I seem to know a little more J than I did 10 years ago, so here is a little cleaner way to get the combinations. It is still slow and won't go beyond the limits of the previous version.
PO=: 13 :'|:(y#2)#:i.*/y#2' M=: 13 :'(x=+/PO y)#"1 PO y' COMB=: 13 :'(i.y)*"2 x M y' PO 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 3 M 5 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 3 COMB 5 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 2 0 2 2 0 2 2 0 0 2 3 3 0 3 3 0 3 0 3 0 4 4 4 0 4 4 0 4 0 0 -----Original Message----- From: programming-boun...@jsoftware.com [mailto:programming-boun...@jsoftware.com] On Behalf Of Henry Rich Sent: Tuesday, June 26, 2012 9:17 PM To: Programming forum Subject: Re: [Jprogramming] permutation list Take the time to ponder R. E. Boss's version (in the Wiki). It is beautiful, and I have tried without success to make any improvement. $ 12 comb 24 2704156 12 In about 1 second. Henry Rich On 6/26/2012 8:54 PM, Linda Alvord wrote: > I wrote a book called "Probability in APL" many years ago. When I > started to learn J I tried to rewrite my code in J. Here is what I > wrote for combinations. > > po=: [: |: ] #: [: i. */ > cr=:[: |: ([ = [: +/ [: po ] $ 2:) #"1 [: po ] $ 2: > comb=:[: |: (! , [) $ ([: , cr) #"1 [: , ([: $ cr) $ [: i. ] > $4 comb 10 > 4 210 > > It might take a little time to remember what I did. > > Linda > > > -----Original Message----- > From: programming-boun...@jsoftware.com > [mailto:programming-boun...@jsoftware.com] On Behalf Of bob therriault > Sent: Tuesday, June 26, 2012 3:02 PM > To: Programming forum > Subject: Re: [Jprogramming] permutation list > > Raul, > > I don't think that there is a 1-1 correspondence between combinations > and permutations, since each combination of items can have a number of > different permutations. In the example you give the number of items is > the same because the difference in the two arguments is 1, but this > would not be true in the general case. > > I am using the definition of combination found here: > http://www.mathwords.com/c/combination_formula.htm > and the formula for permutation found here: > http://www.mathwords.com/p/permutation_formula.htm > > In J the number of combinations is x!y and the number of permutations > is x(!@-~ * !)y, since there are !(y-x) permutations of each > combination. I guess that this would make the correspondence !(y-x) to 1. > > It's been a while since I sat in a combinatorics lecture, so please > correct me if I have this wrong, or I am using the words in a > different way than you. > > Cheers, bob > > On 2012-06-26, at 11:14 AM, Raul Miller wrote: > >> They are certainly different. >> >> 2 comb 3 >> 0 1 >> 0 2 >> 1 2 >> 2 perm 3 >> 0 1 2 >> 0 2 1 >> 1 0 2 >> >> >> In general, for n of m permutations and n of m combinations, the >> permutations are going to be longer (length m instead of length n). >> But the number of distinct items will be the same. >> >> -- >> Raul >> >> On Tue, Jun 26, 2012 at 2:09 PM, Devon McCormick<devon...@gmail.com> > wrote: >>> I thought that in the usual mathematical definition, combinations >>> and permutations differ: for permutations, order matters; for >>> combinations, it does not. Under this definition, the combinations >>> of >>> 3 things is just " i. 3 " - assuming we don't allow replacement? If >>> we do allow replacement, the permutations of 3 things are given by " >>> {3$<i.3 " and the combinations by something like " ~./:~&.>,{3$<i.3 ". >>> >>> Does this seem right? >>> >>> On Tue, Jun 26, 2012 at 12:51 PM, Raul Miller<rauldmil...@gmail.com> > wrote: >>>> Note that the number of combinations and the number of permutions >>>> are > the same. >>>> >>>> And, perm is just: ! A.&i. ] >>>> >>>> It seems like there ought to be a way of putting the permutations >>>> in >>>> 1 to 1 correspondence with the combinations (to give us a concise >>>> expression for combinations). >>>> >>>> -- >>>> Raul >>>> >>>> On Tue, Jun 26, 2012 at 12:41 PM, ed bierly<ebie...@gmail.com> wrote: >>>>> yes combinations not permutations >>>>> thought there might be a way that didn't loop thank you for the >>>>> references >>>>> >>>>> On Tue, Jun 26, 2012 at 12:30 PM, R.E. Boss<r.e.b...@planet.nl> wrote: >>>>> >>>>>> 4 comb 10 >>>>>> >>>>>> >>>>>> R.E. Boss >>>>>> >>>>>> >>>>>>> -----Oorspronkelijk bericht----- >>>>>>> Van: programming-boun...@jsoftware.com [mailto: >>>>>> programming-boun...@jsoftware.com] Namens ed bierly >>>>>>> Verzonden: dinsdag 26 juni 2012 18:15 >>>>>>> Aan: programming@jsoftware.com >>>>>>> Onderwerp: [Jprogramming] permutation list >>>>>>> >>>>>>> what is the best way to get this list of 210 vectors? >>>>>>> >>>>>>> 4!10 >>>>>>> ---------------------------------------------------------------- >>>>>>> - >>>>>>> ----- For information about J forums see >>>>>>> http://www.jsoftware.com/forums.htm >>>>>> >>>>>> ----------------------------------------------------------------- >>>>>> - >>>>>> ---- For information about J forums see >>>>>> http://www.jsoftware.com/forums.htm >>>>>> >>>>> ------------------------------------------------------------------ >>>>> - >>>>> --- For information about J forums see >>>>> http://www.jsoftware.com/forums.htm >>>> ------------------------------------------------------------------- >>>> - >>>> -- For information about J forums see >>>> http://www.jsoftware.com/forums.htm >>> >>> >>> >>> -- >>> Devon McCormick, CFA >>> ^me^ at acm. >>> org is my >>> preferred e-mail >>> -------------------------------------------------------------------- >>> - >>> - For information about J forums see >>> http://www.jsoftware.com/forums.htm >> --------------------------------------------------------------------- >> - For information about J forums see >> http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
