HDU 1796 How many integers can you find(组合数学-容斥原理)
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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 22 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:给你1个数n,再给m个数,问你1~n-1里面有多少个数能被这m个数的任意一个数整除。
利用容斥原理就可以解决。
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;}
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