defmodule Solution do
  @spec max_area(height :: [integer]) :: integer
  def max_area(height) do
    iter(0, height, 0, 0)
  end

  defp iter(prev, [head | tail], head_idx, max_vol) do
    if prev >= head do
      iter(prev, tail, head_idx + 1, max_vol)
    else
      max_vol = iter_inner(head, head_idx, tail, head_idx + 1, max_vol)
      iter(head, tail, head_idx + 1, max_vol)
    end
  end

  defp iter(_, [], _, max_vol), do: max_vol

  defp iter_inner(a, a_idx, [head | tail], head_idx, max_vol) do
    distance = head_idx - a_idx
    min_height = min(a, head)
    volume = min_height * distance
    max_vol = max(max_vol, volume)
    iter_inner(a, a_idx, tail, head_idx + 1, max_vol)
  end

  defp iter_inner(_, _, [], _, max_vol), do: max_vol
end