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("
");
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
", X);
else {
printf("%d is found
", Tmp->Data);
if (Tmp==MinP) printf("%d is the smallest key
", Tmp->Data);
if (Tmp==MaxP) printf("%d is the largest key
", Tmp->Data);
}
}
scanf("%d", &N);
for( i=0; i<N; i++ ) {
scanf("%d", &X);
BST = Delete(BST, X);
}
printf("Inorder:"); InorderTraversal(BST); printf("
");
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
啊，脑子出了问题，总是犯小错误，好在写出来了。
代码：
BinTree Insert( BinTree BST, ElementType X )
{
if(BST == NULL)
{
BST = (BinTree)malloc(sizeof(struct TNode));
if(BST == NULL)return NULL;
BST -> Left = BST -> Right = NULL;
BST -> Data = X;
}
else
{
if(BST -> Data > X)BST -> Left = Insert(BST -> Left,X);
else BST -> Right = Insert(BST -> Right,X);
}
return BST;
}
BinTree Delete( BinTree BST, ElementType X )
{
if(BST != NULL)
{
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 && BST -> Right)
{
BinTree p = FindMin(BST -> Right);
BST -> Data = p -> Data;
BST -> Right = Delete(BST -> Right,BST -> Data);
}
else
{
BinTree p = BST;
if(BST -> Right)BST = BST -> Right;
else if(BST -> Left)BST = BST -> Left;
else BST = NULL;
free(p);
}
return BST;
}
}
else printf("Not Found
");
return BST;
}
Position Find( BinTree BST, ElementType X )
{
if(BST == NULL || BST -> Data == X)return BST;
else if(BST -> Data > X)return Find(BST -> Left,X);
else return Find(BST -> Right,X);
}
Position FindMin( BinTree BST )
{
if(BST == NULL)return NULL;
Position Min = BST;
Position Left = FindMin(BST -> Left);
Position Right = FindMin(BST -> Right);
if(Left && Left -> Data < Min -> Data)Min = Left;
if(Right && Right -> Data < Min -> Data)Min = Right;
return Min;
}
Position FindMax( BinTree BST )
{
if(BST == NULL)return NULL;
Position Max = BST;
Position Left = FindMax(BST -> Left);
Position Right = FindMax(BST -> Right);
if(Left && Left -> Data > Max -> Data)Max = Left;
if(Right && Right -> Data > Max -> Data)Max = Right;
return Max;
}