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Re: Slices time complexity

References (1 earlier) <555b0621$0$2753$c3e8da3$76491128@news.astraweb.com> <mjff5g$met$1@dont-email.me> <555b6db8$0$12996$c3e8da3$5496439d@news.astraweb.com> <adoplatr4fq8nssa9s2pk3bbpmhtkdk775@4ax.com> <555d8ae3$0$11095$c3e8da3@news.astraweb.com>
Date 2015-05-21 18:25 +1000
Subject Re: Slices time complexity
From Chris Angelico <rosuav@gmail.com>
Newsgroups comp.lang.python
Message-ID <mailman.194.1432196751.17265.python-list@python.org> (permalink)

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On Thu, May 21, 2015 at 5:35 PM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
>> You don't need huge. On any algorithm where slices are being used you
>> will have to account for the linear complexity. You seem to be
>> dismissive of this fact, but it can have tremendous performance
>> implications, since it can turn a linear algorithm into a quadratic
>> one just like that.
>
> Sure. And for small enough N, everything is fast.
>
> There's a sorting algorithm, usually called "Bozo sort", which shuffles the
> list, then checks whether it is sorted. If not, it shuffles it again, until
> it is sorted. Bozo sort is a *terrible* algorithm, with no upper limit to
> the worst case, and O(N!) for the average case. And yet, with small lists
> (say, five items) the performance is acceptable if your requirements are
> low.

A less ridiculous, but equally valid, comparison is with
multiplication algorithms. A while ago someone asked about what Python
uses, and on learning that CPython uses Karatsuba [1], suggested that
some other algorithm (I don't remember which) had better asymptotic
complexity. Downside: It'd be slower for smaller numbers, and the
complexity cost of an additional cutoff ("use grade-school up to X,
then Karatsuba up to Y, then Fuerer's") would also negatively impact
performance overall. Grade-school arithmetic is O(N*N) which looks
terrible... but for smallish numbers, its performance is quite
adequate.

ChrisA

[1] https://en.wikipedia.org/wiki/Karatsuba_algorithm

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Slices time complexity Mario Figueiredo <marfig@gmail.com> - 2015-05-18 20:23 +0100
  Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-19 05:36 +1000
    Re: Slices time complexity Mario Figueiredo <marfig@gmail.com> - 2015-05-18 20:49 +0100
      Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-19 06:04 +1000
  Re: Slices time complexity Todd <toddrjen@gmail.com> - 2015-05-18 21:42 +0200
  Re: Slices time complexity Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-18 13:49 -0600
    Re: Slices time complexity Fabien <fabien.maussion@gmail.com> - 2015-05-18 21:54 +0200
      Re: Slices time complexity Todd <toddrjen@gmail.com> - 2015-05-18 22:23 +0200
    Re: Slices time complexity Mario Figueiredo <marfig@gmail.com> - 2015-05-18 22:04 +0100
      Re: Slices time complexity Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-05-18 22:38 +0100
      Re: Slices time complexity Terry Reedy <tjreedy@udel.edu> - 2015-05-18 19:04 -0400
    Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-18 19:20 -0700
      Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-19 15:13 +1000
        Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-18 22:33 -0700
          Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-19 10:12 +0300
            Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-19 18:16 +1000
              Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-19 11:39 +0300
                Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-19 18:50 +1000
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-19 12:35 +0300
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-19 23:44 +1000
                Re: Slices time complexity Christian Gollwitzer <auriocus@gmx.de> - 2015-05-20 23:54 +0200
                Re: Slices time complexity Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-05-19 23:00 +1200
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 11:47 +1000
                Re: Slices time complexity Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2015-05-20 08:07 -0400
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-19 22:42 +1000
                Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-19 23:24 +1000
                Re: Slices time complexity Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-05-20 12:31 +1200
                Re: Slices time complexity Ben Finney <ben+python@benfinney.id.au> - 2015-05-20 10:42 +1000
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-20 07:24 +0300
                Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-19 21:30 -0700
                Re: Slices time complexity Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-05-20 06:06 +0100
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 15:57 +1000
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-20 09:17 +0300
                Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-19 23:23 -0700
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-20 09:46 +0300
                Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-20 00:03 -0700
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-20 10:45 +0300
                List semantics [was Re: Slices time complexity] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 17:23 +1000
                Re: List semantics [was Re: Slices time complexity] Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-05-20 20:54 +1200
                Re: List semantics [was Re: Slices time complexity] Ned Batchelder <ned@nedbatchelder.com> - 2015-05-20 04:08 -0700
                Re: List semantics [was Re: Slices time complexity] Terry Reedy <tjreedy@udel.edu> - 2015-05-20 14:42 -0400
                Re: List semantics [was Re: Slices time complexity] Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-05-21 11:06 +1200
                Re: List semantics [was Re: Slices time complexity] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-21 12:10 +1000
                Re: Slices time complexity "Bartc" <bartc@freeuk.com> - 2015-05-20 10:56 +0100
                Re: Slices time complexity Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2015-05-20 10:16 +0100
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-21 15:19 +1000
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-21 09:20 +0300
                Re: Slices time complexity bartc <bart4858@gmail.com> - 2015-05-21 06:34 -0700
                Re: Slices time complexity MRAB <python@mrabarnett.plus.com> - 2015-05-21 17:50 +0100
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-22 03:16 +1000
                Re: Slices time complexity bart4858@gmail.com - 2015-05-21 12:48 -0700
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 12:26 +1000
                Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-20 12:36 +1000
                Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-19 20:02 -0700
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-19 21:43 +1000
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-19 18:59 +0300
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 03:46 +1000
                Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-20 04:12 +1000
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-19 21:19 +0300
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 10:43 +1000
                Re: Slices time complexity Marko Rauhamaa <marko@pacujo.net> - 2015-05-20 07:30 +0300
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 15:33 +1000
                Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 15:58 +1000
                Re: Slices time complexity Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2015-05-19 15:18 +0100
            Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-19 04:46 -0700
              Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-19 05:14 -0700
          Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-19 18:19 +1000
            Re: Slices time complexity Rustom Mody <rustompmody@gmail.com> - 2015-05-19 04:41 -0700
  Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-19 19:45 +1000
    Re: Slices time complexity Serhiy Storchaka <storchaka@gmail.com> - 2015-05-19 13:15 +0300
    Re: Slices time complexity Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2015-05-19 12:09 +0100
    Re: Slices time complexity "Bartc" <bartc@freeuk.com> - 2015-05-19 15:52 +0100
      Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-20 03:07 +1000
        Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-20 03:19 +1000
        Re: Slices time complexity Mario Figueiredo <marfig@gmail.com> - 2015-05-20 20:51 +0100
          Re: Slices time complexity Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-20 14:33 -0600
          Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-21 06:35 +1000
          Re: Slices time complexity Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-05-20 21:47 +0100
            Re: Slices time complexity Mario Figueiredo <marfig@gmail.com> - 2015-05-20 22:23 +0100
          Re: Slices time complexity Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-05-21 17:35 +1000
            Re: Slices time complexity Chris Angelico <rosuav@gmail.com> - 2015-05-21 18:25 +1000
    Re: Slices time complexity Ian Kelly <ian.g.kelly@gmail.com> - 2015-05-19 09:15 -0600
    Re: Slices time complexity Serhiy Storchaka <storchaka@gmail.com> - 2015-05-19 22:51 +0300

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