defmodule Solution do
  @spec int_to_roman(num :: integer) :: String.t()
  def int_to_roman(num) do
    thousands = div(num, 1000)
    hundreds = div(rem(num, 1000), 100)
    tens = div(rem(num, 100), 10)

    String.duplicate("M", thousands) <>
      to_roman(hundreds, "C", "D", "M") <>
      to_roman(tens, "X", "L", "C") <>
      to_roman(rem(num, 10), "I", "V", "X")
  end

  @spec to_roman(num :: integer, one :: String.t(), five :: String.t(), ten :: String.t()) ::
          String.t()
  defp to_roman(num, one, five, ten) do
    case num do
      x when x <= 3 -> String.duplicate(one, x)
      x when x == 4 -> one <> five
      x when x > 4 and x <= 8 -> five <> String.duplicate(one, x - 5)
      x when x > 8 -> one <> ten
    end
  end
end