defmodule Roman do

  @num_to_roman %{1 => "I", 2 => "II", 3 => "III", 4 => "IV", 5 => "V",
    6 => "VI", 7 => "VII", 8 => "VIII", 9 => "IX", 10 => "X", 20 => "XX",
    30 => "XXX", 40 => "XL", 50 => "L", 60 => "LX", 70 => "LXX", 80 => "LXXX",
    90 => "XC", 100 => "C", 200 => "CC", 300 => "CCC", 400 => "CD", 500 => "D",
    600 => "DC", 700 => "DCC", 800 => "DCCC", 900 => "CM", 1000 => "M",
    2000 => "MM", 3000 => "MMM"}

  @roman_to_num %{"I" => 1, "II" => 2, "III" => 3, "IV" => 4, "V" => 5,
    "VI" => 6, "VII" => 7, "VIII" => 8, "IX" => 9, "X" => 10, "XX" => 20,
    "XXX" => 30, "XL" => 40, "L" => 50, "LX" => 60, "LXX" => 70, "LXXX" => 80,
    "XC" => 90, "C" => 100, "CC" => 200, "CCC" => 300, "CD" => 400, "D" => 500,
    "DC" => 600, "DCC" => 700, "DCCC" => 800, "CM" => 900, "M" => 1000,
    "MM" => 2000, "MMM" => 3000}

  @roman Map.keys @roman_to_num
  @invalid ["IIII", "VV", "XXXX", "LL", "CCCC", "DD", "MMMM"]

  def translate(input) when is_integer(input) do
    find_num(input) |> Enum.map_join(&Map.get(@num_to_roman, &1))
  end

  def translate(input) do
    if :binary.match(input, @invalid) == :nomatch and
    Regex.match?(~r/^["I", "V", "X", "L", "C", "D", "M"]*$/, input) do
      find_roman(input)
    else
      raise ArgumentError, message: "Erratum. Numerus invalidus est."
    end
  end

  defp find_num(number) when number > 3999 do
    raise ArgumentError, message: "Erratum. Numerus nimis magni est."
  end
  defp find_num(number) when number > 999 do
    [1000 * div(number, 1000), 100 * div(rem(number, 1000), 100),
      10 * div(rem(number, 100), 10), rem(number, 10)]
  end
  defp find_num(number) when number > 99 do
    [100 * div(number, 100), 10 * div(rem(number, 100), 10), rem(number, 10)]
  end
  defp find_num(number) when number > 9 do
    [10 * div(number, 10), rem(number, 10)]
  end
  defp find_num(number) when number > 0, do: [number]
  defp find_num(_) do
    raise ArgumentError, message: "Erratum. Numerus invalidus est."
  end

  defp find_roman(input) do
    :binary.matches(input, @roman)
    |> Enum.map(&Map.get(@roman_to_num, :binary.part(input, &1)))
    |> Enum.sum
  end
end