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RE: Friendly Challenge 2: sort by column

• To: mathgroup at smc.vnet.net
• Subject: [mg35024] RE: [mg35005] Friendly Challenge 2: sort by column
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Thu, 20 Jun 2002 02:13:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

> -----Original Message-----
> From: Wolf, Hartmut 
To: mathgroup at smc.vnet.net
> Sent: Wednesday, June 19, 2002 2:44 PM
> Subject: [mg35024] RE: [mg35005] Friendly Challenge 2: sort by column
> 
> 
> 
> > -----Original Message-----
> > From: gleam at flashmail.com [mailto:gleam at flashmail.com]
To: mathgroup at smc.vnet.net
> > Sent: Wednesday, June 19, 2002 11:53 AM
> > Subject: [mg35024] [mg35005] Friendly Challenge 2: sort by column
> > 
> > 
> > 	Once again, I am posting a friendly challenge with the hope of
> > provoking thought and encouraging creativity.  This time, the
> > challenge is to write the "best" sort-by-column function you can.
> > 
> > 	Once again, have already written several such 
> > functions, which I will
> > delay posting these until a number of responses are 
> received.  This is
> > not because I think I am some kind of Mathematica "guru" 
> will all the
> > right answers, but rather to prevent my methods from influencing
> > others.
> > 
> > 	Once again, though I am setting guidelines for this 
> > challenge, I will
> > not be pronouncing some final judgement of a winning algorithm.  I
> > would much prefer that this challenge induces a good 
> discussion of the
> > merits of various approaches and methods.
> > 
> > Description:
> > 
> > The function shall take two arguments: (1) a rectangular matrix and
> > (1) the number of a column in (1).
> > 
> > The function shall sort the rows of (1) according primarily to the
> > element in the column specified by (2).
> > 
> > The function shall not effect sub-elements in a three dimensional
> > matrix.
> > 
> > Example:
> > 
> > a = {{77,27,57,53},
> >      {72,21,40,27},
> >      {96,76,87,27},
> >      {61,97,93,71},
> >      {43,80,21,87}}
> > 
> > In:= f[a, 3]
> > 
> > Out= {{43,80,21,87},
> >       {72,21,40,27},
> >       {77,27,57,53},
> >       {96,76,87,27},
> >       {61,97,93,71}}
> > 
> > You may handle duplicates in the sort column as you see fit, but
> > please explain it for the rest of us, and be prepared give 
> support for
> > this as you would all other behaviors of your function.
> > 
> > Be creative, have fun, and good luck!
> > 
> > Paul
> > 
> > 
> 
> Paul,
> 
> a few quick ideas (leave testing up to you), unbundeled, unsorted:
> 
> (1)
> 
> Transpose[
>   
> RotateRight[Transpose[Sort[Transpose[RotateLeft[Transpose[a], 
> 2]]]], 2]]
> 
> 
> (2)
> 
> RotateRight[Sort[RotateLeft[a,{0,2}]],{0,2}]
> 
> 
> (3)
> 
> Sort[a, #1[[3]] < #2[[3]] &]
> 
> 
> (4)
> 
> a[[Ordering[Transpose[a][[3]]]]]
> 
> 
> --
> Hartmut
> 

consequently I should add

(5)

a[[Ordering[a[[All, 3]]]]]