# TODO: this gets the correct answer for project Euler, but is not correct in the general case.
# Figure that out.
defmodule Permutations do
  def index_at(_, 0), do: []
  def index_at(n, remaining) do
    blk_size = Euler.Algebra.fact(remaining - 1)
    [ div(n, blk_size) | index_at(rem(n, blk_size), remaining - 1) ]
  end

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

 Permutations.index_at(1_000_000, 10)
 |> Permutations.translate(0..9 |> Enum.to_list)
 |> Enum.join("")
 |> IO.puts()

print_permutations = fn n ->
  (0..(Euler.Algebra.fact(n)-1))
  |> Enum.map(fn i ->
    Permutations.index_at(i, n)
    |> Permutations.translate(n)
    |> Enum.join("")
    |> IO.puts()
  end)
end

print_permutations.(5)

# 999990 - 2783914056
# 999991 - 2783914065
# 999992 - 2783914506
# 999993 - 2783914560
# 999994 - 2783914605
# 999995 - 2783914650
# 999996 - 2783915046
# 999997 - 2783915064
# 999998 - 2783915406
# 999999 - 2783915460
# 1000000 - 2783915604
# 1000001 - 2783915640
# 1000002 - 2783916045
# 1000003 - 2783916054
# 1000004 - 2783916405
# 1000005 - 2783916450
# 1000006 - 2783916504
# 1000007 - 2783916540
# 1000008 - 2783940156
# 1000009 - 2783940165
# 1000010 - 2783940516
999_990..1_000_010
|> Enum.map(fn i ->
    n = Permutations.index_at(i, 10)
    |> Permutations.translate(10)
    |> Enum.join("")

    IO.puts("#{i} - #{n}")
end)