# This example solution is partially derived from the Julia base implementation of rational numbers (MIT license) # https://github.com/JuliaLang/julia/blob/52bafeb981bac548afd2264edb518d8d86944dca/base/rational.jl # https://github.com/JuliaLang/julia/blob/52bafeb981bac548afd2264edb518d8d86944dca/LICENSE.md import Base: +, *, ^, -, /, <, <=, inv, show, promote_rule struct RationalNumber{T<:Integer} <: Real num::T den::T # reduce to lowest terms function RationalNumber{T}(num::Integer, den::Integer) where T<:Integer num == den == zero(T) && throw(ArgumentError("zero($T)//zero($T) is not a valid rational number")) num2, den2 = sign(den) < 0 ? Base.divgcd(-num, -den) : Base.divgcd(num, den) new(num2, den2) end end RationalNumber(num::T, den::T) where {T<:Integer} = RationalNumber{T}(num, den) numerator(x::RationalNumber) = x.num denominator(x::RationalNumber) = x.den RationalNumber{T}(x::Integer) where {T<:Integer} = RationalNumber{T}(convert(T, x), convert(T, 1)) promote_rule(::Type{RationalNumber{T}}, ::Type{S}) where {T<:Integer,S<:Integer} = RationalNumber{promote_type(T,S)} show(io::IO, x::RationalNumber) = (show(io, numerator(x)); print(io, "//"); show(io, denominator(x))) # Helper method numden(x::RationalNumber) = numerator(x), denominator(x) # Arithmetics function +(x::RationalNumber, y::RationalNumber) a, b = numden(x) c, d = numden(y) RationalNumber(a * d + b * c, b * d) end -(x::RationalNumber, y::RationalNumber) = x + (-1) * y -(x::RationalNumber) = -1 * x function *(x::RationalNumber, y::RationalNumber) a, b = numden(x) c, d = numden(y) RationalNumber(a * c, b * d) end inv(x::RationalNumber) = RationalNumber(denominator(x), numerator(x)) /(x::RationalNumber, y::RationalNumber) = x * inv(y) ^(x::Real, y::RationalNumber) = x^(numerator(y) / denominator(y)) # Ordering <(x::RationalNumber, y::RationalNumber) = x.den == y.den ? x.num < y.num : x.num * y.den < y.num * x.den <=(x::RationalNumber, y::RationalNumber) = x.den == y.den ? x.num <= y.num : x.num * y.den <= y.num * x.den