// 13_fraction_operators.cpp
// 演示算术与比较运算符重载的 Fraction 分数类

#include <iostream>

class Fraction {
  private:
    int numerator_;
    int denominator_;

  public:
    Fraction(int num = 0, int den = 1) : numerator_(num), denominator_(den) {
        if (denominator_ == 0) {
            denominator_ = 1;
        }
        normalize();
    }

    Fraction& operator+=(const Fraction& rhs) {
        numerator_ = numerator_ * rhs.denominator_ + rhs.numerator_ * denominator_;
        denominator_ *= rhs.denominator_;
        normalize();
        return *this;
    }

    Fraction& operator-=(const Fraction& rhs) {
        numerator_ = numerator_ * rhs.denominator_ - rhs.numerator_ * denominator_;
        denominator_ *= rhs.denominator_;
        normalize();
        return *this;
    }

    Fraction& operator*=(const Fraction& rhs) {
        numerator_ *= rhs.numerator_;
        denominator_ *= rhs.denominator_;
        normalize();
        return *this;
    }

    Fraction operator-() const { return Fraction(-numerator_, denominator_); }

    int num() const { return numerator_; }
    int den() const { return denominator_; }

  private:
    void normalize() {
        int g = gcd(numerator_, denominator_);
        numerator_ /= g;
        denominator_ /= g;
        if (denominator_ < 0) {
            numerator_ = -numerator_;
            denominator_ = -denominator_;
        }
    }

    static int gcd(int a, int b) {
        a = (a < 0) ? -a : a;
        b = (b < 0) ? -b : b;
        while (b != 0) {
            int t = b;
            b = a % b;
            a = t;
        }
        return (a == 0) ? 1 : a;
    }
};

Fraction operator+(Fraction lhs, const Fraction& rhs) {
    lhs += rhs;
    return lhs;
}
Fraction operator-(Fraction lhs, const Fraction& rhs) {
    lhs -= rhs;
    return lhs;
}
Fraction operator*(Fraction lhs, const Fraction& rhs) {
    lhs *= rhs;
    return lhs;
}

bool operator==(const Fraction& l, const Fraction& r) {
    return l.num() == r.num() && l.den() == r.den();
}
bool operator!=(const Fraction& l, const Fraction& r) {
    return !(l == r);
}
bool operator<(const Fraction& l, const Fraction& r) {
    return l.num() * r.den() < r.num() * l.den();
}
bool operator>(const Fraction& l, const Fraction& r) {
    return r < l;
}
bool operator<=(const Fraction& l, const Fraction& r) {
    return !(r < l);
}
bool operator>=(const Fraction& l, const Fraction& r) {
    return !(l < r);
}

std::ostream& operator<<(std::ostream& os, const Fraction& f) {
    os << f.num() << "/" << f.den();
    return os;
}

int main() {
    Fraction a(1, 2), b(1, 3);

    std::cout << a << " + " << b << " = " << (a + b) << std::endl;
    std::cout << a << " - " << b << " = " << (a - b) << std::endl;
    std::cout << a << " * " << b << " = " << (a * b) << std::endl;

    std::cout << a << " + 1 = " << (a + 1) << std::endl;
    std::cout << "2 * " << b << " = " << (2 * b) << std::endl;

    a += b;
    std::cout << "a += b -> a = " << a << std::endl;

    Fraction c(1, 6), d(1, 4);
    std::cout << c << " < " << d << " : " << (c < d) << std::endl;
    std::cout << c << " >= " << d << " : " << (c >= d) << std::endl;

    return 0;
}