defmodule Abacus.Util do
  @moduledoc """
  Utility functions
  """

  @doc """
  Returns the factorial of n.

  ## Example

  ```
iex(2)> factorial(0)
1
iex(3)> factorial(1)
1
iex(4)> factorial(2)
2
iex(5)> factorial(3)
6
iex(6)> factorial(4)
24
iex(7)> factorial(5)
120
```
  """
  @spec factorial(number) :: number
  def factorial(0), do: 1
  def factorial(n) when n > 0 do
    _factorial(1, n, 1)
  end

  def _factorial(n, m, r) when n < m do
     _factorial(n + 1, m, r * (n + 1))
  end

  def _factorial(n, n, r), do: r
end