用质因子去分解质因数

Hankson的趣味题

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#include <bits/stdc++.h>
#define f first
#define s second
using namespace std;

const int N = 50010;
int a, b, c, d;
int prime[N], cnt;
bool vis[N];
pair <int, int > factor[N];
int fcnt;
int res;

void init(int n)
{
    for(int i = 2; i <= n; ++ i)
    {
        if(!vis[i]) prime[cnt ++] = i;
        for(int j = 0;j < cnt && i * prime[j] <= n; ++ j)
        {
            vis[i * prime[j]] = true;
            if(i % prime[j] == 0) break;
        }
    }
}

void dfs(int deep, int p)
{
    if(deep == fcnt) 
    {
        if( __gcd(p,a) == b &&  p  / __gcd(p,c) * c == d) res ++;
        return;
    }
    
    for(int i = 0; i <= factor[deep].s; ++ i)
    {
        dfs(deep + 1,p);
        p *= factor[deep].f;
    }
}

int main()
{
    init(N - 1);
    int T;
    cin >> T;
    while(T --)
    {
        cin >> a >> b >> c >> d;
        int t = d;
        fcnt = 0;
        for(int i = 0; prime[i] * prime[i] <= t; ++ i)
        {
            if(t % prime[i] == 0)
            {
                int b = 0;
                while(t % prime[i] == 0) t /= prime[i], b ++;
                factor[fcnt ++] = {prime[i],b};
            }
        }
        if(t != 1) factor[fcnt ++] = {t,1};
        
        dfs(0,1);
        
        cout << res << endl;
        
        res = 0;
    }
    
    return 0;
}