nth-Fibonacci (in elixir) : naive and TCO (tail-call optimized)

recursion.exs

# naive will not work for larger values of N
defmodule FibNaive do
  def n(0), do: 0
  def n(1), do: 1
  def n(2), do: 1
  def n(n), do: n(n - 1) + n(n - 2)
end

# tail-call optimized (employing dynamic programming)
defmodule FibTailCall do
  def n(n) when n <= 1, do: n
  def n(n), do: fib(n, 2, {0, 1})

  # base case
  defp fib(n, count, {minus_2, minus_1}) when n == count do
    minus_2 + minus_1
  end

  defp fib(n, count, {minus_2, minus_1}) do
    fib(n, count + 1, {minus_1, minus_2 + minus_1})
  end
end


assert FibTailCall.n(0) == 0
assert FibTailCall.n(1) == 1
assert FibTailCall.n(2) == 1
assert FibTailCall.n(3) == 2
assert FibTailCall.n(4) == 3
assert FibTailCall.n(5) == 5
assert FibTailCall.n(15) == 610
assert FibTailCall.n(20) == 6765
assert FibTailCall.n(50) == 12_586_269_025