Binomial Showdown(P2249)

注意其计算的时候要保证边计算边减少其计算的数字不能超过long long的范围。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<ctype.h>
#include<vector>
#include<algorithm>
#include<queue>
#include<set>
#include<stack>
using namespace std;

long long gcd(long long big,long long small)
{
if (big%small==0)
return small;
return gcd(small,big%small);
}

int main()
{
long long i;
long long j;
long long k;
long long  a;

double x=23;
//printf("%.0f\n",x);
long long b;
while (cin>>a>>b)
{
if (!(a+b))
break;

b=min(b,a-b);
k=1;
j=1;
for (i=1;i<=b;i++)
{
k*=(a-i+1);
if (k%i==0)
{
k/=i;
}
else
{
j*=i;
}
long long temp=gcd(k,j);
k/=temp;
j/=temp;
}

cout<<k<<endl;

}

return 0;

}

Binomial Showdown

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 15624		Accepted: 4778

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

Source
Ulm Local 1997