(组合)Binomial Showdown

求组合数

Description

In how many ways can you choose k elements out of n elements, not taking order into account?
Write a program to compute this number.

Input

The input will contain one or more test cases.
Each test case consists of one line containing two integers n (n>=1) and k (0<=k<=n).
Input is terminated by two zeroes for n and k.

Output

For each test case, print one line containing the required number. This number will always fit into an integer, i.e. it will be less than 2³¹.
Warning: Don't underestimate the problem. The result will fit into an integer - but if all intermediate results arising during the computation will also fit into an integer depends on your algorithm. The test cases will go to the limit.

Sample Input

4 2
10 5
49 6
0 0

 

Sample Output

6
252
13983816

 

Author

Ulm Local 1997

 

//Binomial Showdown
#include<stdio.h>
#include<math.h>
double f(double n,double m)
{
     double i,s1,s2;
     if(n==m) return(1);
          if(m<n/2.0)
          {
               m=n-m;
          }
          s1=0;s2=0;
          for(i=m+1;i<=n;i++)
               s1+=log(i);
          for(i=2;i<=n-m;i++)
               s2+=log(i);
          return(exp(s1-s2));
}
int main()
{
     double i,n,m;
     while(scanf("%lf%lf",&n,&m)!=EOF)
     {
          if(n==0&&m==0) break;
          if(n==1&&m==0) printf("1\n");
          else
          {
           printf("%.0f\n",f(n,m));
          }
     }
     return(0);
}