ZOJ 2836 Number Puzzle

Number Puzzle

Time Limit: 2000ms

Memory Limit: 65536KB

This problem will be judged on ZJU. Original ID: 2836
64-bit integer IO format: %lld      Java class name: Main

 

Given a list of integers ($A_1, A_2, ..., A_n$), and a positive integer M, please find the number of positive integers that are not greater than M and dividable by any integer from the given list.

Input

The input contains several test cases.

For each test case, there are two lines. The first line contains N ($1 leq N leq 10$) and $M (1 leq M leq 200000000)$, and the second line contains $A_1, A_2, ..., A_n(1 leq A_i leq 10, for i = 1, 2, ..., N).$

Output

For each test case in the input, output the result in a single line.

Sample Input

3 2
2 3 7
3 6
2 3 7

Sample Output

1
4

 

Source

Zhejiang University Local Contest 2007

Author

MAO, Yiqiang

 

解题：容斥，求是集合中某些数的LCM的倍数且不超过m的数的数量

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxn = 20;
int a[maxn],n,m;
LL gcd(LL a,LL b) {
    return b?gcd(b,a%b):a;
}
LL LCM(LL a,LL b) {
    return a/gcd(a,b)*b;
}
int main() {
    while(~scanf("%d%d",&n,&m)) {
        for(int i = 0; i < n; ++i)
            scanf("%d",a+i);
        LL ret = 0;
        for(int i = 1; i < (1<<n); ++i) {
            int cnt = 0;
            LL x = 1;
            for(int j = 0; j < n; ++j) {
                if((i>>j)&1) {
                    x = LCM(x,a[j]);
                    cnt++;
                }
            }
            if(cnt&1) ret += m/x;
            else ret -= m/x;
        }
        printf("%lld
",ret);
    }
    return 0;
}