針。

裁判測試程序樣例：

#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 ); /* 先序遍歷，由裁判實現，細節不表 */
void InorderTraversal( BinTree BT );  /* 中序遍歷，由裁判實現，細節不表 */

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;
}
/* 你的代碼將被嵌在這裏 */

輸入樣例：

10
5 8 6 2 4 1 0 10 9 7
5
6 3 10 0 5
5
5 7 0 10 3

輸出樣例：

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

代碼；

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->Left=Insert(BST->Left,X);
else if(X>BST->Data)
BST->Right=Insert(BST->Right,X);

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