Natural Sorting algorithms

Just for reference, here is the same approach with a custom comparator. I didn’t bench these but since it doesn’t build tuples it is probably faster:

defmodule Natural do
  def natural_sort(enumerable) do
    Enum.sort(enumerable, __MODULE__)
  end

  def compare(x, y) do
    case do_compare(String.upcase(x), String.upcase(y)) do
      :eq -> do_compare(x, y)
      lt_or_gt -> lt_or_gt
    end
  end

  defp do_compare(x, x), do: :eq
  defp do_compare(x, y) when x > y, do: :gt
  defp do_compare(_, _), do: :lt
end

We updated NaturalSort with changes from @eksperimental. Thanks for fixing those bugs.

You are right. I messed up with the input. Your implementation.

I’m sorry if I misunderstood your comment, but this example is not using the same list shuffled, these are different lists. I believe the result provided is the expected one?

If I reuse the example from your issue it seems fine too:

iex(1)> ~W(a A b) |> Enum.sort_by(&{String.downcase(&1), &1})             
["A", "a", "b"]
iex(2)> ~W(A b a) |> Enum.sort_by(&{String.downcase(&1), &1})
["A", "a", "b"]

Well, this is obvious implication of the fact that Enum.sort* functions are using stable sort algorithms.

Thank you Aleksei for your contribution to the discussion, later one with more time, I will look in detail and see how I can apply those to the NaturalOrder library. There are a few lessons to take from the discussion.

EDIT: the implementation is correct, I had the wrong input

The problem with this approach is that it returns different results depending on the initial order for the same list shuffled.

iex(16)> Enum.sort_by(~w(A B a b), &{String.downcase(&1), &1})
["A", "a", "B", "b"]

iex(17)> Enum.sort_by(~w(a B B b), &{String.downcase(&1), &1})
["a", "B", "B", "b"]

~~Actually I have reported this very same issue to this library just a few hours ago: Issues · BinaryNoggin/natural_order · GitHub

FWIW, I have proposed the custom optimized sorter: Sort items "naturally" in menu, summary, function list, etc. · Issue #1440 · elixir-lang/ex_doc · GitHub

I have this hacky solution which should work but probably isn’t optimal:

Enum.sort_by(~w(A B a b), &{String.downcase(&1), &1})

Mostly. Case should not be ignored, but order should be: A, a, B, b, and not A, B, a, b as sorting by ASCII code does.