Thanks, Roger.
On Wed, Nov 11, 2009 at 8:09 PM, Roger Hui <[email protected]> wrote: >> pairs=: /:~ @ (>/"1 |."_1 ]) @ (_2 ]\ ,@seq) > > pairs=: [: /:~ _2 /:~\ ,@seq > > > > ----- Original Message ----- > From: Roger Hui <[email protected]> > Date: Wednesday, November 11, 2009 11:30 > Subject: Re: [Jprogramming] APWJ exercises for the reader [1 of 4] > To: Programming forum <[email protected]> > >> > Problem 2: How many of the !n permutations of even order n are >> > solutions to problem 1? >> >> Problem 2 probably does not have an easy solution >> as the sequence 2 8 48 1152 34560 (for n=2 4 6 8 10) >> is not a subsequence in the Online Encyclopedia of >> Integer Sequences. >> >> http://www.research.att.com/~njas/sequences/index.html >> >> +/ (2 comb n)&-:@pairs@(A.&(i.n))"0 i.!n=: 2 >> 2 >> +/ (2 comb n)&-:@pairs@(A.&(i.n))"0 i.!n=: 4 >> 8 >> +/ (2 comb n)&-:@pairs@(A.&(i.n))"0 i.!n=: 6 >> 48 >> ... >> >> >> >> ----- Original Message ----- >> From: Roger Hui <[email protected]> >> Date: Wednesday, November 11, 2009 11:03 >> Subject: Re: [Jprogramming] APWJ exercises for the reader [1 of 4] >> To: Programming forum <[email protected]> >> >> > 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 ]\ ,@seq) >> > NB. comb from http://www.jsoftware.com/help/dictionary/cfor.htm >> > >> > (2&comb -: pa...@magicperm)"0 }. 2*i.8 >> > 1 1 1 1 1 1 1 >> > >> > >> > >> > ----- Original Message ----- >> > From: Ian Clark <[email protected]> >> > Date: Wednesday, November 11, 2009 3:56 >> > Subject: [Jprogramming] APWJ exercises for the reader [1 of 4] >> > To: Programming forum <[email protected]> >> > >> > > 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 > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
