defmodule Dutch_national_flag do
  defp ball(:red),   do: 1
  defp ball(:white), do: 2
  defp ball(:blue),  do: 3

  defp random_ball, do: Enum.random([:red, :white, :blue])

  defp random_ball(n), do: (for _ <- 1..n, do: random_ball())

  defp is_dutch([]), do: true
  defp is_dutch([_]), do: true
  defp is_dutch([b,h|l]), do: ball(b) < ball(h) and is_dutch([h|l])
  defp is_dutch(_), do: false

  def  dutch(list), do: dutch([], [], [], list)

  defp dutch(r, w, b, []),              do: r ++ w ++ b
  defp dutch(r, w, b, [:red   | list]), do: dutch([:red | r],  w,  b, list)
  defp dutch(r, w, b, [:white | list]), do: dutch(r, [:white | w], b, list)
  defp dutch(r, w, b, [:blue  | list]), do: dutch(r, w,  [:blue | b], list)

  def problem(n \\ 10) do
    list = random_ball(n)
    if is_dutch(list) do
      IO.puts "The random sequence #{inspect list} is already in the order of the Dutch flag!"
    else
      IO.puts "The starting random sequence is #{inspect list};"
      IO.puts "The ordered sequence is #{inspect dutch(list)}."
    end
  end
end

Dutch_national_flag.problem