Re: Comparing strings from the back?

Date	2012-09-06 06:07 -0400
From	Dave Angel <d@davea.name>
Subject	Re: Comparing strings from the back?
References	(6 earlier) <504761ef$0$29981$c3e8da3$5496439d@news.astraweb.com> <k27osg$q7t$1@news.albasani.net> <50477cbb$0$29981$c3e8da3$5496439d@news.astraweb.com> <mailman.272.1346885254.27098.python-list@python.org> <50485fca$0$29977$c3e8da3$5496439d@news.astraweb.com>
Newsgroups	comp.lang.python
Message-ID	<mailman.287.1346926087.27098.python-list@python.org> (permalink)

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On 09/06/2012 04:33 AM, Steven D'Aprano wrote:
> <snip>
>
> I may have been overly-conservative earlier when I said that on
> average string equality has to compare half the characters. I thought
> I had remembered that from a computer science textbook, but I can't
> find that reference now, so possibly I was thinking of something else.
> (String searching perhaps?). In any case, the *worst* case for string
> equality testing is certainly O(N) (every character must be looked
> at), and the *best* case is O(1) obviously (the first character fails
> to match). But I'm not so sure about the average case. Further thought
> is required. 

For random strings (as defined below), the average compare time is
effectively unrelated to the size of the string, once the size passes
some point.

Define random string as being a selection from a set of characters, with
replacement.  So if we pick some set of characters, say 10 (or 256, it
doesn't really matter), the number of possible strings is 10**N.

The likelihood of not finding a mismatch within k characters is  
(1/10)**k   The likelihood of actually reaching the end of the random
string is (1/10)**N.  (which is the reciprocal of the number of strings,
naturally)

If we wanted an average number of comparisons, we'd have to calculate a
series, where each term is a probability times a value for k.
   sum((k * 9*10**-k) for k in range(1, 10))

Those terms very rapidly approach 0, so it's safe to stop after a few. 
Looking at the first 9 items, I see a value of 1.1111111

This may not be quite right, but the value is certainly well under 2 for
a population of 10 characters, chosen randomly.  And notice that N
doesn't really come into it. 

