rational.cc

#include <iostream>
template <class T>
class Rational {
 public:
  Rational(T a, T b) : p(a), q(b) {
    if (b == 0) throw std::domain_error("ZeroDivisionError");
    while (b) {
      T t = b;
      b = a % b;
      a = t;
    }
    p /= a, q /= a;
    if (q < 0) p = -p, q = -q;
  }
  Rational operator+(const Rational& r) const {
    return Rational(p * r.q + r.p * q, q * r.q);
  }
  Rational operator-(const Rational& r) const {
    return *this + Rational(-r.p, r.q);
  }
  Rational operator*(const Rational& r) const {
    return Rational(p * r.p, q * r.q);
  }
  Rational operator/(const Rational& r) const {
    return *this * Rational(r.q, r.p);
  }
  bool operator==(const Rational& r) const { return p * r.q == r.p * q; }
  bool operator!=(const Rational& r) const { return !(*this == r); }
  bool operator<(const Rational& r) const { return p * r.q < r.p * q; }
  bool operator>(const Rational& r) const { return r < *this; }
  bool operator<=(const Rational& r) const { return !(*this > r); }
  bool operator>=(const Rational& r) const { return !(*this < r); }
  T get_num() const { return p; }
  T get_den() const { return q; }
  friend std::ostream& operator<<(std::ostream& os, const Rational& r) {
    os << r.p;
    if (r.q != 1) os << '/' << r.q;
    return os;
  }

 private:
  T p, q;
};