pascals_triangle.exs

defmodule PascalsTriangle do
  @doc """
  Calculates the rows of a pascal triangle
  with the given height
  Calculated from the bottom up.
  """
  @spec rows(integer) :: [[integer]]
  def rows(0, acc), do: acc
  def rows(num) do
    num
    |> do_pascal
  end


  defp do_pascal(num, acc \\ [])
  defp do_pascal(0, acc), do: acc
  defp do_pascal(num, acc) do
    row = num - 1
    |> get_list_from_range
    |> get_pascal(num - 1)
    do_pascal(num - 1, [row | acc])
  end

  defp get_list_from_range(n) do
    Enum.into(0..n, [])
  end

  defp get_pascal(list, row) do
    List.foldr(list, [], fn(x, acc) ->
      [n_choose_k(row, x) | acc]
    end)
  end

  @doc """
  Calculates the factorial of a number.
  n!
  """
  @spec fact(integer) :: integer
  def fact(n) do
    do_fact(n)
  end
  defp do_fact(n, acc \\ 1)
  defp do_fact(0, acc), do: acc
  defp do_fact(1, acc), do: acc
  defp do_fact(n, acc) do
    do_fact(n-1, n*acc)
  end

  @doc """
  Calculates n choose k
  n! / ( k! * (n-k)! )
  """
  def n_choose_k(n, k) do
    div(fact(n), fact(k) * fact(n-k))
  end
end