Google Code Jam Qualification Round 2021 Cheating Detection

E.cpp

#include <iostream>
#include <vector>
#include <string>
#include <cmath>
using namespace std;

double f(double x)
{
    return 1/(1+exp(-x));
}

double F(double x)
{
    return -log(1-f(x));
}

double skill(double p)
{
    double l = -3.;
    double r = 3.;
    for (int i=0; i<100; i++)
    {
        double m = (l+r)*.5;
        //  (1/6)∫[-3<=x<=3](f(m-x))
        //  = (1/6)(-F(m-x)[-3<=x<=3])
        //  = (1/6)(-F(m-3)+F(m+3))
        ((-F(m-3)+F(m+3))/6<p ? l : r) = m;
    }
    return l;
}

int main()
{
    int T;
    cin>>T;
    int P;
    cin>>P;

    for (int t=1; t<=T; t++)
    {
        vector<vector<int>> A(100, vector<int>(10000));
        for (int i=0; i<100; i++)
        {
            string s;
            cin>>s;
            for (int j=0; j<10000; j++)
                A[i][j] = s[j]-'0';
        }

        vector<double> S(100);
        for (int i=0; i<100; i++)
        {
            int s = 0;
            for (int j=0; j<10000; j++)
                s += A[i][j];
            S[i] = skill(s/10000.);
        }

        vector<double> Q(10000);
        for (int i=0; i<10000; i++)
        {
            int s = 0;
            for (int j=0; j<100; j++)
                s += A[j][i];
            Q[i] = -skill(s/100.);
        }

        vector<double> X(100);
        for (int i=0; i<100; i++)
        {
            for (int j=0; j<10000; j++)
                if (A[i][j]==0)
                    X[i] += -log(1-f(S[i]-Q[j]));
                else
                    X[i] += -log(f(S[i]-Q[j]));
            int s = 0;
            for (int j=0; j<10000; j++)
                s += A[i][j];
            double p = s/10000.;
            X[i] = X[i]/10000 - (-p*log(p)-(1-p)*log(1-p));
        }

        int ans = 0;
        for (int i=1; i<100; i++)
            if (X[i]>X[ans])
                ans = i;
        ans++;

        cout<<"Case #"<<t<<": "<<ans<<endl;
    }
}