Cod sursa(job #2467818)

Utilizator pishcotMiruna Turbatu pishcot Data 5 octombrie 2019 08:47:47
Problema Invers modular Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 0.85 kb
#include <bits/stdc++.h>
//#define nat long long

using namespace std;

ifstream fin("inversmodular.in");
ofstream fout("inversmodular.out");
int a, n;

/**

Phi(n) = n *(p1-1) * (p2 - 1) * ... * (pk - 1)/(p1 * p2 *...*pk)
p1,p2,p3...pk - factorii lui n

*/

int phi(int n)
{
    ///complexitate O(sqrt(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 lgput(int a, int n, int mod)
{
    int p = 1;
    while(n)
    {
        if(n % 2 == 1) p = 1LL * p * a % mod;
        n /= 2;
        a = 1LL * a * a % mod;
    }
    return p;
}

int main()
{
    fin >> a >> n;
    fout << (lgput(a, (phi(n) - 1), n));
    return 0;
}