defmodule Euler.Algebra do
  def divisors(n) do
    [ 1 |
    (for i <- 2..floor(:math.sqrt(n))//1,
      j = div(n, i),
      j == n / i do
        if i !== j, do: [i,j], else: [i]
    end |> Enum.flat_map(&(&1))) ]
  end

  defp fact(1, acc), do: acc
  defp fact(n, acc), do: fact(n - 1, n * acc)
  @doc """
  Computes n!
  """
  def fact(0), do: 1
  def fact(1), do: 1
  def fact(n), do: fact(n - 1, n)

  defp digit_sum(0, acc), do: acc
  defp digit_sum(n, acc), do: digit_sum(div(n, 10), rem(n, 10) + acc)
  @doc """
  Returns the sum of the digits of `n`.
  """
  def digit_sum(n), do: digit_sum(n, 0)

  def fib(0), do: 1
  def fib(1), do: 1
  def fib(n) do
    cache = Process.get(:fib, %{})
    case Map.get(cache, n, nil) do
      nil ->
        value = fib(n - 1) + fib(n - 2)
        cache = Process.get(:fib, %{}) |> Map.put_new(n, value)
        Process.put(:fib, cache)
        value
      m -> m
    end
  end

  def num_digits(0, acc), do: acc
  def num_digits(n, acc), do: num_digits(div(n,10),acc+1)
  def num_digits(0), do: 1
  def num_digits(n) do
    num_digits(n, 0)
  end
end