Cod sursa(job #1096071)

Utilizator Dddarius95Darius-Florentin Neatu Dddarius95 Data 1 februarie 2014 15:02:34
Problema Invers modular Scor 100
Compilator cpp Status done
Runda Arhiva educationala Marime 0.7 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;
     D=gcd(b,a % b, x0,y0);
     x=y0;
     y=x0-(a/b)*y0;
     return D;
}


int main()
{
     long long A,N,inv,ins;
     f>>A>>N;
     gcd(A,N,inv,ins);
     while(inv<=0)inv+=N;
     g<<inv<<'\n';
     return 0;
}