extended-euclid.cpp File Reference

#include <cstdlib>
#include <cmath>
#include <iostream>
#include <iomanip>
#include <string>
#include "DGtal/arithmetic/IntegerComputer.h"

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Functions
void	usage (int, char **argv)
int	main (int argc, char **argv)

Detailed Description

Author

Jacques-Olivier Lachaud (jacqu.nosp@m.es-o.nosp@m.livie.nosp@m.r.la.nosp@m.chaud.nosp@m.@uni.nosp@m.v-sav.nosp@m.oie..nosp@m.fr ) Laboratory of Mathematics (CNRS, UMR 5127), University of Savoie, France

Date

2012/02/06

An example file named extended-euclid.

This file is part of the DGtal library.

Definition in file extended-euclid.cpp.

Function Documentation

main()

int main	(	int	argc,
		char **	argv )

Main.

[extended-euclid-types]

[extended-euclid-types]

[extended-euclid-instantiation]

[extended-euclid-instantiation]

[extended-euclid-process]

[extended-euclid-process]

Definition at line 57 of file extended-euclid.cpp.

{
  if ( argc < 4 )
    {
      usage( argc, argv );
      return 0;
    }
 
  typedef BigInteger Integer;
  typedef IntegerComputer<Integer> IC;
 
  Integer a( argv[ 1 ] );
  Integer b( argv[ 2 ] );
  Integer c( argv[ 3 ] );
  IC ic;
  Integer g = ic.gcd( a, b );
  if ( ic.isZero( a ) || ic.isZero( b ) )
    {
      std::cerr << "[Error] parameters a and b should be non-null." << std::endl;
      return 1;
    }
  if ( ic.isNotZero( c % g ) )
    {
      std::cerr << "[Error] parameter c should be a multiple of gcd(a,b)." << std::endl;
      return 2;
    }
 
  IC::Vector2I X = ic.extendedEuclid( a, b, c );
  std::cout << "x=" << X[ 0 ] << " y=" << X[ 1 ] << std::endl;
  Integer d = a*X[ 0 ] + b*X[ 1 ];
  if ( c != d )
    {
      std::cerr << "[Internal Error] Output of extended Euclid algorithm is incorrect: " << d << " != " << c 
                << ". This should not happen." << std::endl;
      return 3;
    }
  return 0;
}

usage()

void usage	(	int	,
		char **	argv )

Definition at line 47 of file extended-euclid.cpp.

{
  std::cerr << "Usage: " << argv[ 0 ] << " <a> <b> <c>" << std::endl;
  std::cerr << "\t - solves the diophantine equation ax+by=c by the extended Euclid algorithm." << std::endl;
  std::cerr << "\t - note: c should be a multiple of gcd(a,b)." << std::endl;
}