HDU 1796 How many integers can you find（组合数学-容斥原理）

How many integers can you find

Problem Description

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.

Input

There are a lot of cases. For each case, the first line contains two integers N and M. The follow line contains the M integers, and all of them are different from each other. 0<N<2^31,0<M<=10, and the M integer are non-negative and won’t exceed 20.

Output

For each case, output the number.

Sample Input

12 2
2 3

Sample Output

7

Author

wangye

Source

2008
“Insigma International Cup” Zhejiang Collegiate Programming Contest - Warm Up（4）

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题目大意：


解题思路：




解题代码：

#include <iostream>
#include <cstdio>
#include <vector>
using namespace std;

typedef long long ll;
int n,m,a[20];

ll gcd(ll a,ll b){
return b>0 ? gcd(b,a%b):a;
}

int main(){
while(scanf("%d%d",&n,&m)!=EOF){
int ans=0;
vector <int> v;
for(int i=0;i<m;i++){
scanf("%d",&a[i]);
if(a[i]>0) v.push_back(a[i]);
}
m=v.size();
for(int i=1;i<(1<<m);i++){
int cnt=0;
ll x=1;
for(int t=0;t<m;t++){
if(i&(1<<t)){
cnt++;
x=x*v[t]/gcd(x,v[t]);
}
}
if( cnt&1 ) ans+=(n-1)/x;
else ans-=(n-1)/x;
}
cout<<ans<<endl;
}
return 0;
}