StrongPrimePower.cc

using namespace std;
using ll = long long;
class StrongPrimePower {
    public:
        bool isPrime(int p){
            for(int i=2;i*i<=p;++i) if(p%i==0) return false;
            return true;
        }

    vector<int> baseAndExponent(string sn) {
        ll n = stoll(sn);
        for(int q=2;q<=59;++q){
            double dp = pow(n, 1.0/q);//double pow (double base, double exponent);
            // cout<<dp<<endl;
            int p = round(dp);//don't cast, that's round down
            if(!isPrime(p)) continue;//p needs to be prime
            ll x=1L;
            for(int i=0;i<q;++i) x*=p;//raise it to the q-th power, and check if it equals to n
            if(x==n) return {p,q};
        }
        return {};
    }
};

// we can see n^2/1, n^3/1 ... as follows
Expected: [ 2, 59 ]
Testcase #4 ... 
759250124.99
832255.32
27554.49
3565.78
912.28
344.55
166.00
94.06
59.71
41.17
30.20
23.24
18.56
15.28
12.88
11.09
9.70
8.61
7.73
7.01
6.42
5.92
5.50
5.13
4.82
4.55
4.31
4.10
3.91
3.74
3.59
3.45
3.33
3.22
3.11
3.02
2.93
2.85
2.78
2.71
2.65
2.59
2.53
2.48
2.43
2.39
2.34
2.30
2.27
2.23
2.20
2.16
2.13
2.10
2.08
2.05
2.02
2.00