# What is the "functional" way of doing this?

Ricardo Aráoz ricaraoz at gmail.com
Tue Jul 31 20:34:18 CEST 2007

```Steven D'Aprano wrote:
> On Tue, 31 Jul 2007 09:01:42 -0300, Ricardo Aráoz wrote:
>
>> Considering I am a beginner I did a little test. Funny results too. The
>> function I proposed (lists1.py) took 11.4529998302 seconds, while the
>> other one (lists2.py) took 16.1410000324 seconds, thats about 40% more.
>> They were run in IDLE from their own windows (F5).
>
> [snip code]
>
> You may find that using the timeit module is better than rolling your own
> timer.
>
>>>> def recursive_func(n):
> ...     if n > 0:
> ...             return [n % 26] + recursive_func(n/26)
> ...     else:
> ...             return []
> ...
>>>> def generator_func(n):
> ...     def mseq(n):
> ...             while n > 0:
> ...                     n, a = divmod(n, 26)
> ...                     yield a
> ...     return list(mseq(n))
> ...
>>>> import timeit
>>>> N = 10**6+1
>>>> timeit.Timer("recursive_func(N)",
> ... "from __main__ import N, recursive_func").repeat()
> [16.48972487449646, 17.000514984130859, 16.520529985427856]
>>>> timeit.Timer("generator_func(N)",
> ... "from __main__ import N, generator_func").repeat()
> [27.938560009002686, 28.970781087875366, 23.977837085723877]
>
>
> If you're going to compare speeds, you should also test this one:
>
>>>> def procedural_func(n):
> ...     results = []
> ...     while n > 0:
> ...         n, a = divmod(n, 26)
> ...         results.append(a)
> ...     return results
> ...
>>>> timeit.Timer("procedural_func(N)",
> ... "from __main__ import N, procedural_func").repeat()
> [15.577107906341553, 15.60145378112793, 15.345284938812256]
>
>
> I must admit that I'm surprised at how well the recursive version did, and
> how slow the generator-based version was. But I'd be careful about drawing
> grand conclusions about the general speed of recursion etc. in Python from
> this one single example. I think this is simply because the examples tried
> make so few recursive calls. Consider instead an example that makes a few
> more calls:
>
>>>> N = 26**100 + 1
>>>>
>>>> timeit.Timer("recursive_func(N)",
> ... "from __main__ import N, recursive_func").repeat(3, 10000)
> [7.0015969276428223, 7.6065640449523926, 6.8495190143585205]
>>>> timeit.Timer("generator_func(N)",
> ... "from __main__ import N, generator_func").repeat(3, 10000)
> [3.56563401222229, 3.1132731437683105, 3.8274538516998291]
>>>> timeit.Timer("procedural_func(N)",
> ... "from __main__ import N, procedural_func").repeat(3, 10000)
> [3.3509068489074707, 4.0872640609741211, 3.3742849826812744]
>
>

Yup! As soon as the size of the list increases the generator function
gets better (50% in my tests). But it's interesting to note that if the
list is within certain limits (I've tested integers (i.e. 2,100,000,000
=> 7 member list)) and you only vary the times the funct. is called then
the recursive one does better.

```