HDU 1796 How many integers can you find（容斥原理）

http://acm.hdu.edu.cn/showproblem.php?pid=1796

这篇文章对容斥原理讲解很清楚 http://www.cppblog.com/vici/archive/2011/09/05/155103.html

#include <iostream>
#include<cstdio>
#include<string.h>
#include<cmath>
#define LL long long
using namespace std;
LL sum,x[21],n;
int m;
int gcd(int x,int y)
{
    return y==0?x:gcd(y,x%y);
}
void dfs(int num,int i,LL y)
{
    int j;
    y = y*x[i]/(gcd(y,x[i]));
    if(num%2!=0)
    sum+=(n-1)/y;
    else
    sum-=(n-1)/y;
    for(j = i+1 ; j <= m ; j++)
    {
        if(x[j]!=0)
        dfs(num+1,j,y);
    }
}
int main()
{
    int i,j,k;
    while(cin>>n>>m)
    {
        sum = 0;
        for(i = 1; i <= m ; i++)
        cin>>x[i];
        for(i = 1 ; i <= m ; i++)
        {
            if(x[i]!=0)
            dfs(1,i,x[i]);
        }
        cout<<sum<<endl;
    }
    return 0;
}