defmodule BinarySearch do
  def binary_search(_numbers, _key, low, high) when low > high do
    :not_found
  end

  @spec binary_search(list, integer, integer, integer) :: integer | :not_found
  def binary_search(numbers, key, low, high) do
    md = low + Integer.floor_div(high-low, 2)
    IO.inspect(md)
    case elem(numbers, md) do
      x when x > key -> binary_search(numbers, key, low, md-1)
      x when x < key -> binary_search(numbers, key, md+1, high)
      x when x == key -> md
    end
  end

  @spec search(tuple, integer) :: {:ok, integer} | :not_found
  def search(numbers, key) do
    case binary_search(numbers, key, 0, tuple_size(numbers)-1) do
      :not_found -> :not_found
      x -> {:ok, x}
    end
  end
end