Padovan sequence: Difference between revisions
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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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The L-system, recurrence and floor based algorithms match to n=31.
</pre>
=={{header|FreeBASIC}}==
{{trans|11l}}
<syntaxhighlight lang="vbnet">Const As Double pp = 1.324717957244746025960908854
Const As Double ss = 1.0453567932525329623
Function padovan1(Byval n As Integer) As Integer
Dim As Integer a, b, c, d, i
a = 1: b = 1: c = 1
d = 1
For i = 1 To (n - 3)
d = a + b
a = b : b = c : c = d
Next i
Return d
End Function
Function padovan2(Byval n As Integer) As Integer
Dim As Double p = 1.0
For i As Integer = 1 To (n - 1)
p *= pp
Next i
Return Fix(p / ss)
End Function
Function padovan3(Byval n As Integer) As String
Dim As String sgte, s = "A"
Dim As Integer i, j, c
Dim As String rules(1 To 3) = {"B", "C", "AB"}
For i = 1 To n
sgte = ""
For j = 1 To Len(s)
Select Case Mid(s, j, 1)
Case "A" : c = 1
Case "B" : c = 2
Case "C" : c = 3
End Select
sgte &= rules(c)
Next j
s = sgte
Next i
Return s
End Function
Dim As Integer n
Print "First 20 terms of the Padovan sequence:"
For n = 1 To 20
Print padovan1(n); '" ";
Next
n = 1
Dim As Boolean areEqual = True
Dim As Integer list1(64), list2(64)
Do While n <= 64 And areEqual = False
list1(n) = padovan1(n)
list2(n) = padovan2(n)
If list1(n) <> list2(n) Then areEqual = False
n += 1
Loop
Print !"\nThe first 64 iterative and calculated values ";
Print Iif(areEqual, "are the same.", "differ.")
Print !"\nFirst 10 L-system strings:"
For n = 0 To 9
Print padovan3(n); " ";
Next
Print
areEqual = True
Dim As Integer list3(31)
Print !"\nLengths of the 32 first L-system strings:"
For n = 0 To 31
list3(n) = Len(padovan3(n))
Print list3(n); '" ";
If list3(n) <> list1(n) Then areEqual = False
Next
Print !"\nThese lengths are";
Print Iif(areEqual, " the 32 first terms of the Padovan sequence.", " not the 32 first terms of the Padovan sequence.")
Sleep</syntaxhighlight>
{{out}}
<pre>First 20 terms of the Padovan sequence:
1 1 1 2 2 3 4 5 7 9 12 16 21 28 37 49 65 86 114 151
The first 64 iterative and calculated values are the same.
First 10 L-system strings:
A B C AB BC CAB ABBC BCCAB CABABBC ABBCBCCAB
Lengths of the 32 first L-system strings:
1 1 1 2 2 3 4 5 7 9 12 16 21 28 37 49 65 86 114 151 200 265 351 465 616 816 1081 1432 1897 2513 3329 4410
These lengths are not the 32 first terms of the Padovan sequence.</pre>
=={{header|Go}}==
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