POJ - 1942 D - Paths on a Grid 组合数

Paths on a Grid

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 25331		Accepted: 6324

Description

Imagine you are attending your math lesson at school. Once again, you are bored because your teacher tells things that you already mastered years ago (this time he's explaining that (a+b) ²=a ²+2ab+b ²). So you decide to waste your time with drawing modern art instead. 

Fortunately you have a piece of squared paper and you choose a rectangle of size n*m on the paper. Let's call this rectangle together with the lines it contains a grid. Starting at the lower left corner of the grid, you move your pencil to the upper right corner, taking care that it stays on the lines and moves only to the right or up. The result is shown on the left: 

Really a masterpiece, isn't it? Repeating the procedure one more time, you arrive with the picture shown on the right. Now you wonder: how many different works of art can you produce?

Input

The input contains several testcases. Each is specified by two unsigned 32-bit integers n and m, denoting the size of the rectangle. As you can observe, the number of lines of the corresponding grid is one more in each dimension. Input is terminated by n=m=0.

Output

For each test case output on a line the number of different art works that can be generated using the procedure described above. That is, how many paths are there on a grid where each step of the path consists of moving one unit to the right or one unit up? You may safely assume that this number fits into a 32-bit unsigned integer.

Sample Input

5 4
1 1
0 0

Sample Output

126
2

Source

Ulm Local 2002

第一次做这个题是dp做的，学习了组合数，发现组合数更简单

无论怎么走肯定要走n+m这么长的路，在这么长的路里选n个向下走的

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<string>
#include<algorithm>
#include<queue>
#include<vector>
#include<map>
#include<set>
typedef long long ll;
using namespace std;
ll myc(ll n,ll r)
{
	ll sum=1;
	for(int i=1;i<=r;i++)
	{
		sum=sum*(n-i+1)/i;
	}
	return sum;
}
int main()
{
	ll a,b;
	while(~scanf("%lld %lld",&a,&b),a+b)
	{
		if(a==0||b==0)
		printf("1\n");
		else
		printf("%lld\n",myc(a+b,a));
	}
	return 0;
 }