defmodule MaxDoubleSliceSum do
  def max_double_slice_sum(a) when length(a) < 3, do: 0

  def max_double_slice_sum(a) do
    size = length(a)
    a_map = a |> Enum.with_index() |> Map.new(fn {v, i} -> {i, v} end)

    p1 = build_p1(size, a_map)
    p2 = build_p2(size, a_map)

    1..(size - 2)
    |> Enum.map(fn i -> Map.get(p1, i) + Map.get(p2, i) end)
    |> Enum.max()
  end

  defp build_p1(size, a_map) do
    Enum.reduce(2..(size - 2)//1, %{1 => 0}, fn i, p1 ->
      value = max(0, Map.get(p1, i - 1) + Map.get(a_map, i - 1))
      Map.put(p1, i, value)
    end)
  end

  defp build_p2(size, a_map) do
    Enum.reduce(2..(size - 2)//1, %{size - 2 => 0}, fn i, p2 ->
      key = size - i - 1
      value = max(0, Map.get(p2, size - i) + Map.get(a_map, size - i))
      Map.put(p2, key, value)
    end)
  end
end