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
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 )
{
BinTree p;
if ( !BST )
{
printf("Not Found\n");
return BST;
}
if ( BST->Data > X)
{
BST->Left = Delete( BST->Left, X);
}
else if ( BST->Data < X)
{
BST->Right = Delete( BST->Right, X);
}
else
{
if ( BST->Right && BST->Left )
{
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;
}
Position Find( BinTree BST, ElementType X )
{
if ( !BST )
{
return NULL;
}
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 )
{
while ( BST->Left )
{
BST = BST->Left;
}
}
return BST;
}
Position FindMax( BinTree BST )
{
if ( BST )
{
while ( BST->Right )
{
BST = BST->Right;
}
}
return BST;
}