56 lines
1.8 KiB
Elixir
56 lines
1.8 KiB
Elixir
# Padovan sequence as a Stream
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defmodule Padovan do
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def stream do
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Stream.resource(
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fn -> {1, 1, 1} end,
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fn {a, b, c} ->
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next_value = a + b
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{[a], {b, c, next_value}}
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end,
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fn _ -> :ok end
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)
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end
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end
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# Padovan floor function
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defmodule PadovanFloorFunction do
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@p 1.324717957244746025960908854
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@s 1.0453567932525329623
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def padovan_f(n), do: trunc((:math.pow(@p, n - 1) / @s) + 0.5)
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end
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# Calculate and print the first 20 elements of the Padovan sequence and the floor function
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padovan_sequence = Padovan.stream() |> Enum.take(20)
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padovan_floor_function = Enum.map(0..19, &PadovanFloorFunction.padovan_f(&1))
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IO.puts("Recurrence Padovan: #{inspect(padovan_sequence)}")
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IO.puts("Floor function: #{inspect(padovan_floor_function)}")
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# Check if the sequences are equal up to n
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n = 63
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bool = Enum.map(0..(n-1), &PadovanFloorFunction.padovan_f(&1)) == Padovan.stream() |> Enum.take(n)
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IO.puts("Recurrence and floor function are equal up to #{n}: #{bool}.")
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# L-system generator as a Stream
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defmodule LSystem do
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def stream(axiom \\ "A", rules \\ %{"A" => "B", "B" => "C", "C" => "AB"}) do
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Stream.iterate(axiom, fn string ->
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string
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|> String.graphemes()
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|> Enum.map(&Map.get(rules, &1, ""))
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|> Enum.join()
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end)
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end
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end
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# Calculate and print the first 10 elements of the L-system
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l_system_sequence = LSystem.stream() |> Enum.take(10)
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IO.puts("First 10 elements of L-system: #{l_system_sequence |> Enum.join(", ")}")
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# Check if the sizes of the L-system strings match the Padovan sequence
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n = 32
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l_system_sizes = LSystem.stream() |> Enum.take(n) |> Enum.map(&String.length/1)
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bool = l_system_sizes == Padovan.stream() |> Enum.take(n)
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IO.puts("Sizes of first #{n} L_system strings equal to recurrence Padovan? #{bool}.")
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