roman_numerals.ex

defmodule Roman do
  defp num_lookup({0, _}), do: ""
  defp num_lookup({1, 1}), do: "I"
  defp num_lookup({5, 1}), do: "V"
  defp num_lookup({1, 2}), do: "X"
  defp num_lookup({5, 2}), do: "L"
  defp num_lookup({1, 3}), do: "C"
  defp num_lookup({5, 3}), do: "D"
  defp num_lookup({1, 4}), do: "M"

  defp num_lookup({4, pos}), do: num_lookup({1, pos}) <> num_lookup({5, pos})
  defp num_lookup({9, pos}), do: num_lookup({1, pos}) <> num_lookup({1, pos + 1})

  defp num_lookup({num, pos}) do
    # num is in [2, 3, 6, 7, 8] so we'll concatenate 0 or 5 with as many 1s as needed
    rem = div(num, 5) * 5
    num_lookup({rem, pos}) <> String.duplicate(num_lookup({1, pos}), num - rem)
  end

  @doc """
  Convert the number to a roman number.
  """
  @spec numerals(pos_integer) :: String.t()
  def numerals(number) do
    number
    |> Integer.digits()
    |> (&Enum.zip(&1, length(&1)..1)).()
    |> Enum.map_join(&num_lookup/1)
  end
end