n_product.ex

defmodule T do

  defp init_cursor(dimension) do (for _ <- 1..dimension, do: 0) end

  defp increment_cursor(cursor, depth) do
      max = depth-1
      cursor
      |>List.foldr(
        {1, false, []},
        fn elem, {carry, unique, acc} ->
          case elem + carry do
            ^depth -> {1, unique, [0   | acc]}
            ^max   -> {0, true  , [max | acc]}
             sum   -> {0, unique, [sum | acc]}
          end
        end)
  end

  defp next_cursor(acc, cursor, depth) do
    case increment_cursor(cursor, depth) do
      {1, _unique, _cursor}   -> acc # carry out, so we have hit the max depth
      {_carry, true, cursor}  -> next_cursor([cursor | acc], cursor, depth)
      {_carry, false, cursor} -> next_cursor(acc, cursor, depth) # not unique, seen in lower depth
    end
  end

  defp product_at_depth(dimension, 1) do [init_cursor(dimension)] end

  defp product_at_depth(dimension, depth) do
    next_cursor([], init_cursor(dimension), depth)
    |> Enum.reverse
  end

  def product(dimension, depth) when dimension >= 1 and depth >= 1 do
    for i <- 1..depth do product_at_depth(dimension, i) end
  end
  
end