容斥定理

给定a1,a2,.....,am,求1到n的整数中至少可以整除a中一个元素的数有多少个？3

#include<stdio.h>
#define ll long long
int a[1001];
int n,m;
ll gcd(ll a, ll b)
{
    if(a<=0||b<=0)
        return -1;
    else if(a>b)
        return gcd(a-b, b);
    else if(a<b)
        return gcd(a, b-a);
    else
        return a;
}
void solve()
{
    ll res = 0;
    for(int i=1 ; i<(1<<m) ; i++)
    {
        int num=0;
        for(int j=i ; j!=0 ; j>>=1)
        num+=j&1;
        ll lcm = 1;
        for(int j=0 ; j<m ; j++)
        {
            if(i>>j&1)
            {
                lcm=lcm/gcd(lcm,a[j])*a[j];
                if(lcm>n)
                break;
            }
        }
        if(num%2==0)
        res-=n/lcm;
        else res+=n/lcm;
    }
    printf("%d\n",res);
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=0 ; i<m ; i++)
    scanf("%d",&a[i]);
    solve();
    return 0;
}

 

转载于:https://www.cnblogs.com/shuaihui520/p/9400584.html