ratio.cpp

#include <numeric>

#include <cassert>

class ratio
{

    std::size_t n, d; // numerator, denominator

    void
    assign(std::size_t nn, std::size_t dd)
    {
        std::size_t gcd = std::gcd(nn, dd);
        n = nn / gcd;
        d = dd / gcd;
    }

public :

    ratio(std::size_t nn, std::size_t dd = 1)
        : n(nn), d(dd)
    { ; }

    ratio & operator = (std::size_t r) { n = r; d = 1; return *this; }

    ratio & operator += (ratio const & r) { assign(n * r.d + r.n * d, d * r.d); return *this; }
    ratio & operator -= (ratio const & r) { assert(!(n * r.d < r.n * d)); assign(n * r.d - r.n * d, d * r.d); return *this; }
    ratio & operator *= (ratio const & r) { assign(n * r.n, d * r.d); return *this; }
    ratio & operator /= (ratio const & r) { assign(n * r.d, d * r.n); return *this; }

    friend ratio operator + (ratio l, ratio const & r) { return l += r; }
    friend ratio operator - (ratio l, ratio const & r) { return l -= r; }
    friend ratio operator * (ratio l, ratio const & r) { return l *= r; }
    friend ratio operator / (ratio l, ratio const & r) { return l /= r; }

    ratio & operator += (std::size_t r) { assign(n * r, d); return *this; }
    ratio & operator -= (std::size_t r) { assign(n, d * r); return *this; }
    ratio & operator *= (std::size_t r) { assign(n * r, d); return *this; }
    ratio & operator /= (std::size_t r) { assign(n, d * r); return *this; }

    friend ratio operator + (ratio l, std::size_t r) { return l += r; }
    friend ratio operator - (ratio l, std::size_t r) { return l -= r; }
    friend ratio operator * (ratio l, std::size_t r) { return l *= r; }
    friend ratio operator / (ratio l, std::size_t r) { return l /= r; }

    bool operator == (ratio const & r) const { return (n == r.n) && (d == r.d); }
    bool operator <  (ratio const & r) const { return n * r.d < r.n * d; }

};