Cod sursa(job #2467821)

Utilizator Rares5000Baciu Rares Rares5000 Data 5 octombrie 2019 08:48:39
Problema Invers modular Scor 0
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 0.95 kb
#include <iostream>
#include <fstream>;

using namespace std;

/**
Phi(n) = n * (p1 - 1) * (p2 - 1) * ... (pk - 1) / (p1 * p2 * ... * pk)
unde p1, ... , pk - factorii lui n

Phi(12) = 12 *
*/

/// Complexitatea O(sqrt(n))
int Phi(int n)
{
    int sol = n, p;
    for(p = 2; p * p <= n && n > 1; p++)
    {
        if(n % p == 0)
            sol = sol / p * (p - 1);
        while(n % p == 0)
            n /= p;
    }
    if(n > 1)
        sol = sol / n * (n - 1);
    return sol;
}


int LogP(int a, int n, int Mod)
{
    int p = 1;
    while(n > 0)
    {
        if(n % 2 == 1)
            p = 1LL * p * a % Mod;
        n /= 2;
        a = a * a % Mod;
    }
    return p;
}
int main()
{
    int a, n, phi;
    ifstream fin("invermodular.in");
    ofstream fout("inversmodular.out");
    fin >> a >> n;
    phi = Phi(n);
    fout << LogP(a, phi - 1, n) << "\n";
    fin.close();
    fout.close();
    return 0;
}