HDU 1796 How many integers can you find
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
题解:基本容斥;我们可用二进制压缩,枚举每一个状态。加上奇数的倍数,减去偶数个个数的倍数;
参考代码:
#include<bits/stdc++.h> using namespace std; typedef long long LL; LL n,m,a[11],num[1<<11],cnt,ans; LL work(int x) { LL flag1=1,flag2=1; for(int i=0;i<=m-1;i++) { LL temp=1<<i; if(x&temp) cnt++,flag2=__gcd(a[i],flag1),flag1=a[i]*flag1/flag2; } return flag1; } int main() { while(~scanf("%lld%lld",&n,&m)) { ans=0; for(LL i=0;i<m;i++) { scanf("%lld",a+i); if(a[i]==0) i--,m--; } for(LL i=1;i<(1<<m);i++) { cnt=0; LL sum=work(i); if(cnt&1) ans=ans+(n-1)/sum; else ans=ans-(n-1)/sum; } printf("%d\n",ans); } return 0; }