Open Judge 1664 Placing apples

Description

We are going to place M same apples into N same plates.

There could be some empty plates.

How many methods do we have?

When we have 7 applesand 3 plates, the methods, (1, 5, 1) and (5, 1, 1) are the same.

Input

The first line is the number of test cases, t. 0<=t<=20

The next t lines are test cases containing two numbers, M and N. 1<=M, N<=10.

Output

Output the numbers of method in each test case in one line.

这道题的确有数学公式，但是！我们做的是搜索题。能用搜索解决的问题，为什么一定要去推数学公式呢？

首先要解决的就是重复问题，我的解决方案是让数组有序排列，这样就不会有重复情况了。

然后是dfs的退出条件，这里只要dfs到了（n+1）位就证明找到了吗？不一定！还要目前种的苹果总数达到m

同样的，要是目前苹果总数超过m，不用搜索了，直接退出好了。

#include<stdio.h>
#include<string.h>
#include<ctype.h>
#include<iostream>
#include<math.h>
#include<algorithm>
using namespace std;
int ans,a[100];
int t;
int m,n;

void dfs(int x)
{
int sum=0;
for(int i=1;i<x;i++)
sum+=a[i];
if(sum>m)
return ;
if((x==n+1)&&(sum==m))
{

ans++;
return ;
}
if(x==n+1)
return ;
for(int i=m;i>=0;i--)
{
if(i>=a[x-1])
{
a[x]=i;
dfs(x+1);
a[x]=-1;
}
else
{
return ;
}
}

}
int main(void)
{
//int t;

scanf("%d",&t);

while(t--)
{

scanf("%d%d",&m,&n);
memset(a,-1,sizeof(a));

ans=0;
dfs(1);
//printf("%d\n",t);
printf("%d\n",ans);
}

return 0;
}