B - How many integers can you find

Posted 2022-07-16 zjydeoneday

  Now you get a number N, and a M-integers set, you should find out how many integers which are small than N, that they can divided exactly by any integers in the set. For example, N=12, and M-integer set is 2,3, so there is another set 2,3,4,6,8,9,10, all the integers of the set can be divided exactly by 2 or 3. As a result, you just output the number 7.

题目大意：给你一个数n，和m个0~20的整数i，让你求1~n-1中是i的倍数的数有几个。

显然，这是一个容斥定理的题，求对1~（n-1）中所有m个i的倍数的数的个数。并且m<=10,因此我们用二进制枚举法就能够列出所有的情况。

需要注意的就是m个数，把这m个数先化成互质的。最后在套用模板即可。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
ll a[500];
int main()

    ll n, m;
    while(~scanf("%lld%lld",&n,&m))
    
        
        int top = 0;
        for(int i = 0; i < m; ++ i)
        
            ll x;
            cin >> x;
            if(x != 0)                  
                a[top++] = x;
        
        ll ans = 0,sum,num;
        for(int i = 1; i < (1 << top); ++ i)
        
            num=0,sum=1;
            for(int j = 0; j < top; ++ j)
            
                if((i >> j) & 1)
                
                    num++;
                    sum = sum * a[j] /(__gcd(sum, a[j]));
                
            
            if(num % 2)
            
                ans += (n - 1) / sum;   
            
            else
            
                ans -= (n - 1) / sum;
            
        
        cout << ans << endl;
    
    return 0;

以上。