[Jprogramming] APWJ exercises for the reader [1 of 4]

[Roger Hui]

Solution to Problem 1:

magicperm=: C. @ < @ (|.@:>: , }.) @ (i.&.-:)

   magicperm 2
0 1
   magicperm 4
0 2 3 1
   magicperm 6
0 2 4 1 5 3
   magicperm 8
0 2 4 1 6 3 7 5

Check:

seq  =: 3 : 'y {^:(}:i.#y) i.#y'
pairs=: /:~ @ (>/"1 |."_1 ]) @ (_2 ]\ , at seq)
NB. comb from  http://www.jsoftware.com/help/dictionary/cfor.htm

   (2&comb -: pairs at magicperm)"0 }. 2*i.8
1 1 1 1 1 1 1



----- Original Message -----
From: Ian Clark <earthspotty at googlemail.com>
Date: Wednesday, November 11, 2009 3:56
Subject: [Jprogramming] APWJ exercises for the reader [1 of 4]
To: Programming forum <programming at jsoftware.com>

> In At Play With J Edn 1, there were 4 questions left as 
> exercises for
> the reader. In Edn 2 we want to provide the answers in an Appendix.
> 
> Just so I don't get them wrong, could the forum please suggest what
> the answers should be? You may have to refer to the Wiki page.
> 
> I'm putting each question in a separate thread.
> 
> +++++
> In Chapter 5 Jacobi's method
> http://www.jsoftware.com/jwiki/Doc/Articles/Play113 [see midway]
> 
> "Problem 1: Define a verb which takes as argument a positive even
> integer n and yields a permutation which, repeatedly applied to a
> conforming identity permutation, produces, in successive pairs of
> items, all possible choices of 2 items from n, with no duplications.
> 
> Problem 2: How many of the !n permutations of even order n are
> solutions to problem 1?"
> +++++
> 
> Ian Clark
> Subeditor, APWJ Edn 2