Padovan sequence: Difference between revisions
Add Elixir implementation
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Length of first 32 strings produced from the L-system = Padovan sequence
</pre>
=={{header|Elixir}}==
{{trans|Ruby}}
<syntaxhighlight lang="Elixir"># Padovan sequence as a Stream
defmodule Padovan do
def stream do
Stream.resource(
fn -> {1, 1, 1} end,
fn {a, b, c} ->
next_value = a + b
{[a], {b, c, next_value}}
end,
fn _ -> :ok end
)
end
end
# Padovan floor function
defmodule PadovanFloorFunction do
@p 1.324717957244746025960908854
@s 1.0453567932525329623
def padovan_f(n), do: trunc((:math.pow(@p, n - 1) / @s) + 0.5)
end
# Calculate and print the first 20 elements of the Padovan sequence and the floor function
padovan_sequence = Padovan.stream() |> Enum.take(20)
padovan_floor_function = Enum.map(0..19, &PadovanFloorFunction.padovan_f(&1))
IO.puts("Recurrence Padovan: #{inspect(padovan_sequence)}")
IO.puts("Floor function: #{inspect(padovan_floor_function)}")
# Check if the sequences are equal up to n
n = 63
bool = Enum.map(0..(n-1), &PadovanFloorFunction.padovan_f(&1)) == Padovan.stream() |> Enum.take(n)
IO.puts("Recurrence and floor function are equal up to #{n}: #{bool}.")
# L-system generator as a Stream
defmodule LSystem do
def stream(axiom \\ "A", rules \\ %{"A" => "B", "B" => "C", "C" => "AB"}) do
Stream.iterate(axiom, fn string ->
string
|> String.graphemes()
|> Enum.map(&Map.get(rules, &1, ""))
|> Enum.join()
end)
end
end
# Calculate and print the first 10 elements of the L-system
l_system_sequence = LSystem.stream() |> Enum.take(10)
IO.puts("First 10 elements of L-system: #{l_system_sequence |> Enum.join(", ")}")
# Check if the sizes of the L-system strings match the Padovan sequence
n = 32
l_system_sizes = LSystem.stream() |> Enum.take(n) |> Enum.map(&String.length/1)
bool = l_system_sizes == Padovan.stream() |> Enum.take(n)
IO.puts("Sizes of first #{n} L_system strings equal to recurrence Padovan? #{bool}.")</syntaxhighlight>
{{out}}
<pre>
Recurrence Padovan: [1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151]
Floor function: [1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151]
Recurrence and floor function are equal up to 63: true.
First 10 elements of L-system: A, B, C, AB, BC, CAB, ABBC, BCCAB, CABABBC, ABBCBCCAB
Sizes of first 32 L_system strings equal to recurrence Padovan? true.
</pre>
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