-- 

DaveA

Thread

Comparing strings from the back? Roy Smith <roy@panix.com> - 2012-09-03 21:54 -0400
  Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-04 12:07 +1000
  Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-04 02:17 +0000
    Re: Comparing strings from the back? Dan Sommers <dan@tombstonezero.net> - 2012-09-03 21:56 -0700
    Re: Comparing strings from the back? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-09-04 08:50 +0100
    Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-04 18:32 +0200
      Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-04 18:07 +0000
        Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-05 11:17 +0200
      Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-05 07:59 +1000
        Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-05 11:24 +0200
          Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-05 11:43 +0200
            Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-05 14:30 +0000
              Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-05 16:51 +0200
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-05 16:24 +0000
                Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-05 22:47 +0000
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-06 08:33 +0000
                Re: Comparing strings from the back? Dave Angel <d@davea.name> - 2012-09-06 06:07 -0400
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-07 04:06 +0000
                Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-07 19:10 +0000
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-08 00:55 +0000
                Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-08 11:53 +0000
                RE: Comparing strings from the back? "Prasad, Ramit" <ramit.prasad@jpmorgan.com> - 2012-09-13 18:39 +0000
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-13 15:37 -0400
                Re: Comparing strings from the back? alex23 <wuwei23@gmail.com> - 2012-09-13 20:48 -0700
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-14 00:46 -0400
                Re: Comparing strings from the back? alex23 <wuwei23@gmail.com> - 2012-09-13 21:54 -0700
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-14 01:38 -0400
                Re: Comparing strings from the back? alex23 <wuwei23@gmail.com> - 2012-09-13 23:06 -0700
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-14 04:03 -0400
                Re: Comparing strings from the back? alex23 <wuwei23@gmail.com> - 2012-09-14 01:20 -0700
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-14 04:53 -0400
                Re: Comparing strings from the back? alex23 <wuwei23@gmail.com> - 2012-09-14 03:26 -0700
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-14 07:36 -0400
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-14 10:16 +0000
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-14 07:43 -0400
                RE: Comparing strings from the back? "Prasad, Ramit" <ramit.prasad@jpmorgan.com> - 2012-09-14 22:43 +0000
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-14 23:10 -0400
                Re: Comparing strings from the back? alex23 <wuwei23@gmail.com> - 2012-09-16 18:11 -0700
                Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-17 14:05 +1000
                Re: Comparing strings from the back? alex23 <wuwei23@gmail.com> - 2012-09-16 23:06 -0700
                Re: Comparing strings from the back? Ethan Furman <ethan@stoneleaf.us> - 2012-09-17 13:35 -0700
                Re: Comparing strings from the back? Neil Hodgson <nhodgson@iinet.net.au> - 2012-09-18 09:14 +1000
                Re: Comparing strings from the back? Ethan Furman <ethan@stoneleaf.us> - 2012-09-18 08:12 -0700
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-18 11:55 -0400
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-18 11:59 -0400
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-18 12:17 -0400
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-19 00:47 +0000
                Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-19 02:20 +1000
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-18 16:40 -0400
                Re: Comparing strings from the back? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-09-19 00:48 +0100
                Re: Comparing strings from the back? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-09-13 20:53 +0100
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-13 17:06 -0400
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-14 03:39 +0000
                Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-14 14:15 +1000
                Re: Comparing strings from the back? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-09-13 22:17 +0100
                Re: Comparing strings from the back? Dwight Hutto <dwightdhutto@gmail.com> - 2012-09-13 17:35 -0400
                RE: Comparing strings from the back? "Prasad, Ramit" <ramit.prasad@jpmorgan.com> - 2012-09-14 21:32 +0000
                Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-07 19:40 +0000
                Re: Comparing strings from the back? Gelonida N <gelonida@gmail.com> - 2012-09-08 17:52 +0200
                Re: Comparing strings from the back? Duncan Booth <duncan.booth@invalid.invalid> - 2012-09-10 08:59 +0000
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-10 13:45 +0000
                Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-10 14:06 +0000
                Re: Comparing strings from the back? Duncan Booth <duncan.booth@invalid.invalid> - 2012-09-11 09:51 +0000
                Re: Comparing strings from the back? Terry Reedy <tjreedy@udel.edu> - 2012-09-11 11:55 -0400
                Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-11 00:26 +1000
                Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-10 14:32 +0000
                Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-10 14:43 +0000
                Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-11 00:56 +1000
                Re: Comparing strings from the back? Duncan Booth <duncan.booth@invalid.invalid> - 2012-09-11 09:41 +0000
                Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-06 12:04 +0100
                Re: Comparing strings from the back? Steve Howell <showell30@yahoo.com> - 2012-09-14 17:51 -0700
                Re: Comparing strings from the back? Roy Smith <roy@panix.com> - 2012-09-06 08:13 -0400
                Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-06 22:29 +1000
                Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-06 15:43 +0200
                Re: Comparing strings from the back? Dave Angel <d@davea.name> - 2012-09-06 10:23 -0400
                Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-06 16:33 +0200
                Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-06 16:42 +0200
                Re: Comparing strings from the back? Dave Angel <d@davea.name> - 2012-09-06 11:54 -0400
                Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-06 16:34 +0200
                Re: Comparing strings from the back? Gelonida N <gelonida@gmail.com> - 2012-09-08 17:50 +0200
                Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-06 15:37 +0200
                Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-07 00:39 +1000
                Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-06 17:36 +0200
                Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-06 17:44 +0200
                Re: Comparing strings from the back? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-09-07 04:07 +0000
  Re: Comparing strings from the back? Terry Reedy <tjreedy@udel.edu> - 2012-09-04 01:13 -0400
  Re: Comparing strings from the back? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-09-04 08:56 +0100
  Re: Comparing strings from the back? Alain Ketterlin <alain@dpt-info.u-strasbg.fr> - 2012-09-04 11:58 +0200
  Re: Comparing strings from the back? Neil Hodgson <nhodgson@iinet.net.au> - 2012-09-05 12:18 +1000
    Re: Comparing strings from the back? MRAB <python@mrabarnett.plus.com> - 2012-09-05 03:39 +0100
    Re: Comparing strings from the back? Roy Smith <roy@panix.com> - 2012-09-04 22:48 -0400
    Re: Comparing strings from the back? Johannes Bauer <dfnsonfsduifb@gmx.de> - 2012-09-05 16:33 +0200
  Re: Comparing strings from the back? Peter Otten <__peter__@web.de> - 2012-09-05 10:29 +0200
  Re: Comparing strings from the back? Chris Angelico <rosuav@gmail.com> - 2012-09-05 18:33 +1000
  Re: Comparing strings from the back? Peter Otten <__peter__@web.de> - 2012-09-05 11:48 +0200
  Re: Comparing strings from the back? Peter Otten <__peter__@web.de> - 2012-09-05 17:45 +0200
  Re: Comparing strings from the back? Dan Goodman <dg.gmane@thesamovar.net> - 2012-09-10 18:07 +0200
  Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-10 16:33 +0000
  Re: Comparing strings from the back? Dan Goodman <dg.gmane@thesamovar.net> - 2012-09-10 19:32 +0200
  Re: Comparing strings from the back? Dan Goodman <dg.gmane@thesamovar.net> - 2012-09-10 19:44 +0200
  Re: Comparing strings from the back? Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2012-09-10 21:52 +0000

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