defmodule Euler.Combinatorics.Permutations do
  defp index_at(_, 0, acc), do: acc |> Enum.reverse()
  defp index_at(n, remaining, acc) do
    blk_size = Euler.Algebra.fact(remaining - 1)
    index_at(rem(n, blk_size), remaining - 1, [ div(n, blk_size) | acc ])
  end

  @doc """
  Generates the n-th indexed permutation in the lexicographically ordered list of `remaining` digits. 
  """
  def index_at(n, remaining) do
    index_at(n, remaining, [])
    |> translate(remaining)
  end

  defp translate(a, n) when is_number(n), do: translate(a, (0..(n-1)) |> Enum.to_list)
  defp translate(_, []), do: []
  defp translate([next | rest], allowed) do
    [ (allowed |> Enum.at(next)) | translate(rest, allowed |> List.delete_at(next)) ]
  end
end