Devon McCormick wrote: > > These brute force methods may give an answer for very small problems like > this example but they generally scale very poorly. > > On Sun, Apr 10, 2011 at 7:41 PM, Marshall Lochbaum < > [email protected]> wrote: > >> The following verb handily produces the possible distributions given a >> set >> of weights. Good luck finding which combinations gave you those sums! >> >> NB. x is (#boxes),(upper bound), y is weights to use >> NB. finds the unique (sorted) sums of groupings of y so that no sum >> exceeds >> the upper bound. >> sums=.4 :0 >> 'nbox bound'=.x >> y=.\:~ y >> s=.,: nbox$0 >> for_e. y do. >> s=.(#~ bound >: {."1) ~. \:~"1 ,/ s+"1/ e* =i.nbox >> end. >> s >> ) >> >> 4 124 sums m >> 124 124 124 121 >> 124 124 123 122 >> 124 123 123 123 >> >> Marshall >> >> -----Original Message----- >> From: [email protected] [mailto: >> [email protected]] On Behalf Of Viktor Cerovski >> Sent: Sunday, April 10, 2011 6:45 PM >> To: [email protected] >> Subject: Re: [Jprogramming] Weight distribution problem >> >> >> >> Skip Cave-3 wrote: >> > >> > [...] >> > To make the problem more concrete, Paul gives a specific example of >> > the problem. There are four buckets, and 20 masses. The masses are 23, >> > 43, 12, 54, 7, 3, 5, 10, 54, 55, 26, 9, 9, 43, 54, 1, 8, 6, 38, 33 >> > respectively. What distribution of the 20 masses gives the smallest >> > mass difference between the four buckets? >> > >> > Paul gives a link to his proposed solution, which I have not examined >> > as yet, since I want to see how far I can get with a J solution. >> > [...] >> > >> After some quick tries with J, I got a bunch of 123 123 123 124 >> distributions, and they are all mutually different. >> Here is one of them: >> >> conf >> 0 0 2 3 1 0 3 3 0 2 1 1 2 1 3 1 2 2 1 2 >> 23 43 12 54 7 3 5 10 54 55 26 9 9 43 54 1 8 6 38 33 >> >> +//./conf >> 123 123 123 124 >> >> </./conf >> ┌──────────┬──────────────┬──────────┬──────────────┐ >> │23 43 3 54│12 55 9 8 6 33│54 5 10 54│7 26 9 43 1 38│ >> └──────────┴──────────────┴──────────┴──────────────┘ >> >
I haven't given any method. Which size of the problem would you consider nontrivial? > > -- > View this message in context: > http://old.nabble.com/Weight-distribution-problem-tp31365679s24193p31366193.html > Sent from the J Programming mailing list archive at Nabble.com. > > ---------------------------------------------------------------------- > 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 -- View this message in context: http://old.nabble.com/Weight-distribution-problem-tp31365679s24193p31369301.html Sent from the J Programming mailing list archive at Nabble.com. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
