collatz_elixir.ex

defmodule Collatz do
  def call(n, cache), do: call(n, 0, cache)
  def call(1, length, _), do: length + 1
  def call(n, length, cache), do: get(n, length, cache, cache[n])

  defp get(n, length, cache, nil), do: call(next(n), length, cache) + 1
  defp get(_, _, _, value), do: value

  defp next(n) when rem(n, 2) == 0, do: div(n, 2)
  defp next(n) when rem(n, 2) == 1, do: n * 3 + 1
end

defmodule Main do
  def run(min, limit), do: run(min, %{}, limit, {0, 0})
  def run(n, _, limit, result) when n > limit, do: result
  def run(n, cache, limit, result), do: cache_and_loop(n, cache, limit, result, Collatz.call(n, cache))
  def cache_and_loop(n, cache, limit, result, length) do
    run(n + 1, Map.put_new(cache, n, length), limit, max(n, length, result))
  end

  defp max(n, length, {_, max_length}) when length > max_length, do: {n, length}
  defp max(_, _, result), do: result
end

IO.inspect Main.run(1, 1_000_000)