> 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
