删除时，递归的是找X的路径，当找到以后（有四种情况，这个结点有两个分支，各有一个分支，没有分支）。如果有这个结点有两个分支，找到比这个结点大一点的结点替代它，同时，接着递归找到比这个结点大一点的结点删除它。思考递归时，思考两层递归就可以，dfs（i+1）结束以后到dfs（i）
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#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;
}
void PreorderTraversal( BinTree BT )
{
if(BT!=NULL)
{
printf(" %d",BT->Data);
PreorderTraversal(BT->Left);
PreorderTraversal(BT->Right);
}
}
void InorderTraversal( BinTree BT )
{
if(BT!=NULL)
{
InorderTraversal(BT->Left);
printf(" %d",BT->Data);
InorderTraversal(BT->Right);
}
}
BinTree Insert( BinTree BST, ElementType X )
{
if(BST==NULL)
{
struct TNode *p = (struct TNode*)malloc(sizeof(struct TNode));
p->Left = NULL;
p->Right = NULL;
p->Data = X;
return p;
}
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 )
{
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(X == BST->Data)
{
if(BST->Left && BST->Right)
{
BinTree p = FindMin(BST->Right);
BST->Data = p->Data;
BST->Right = Delete(BST->Right,p->Data);
}
else if(BST->Right)
{
BST=BST->Right;
}
else if(BST->Left)
{
BST=BST->Left;
}
else
{
BST=NULL;
}
}
}
return BST;
}
Position Find( BinTree BST, ElementType X )
{
if(!BST) return NULL;
if(X==BST->Data) return BST;
else if(X > BST->Data)
{
return Find(BST->Right, X );
}
else if(X < BST->Data)
{
return Find(BST->Left, X );
}
}
Position FindMin( BinTree BST)
{
if(!BST) return NULL;
while(BST->Left)
{
BST=BST->Left;
}
return BST;
}
Position FindMax( BinTree BST )
{
if(!BST) return NULL;
while(BST->Right)
{
BST=BST->Right;
}
return BST;
}
