Cod sursa(job #1096067)

Utilizator Dddarius95Darius-Florentin Neatu Dddarius95 Data 1 februarie 2014 14:54:06
Problema Invers modular Scor 50
Compilator cpp Status done
Runda Arhiva educationala Marime 0.71 kb
/*Invers modular - log(N)
daca gcd(A,N)=1
A*X=1 (mod N ) X e inversul lui A
din gcd extins avem oricare are fi A,N
exista X,Y a.i. AX+BY=gcd(A,B)
deci exista X,y a.i. AX+NY=1
AX+NY=1 (mod N ) <=> AX=1 (mod N)
*/
#include <fstream>
using namespace std;
ifstream f("inversmodular.in");
ofstream g("inversmodular.out");

long long N,A,X,Y;

long long gcd(long long a,long long b,long long &x,long long &y)
{
     if(!b) { x=1 ,y=0; return a; }
     long long x0,y0,d=gcd( b , a % b , x0 , y0 );
     x=y0;
     y=x0-(a/b)*y0;
     return d;
}
int main()
{
     f>>N>>A;
     gcd(A,N,X,Y);
     while(Y<=0)Y+=N;
     g<<Y<<'\n';
     //g<<X<< ' '<<Y<<'\n';
     //g<<X<<'\n';
     return 0;
}