[Haskell-cafe] k-minima in Haskell

[Thomas Hartman]

Rereading this, I see in fact apfelmus explains this is

"O(n + k*log n)" for the first k elements, which this discussion also
maintains is the best case. So, there's no discrepancy.

I think this is a very valuable post to read for the explanation.

2007/4/13, Thomas Hartman <tphyahoo at gmail.com>:
> Trying to understand this better I also came across
>
> http://groups.google.de/group/fa.haskell/browse_thread/thread/1345c49faff85926/8f675bd2aeaa02ba?lnk=st&q=%22I+assume+that+you+want+to+find+the+k%27th+smallest+element%22&rnum=1&hl=en#8f675bd2aeaa02ba
>
> where apfulmus gives an implementation of mergesort, which he claims
>
> "runs in O(n) time instead of the expected O(n log n)"
>
> Does that mean you can have the k minima in O(n) time, where n is
> length of list, which would seem to be an improvement?
>
>   mergesort []  = []
>   mergesort xs  = foldtree1 merge $ map return xs
>
>   foldtree1 f [x] = x
>   foldtree1 f xs  = foldtree1 f $ pairs xs
>      where
>      pairs []        = []
>      pairs [x]       = [x]
>      pairs (x:x':xs) = f x x' : pairs xs
>
>   merge []     ys     = ys
>   merge xs     []     = xs
>   merge (x:xs) (y:ys) =
>       if x <= y then x:merge xs (y:ys) else y:merge (x:xs) ys
>
>
> 2007/4/13, Thomas Hartman <tphyahoo at gmail.com>:
> > And for reference, here is again stefan's "stable" quicksort from his
> > earlier post.
> >
> > "
> > sort [] = []
> > sort l@(x:_) = filter (<x) l ++ filter (==x) l ++ filter (>x) l
> >
> > (A stable quicksort, btw)
> > "
> >
> > This is the code whose legitimacy I am requesting confirmation of.
> >
> > 2007/4/13, Thomas Hartman <tphyahoo at gmail.com>:
> > > > > You may be missing a few recursive calls there :-)
> > > >
> > > > Indeed.
> > >
> > > I'm confused.
> > >
> > > Is this a legitimate stable quicksort, or not? (My guess is, it is
> > > indeed legit as written.)
> > >
> > > This was also the first I have heard of stability as a sort property.
> > >
> > > http://perldoc.perl.org/sort.html may shed some light on this...
> > >
> > > "A stable sort means that for records that compare equal, the original
> > > input ordering is preserved. Mergesort is stable, quicksort is not. "
> > >
> > > Is this description a fair characterization of stability for the
> > > current discussion?
> > >
> > > I'm a bit confused but if I understand correctly sort from the prelude
> > > is non stable quicksort, which has O(k n^2) as the worst case, whereas
> > > stable quicksort has O( k* log n + n).
> > >
> > > non-stable quicksort is just sort from the prelude:
> > >
> > > qsort []     = []
> > > qsort (x:xs) = qsort (filter (< x) xs) ++ [x] ++ qsort (filter (>= x) xs)
> > >
> > > If any in the above was incorrect, please holler.
> > >
> > > 2007/4/12, Stefan O'Rear <stefanor at cox.net>:
> > > > On Wed, Apr 11, 2007 at 09:20:12PM -0700, Tim Chevalier wrote:
> > > > > On 4/11/07, Stefan O'Rear <stefanor at cox.net> wrote:
> > > > > >
> > > > > >If you want to be really explicit about it, here is a sort that will
> > > > > >work:
> > > > > >
> > > > > >sort [] = []
> > > > > >sort l@(x:_) = filter (<x) l ++ filter (==x) l ++ filter (>x) l
> > > > > >
> > > > > >(A stable quicksort, btw)
> > > > >
> > > > > You may be missing a few recursive calls there :-)
> > > >
> > > > Indeed.
> > > >
> > > > Stefan
> > > > _______________________________________________
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> > > >
> > >
> >
>