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RE: Friendly Challenge 2: sort by column

• To: mathgroup at smc.vnet.net
• Subject: [mg35018] RE: [mg35005] Friendly Challenge 2: sort by column
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Thu, 20 Jun 2002 02:13:13 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

> -----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: [mg35018] [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