Codeforces 895C

本文介绍了一种算法,用于计算给定整数集合中所有子集的个数,这些子集的乘积为平方数。通过预处理质因子并使用位运算优化,实现了高效的求解。

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题意:找出n个数的所有子集中乘起来是平方数的个数

思路:,一个数如果是平方数,那么它的所有质因子都是偶数个,ai小于等于70,所以可以预处理出所有质因子,然后再判断每一个数含有多少个质因子,如果是偶数个,那么这个数肯定是平方数,肯定可以被选作为集合中的元素,如果这个数含有某个质因子奇数个,那么就先把质因子那一位用1表示放在一个容器里,等到再有奇数质因子的标记被放进来,就看是不是同一个质因子,如果是的话,那么这两个数相乘就会有偶数个质因子,所以可选。最后的结果就是筛选出n个数中所有可选的数,对于每一个数,有选或者不选两种,所以就是2的k次方,全都不选乘积是0,所以减掉。


#include<bits/stdc++.h>
using namespace std;
#define maxn 75
#define mod 1000000007
bool isprime(int x)
{
    for(int i=2;i*i<=x;i++){
        if(x%i ==0 ) return false;
    }
    return true;
}
int main()
{
    int n;
    int pri[maxn],k=0;
    for(int i=2;i<=70;i++){
        if(isprime(i)) pri[k++]=i;
    }
    vector <int> ve;
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        int t=0;
        int m;
        scanf("%d",&m);
        for(int j=0;j<k;j++){
            while(m%pri[j]==0){
                 m/=pri[j];
                 t^=(1<<j);
            }
        }
        //cout<<t<<"front"<<endl;
        for(int ii=0;ii<ve.size();ii++) t=min(t,t^ve[ii]);
       // cout<<t<<"last"<<endl;
        if(t) ve.push_back(t);
    }
    int ans=1;
    for(int i=ve.size();i<n;i++){
         ans*=2;
         ans%=mod;
    }
    ans=(ans + mod - 1)%mod;
    cout<<ans<<endl;
}

### Codeforces Problem 1332C Explanation The provided references pertain specifically to problem 742B on Codeforces rather than problem 1332C. For an accurate understanding and solution approach for problem 1332C, it's essential to refer directly to its description and constraints. However, based on general knowledge regarding competitive programming problems found on platforms like Codeforces: Problem 1332C typically involves algorithmic challenges that require efficient data structures or algorithms such as dynamic programming, graph theory, greedy algorithms, etc., depending upon the specific nature of the task described within this particular question[^6]. To provide a detailed explanation or demonstration concerning **Codeforces problem 1332C**, one would need direct access to the exact statement associated with this challenge since different tasks demand tailored strategies addressing their unique requirements. For obtaining precise details about problem 1332C including any sample inputs/outputs along with explanations or solutions, visiting the official Codeforces website and navigating to contest number 1332 followed by examining section C is recommended. ```python # Example pseudo-code structure often seen in solving competitive coding questions. def solve_problem_1332C(input_data): # Placeholder function body; actual logic depends heavily on the specifics of problem 1332C. processed_result = process_input(input_data) final_answer = compute_solution(processed_result) return final_answer input_example = "Example Input" print(solve_problem_1332C(input_example)) ```
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