Rational.hpp

#ifndef RATIONAL_NUM
#define RATIONAL_NUM

#include <sstream>
#include <string>

class Rational {
public:

  Rational()
  : num(0), den(1)
  {}

  Rational( int num, int den = 1 )
  : num(num), den(den)
  {}

  Rational operator+ ( const Rational &r )
  {
    Rational l = *this;
    Rational ret;

    ret.den = lcm( l.den, r.den );
    ret.num = l.num*ret.den/l.den+r.num*ret.den/r.den;

    return ret;
  }

  Rational operator- ( const Rational &r )
  {
    Rational l = *this;
    Rational ret;

    ret.den = lcm( l.den, r.den );
    ret.num = l.num*ret.den/l.den-r.num*ret.den/r.den;

    return ret;
  }
  
  Rational operator* ( const Rational &r )
  {
    Rational l = *this;
    Rational ret;

    ret.den = l.den*r.den;
    ret.num = l.num*r.num;

    return ret;
  }

  Rational operator/ ( const Rational &r )
  {
    Rational l = *this;
    Rational ret;

    ret.den = l.den*r.num;
    ret.num = l.num*r.den;

    return ret;
  }

  Rational& operator+= ( const Rational &r )
  {
    Rational l = *this;

    this->den = lcm( l.den, r.den );
    this->num = l.num*this->den/l.den+r.num*this->den/r.den;

    return *this;
  }

  Rational& operator-= ( const Rational &r )
  {
    Rational l = *this;
    
    this->den = lcm( l.den, r.den );
    this->num = l.num*this->den/l.den-r.num*this->den/r.den;

    return *this;
  }
  
  Rational& operator*= ( const Rational &r )
  {
    Rational l = *this;

    this->den = l.den*r.den;
    this->num = l.num*r.num;

    return *this;
  }

  Rational& operator/= ( const Rational &r )
  {
    Rational l = *this;
    
    this->den = l.den*r.num;
    this->num = l.num*r.den;

    return *this;
  }

  int getDenominator() const
  { return den; }

  int getNumerator() const
  { return num; }

  std::string toString() const
  {
    std::ostringstream oss;

    oss << num;
    oss << "/";
    oss << den;

    return oss.str();
  }

  void simplify()
  {
    int g = gcd( this->den, this->num );
    this->den /= g;
    this->num /= g;

    return;
  }

private:
  int den, num;

  int gcd( int a, int b )
  { return b ? gcd(b,a%b) : a; }

  int lcm( int a, int b )
  { return a/gcd(a,b)*b; }
};

#endif