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From: Oleg <oleg_inconnu@myrealbox.com>
To: Xavier Leroy <xavier.leroy@inria.fr>, Issac Trotts <ijtrotts@ucdavis.edu>
Subject: Re: [Caml-list] function
Date: Sat, 7 Dec 2002 12:31:33 -0500
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References: <20021203232211.GC22545@beech> <20021206213120.GC696@boson.ucdavis.edu> <20021207112814.A23052@pauillac.inria.fr>
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On Saturday 07 December 2002 05:28 am, Xavier Leroy wrote:
> > If the given list has L elements, each with S items, then flatten sho=
uld
> > O((L*S)*L) =3D O(S*L^2) time, since you have to keep on churning thro=
ugh
> > every single element in the ever-expanding l at every recursive flatt=
en
> > call.  That's too bad.
> > Here's an experiment I tried:
> > [...]
> > I guess it looks linear because of the small input size.
>
> It's always a good idea to do experimental measurements to confirm a
> complexity analysis, just to make sure you haven't goofed.  But when
> the measurements disagree with the analysis, you're supposed to go
> back to the analysis and find the flaw in it, not discard the
> experiment :-)
>
> More seriously: l1 @ l2 takes time O(length(l1)); the length of l2
> doesn't matter since l2 isn't copied.  This gives List.flatten a
> complexity of O(S*L) in your example (list of length L, each list
> element being of length S). =20

You are right. I had the incorrect mental picture of (@) being called wit=
h the=20
increasingly large first argument: S + 2*S +... + (L-1)*S =3D O(S*L^2).=20

Cheers
Oleg

> This is optimal for immutable,
> singly-linked lists.
>
> - Xavier Leroy

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