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│ > └──────────┴──────────────┴──────────┴──────────────┘ > > > -- > 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
