poj3219--Binomial Coefficients

Description

The binomial coefficient C(n, k) has been extensively studied for its importance in combinatorics. Binomial coefficients can be recursively defined as follows:

C(n, 0) = C(n, n) = 1 for all n > 0;
C(n, k) = C(n − 1, k − 1) + C(n − 1, k) for all 0 < k < n.

Given n and k, you are to determine the parity of C(n, k).

Input

The input contains multiple test cases. Each test case consists of a pair of integers n and k (0 ≤ k ≤ n < 2³¹, n > 0) on a separate line.

End of file (EOF) indicates the end of input.

Output

For each test case, output one line containing either a “0” or a “1”, which is the remainder of C(n, k) divided by two.

Sample Input

1 1
1 0
2 1

Sample Output

1
1
0

/////////////////////////////////////////////////////////////////

题意是判断C（n,m）是奇数还是偶数

# include<stdio.h>

int fuan(int n)

{

       int sum=0;

       while(n>=2)

       {

              sum+=n/2;

              n=n/2;

       }

       return sum;

}

int main()

{

       int x,y,a,b,c;

       while(scanf("%d%d",&x,&y)!=EOF)

       {

              a=b=c=0;

              a=fuan(x);

              b=fuan(y);

              c=fuan(x-y);

              if(a>b+c)

                     printf("0\n");

              else

                     printf("1\n");

       }

       return 0;

}

 主要是看n!中含2的因子个数与(n-m)!,m!中含2因子个数和的比较！

 

求n的阶乘中含i的因子个数；

count=0;

while(n>=i)
{

count+=n/i;

n/=i;

}