As I pointed out some days ago, 29/10/17. Ruskey himself, I think, discusses the “bijection” between the “restricted growth functions” and the required sets. You can defer converting the linear array to boxes or omit that stage altogether according to need.
Cheers, Mike Please reply to [email protected]. Sent from my iPad > On 5 Nov 2017, at 10:40, Erling Hellenäs <[email protected]> wrote: > > Hi all! > > If you remove the last statement of parRuskeyE, you get a program that is > much faster, uses much less memory and is more useful. > > parRuskeyE =: 4 : 0 > > r=. (,: i.y) SE (x-1);y-1 > > r </."1 i.y > > ) > > > parRuskeyEx =: 4 : 0 > > (,: i.y) SE (x-1);y-1 > > ) > > > ts'5 parRuskeyE 10' > 0.113852 3.89539e7 > ts'5 parRuskeyEx 10' > 0.0392047 8.39949e6 > > 2 parRuskeyE 3 > ┌───┬───┐ > │0 2│1 │ > ├───┼───┤ > │0 │1 2│ > ├───┼───┤ > │0 1│2 │ > └───┴───┘ > 2 parRuskeyEx 3 > 0 1 0 > 0 1 1 > 0 0 1 > (2 parRuskeyEx 3)</."1 [2 3 7 > ┌───┬───┐ > │2 7│3 │ > ├───┼───┤ > │2 │3 7│ > ├───┼───┤ > │2 3│7 │ > └───┴───┘ > > Cheers, > > Erling Hellenäs > > > > >> On 2017-11-04 18:00, 'Skip Cave' via Programming wrote: >> So, given the full parution set of say 3 par 4 >> >> ]a =. 3 par 4 >> >> ┌───┬───┬───┐ >> >> │0 1│2 │3 │ >> >> ├───┼───┼───┤ >> >> │0 2│1 │3 │ >> >> ├───┼───┼───┤ >> >> │0 │1 2│3 │ >> >> ├───┼───┼───┤ >> >> │0 3│1 │2 │ >> >> ├───┼───┼───┤ >> >> │0 │1 3│2 │ >> >> ├───┼───┼───┤ >> >> │0 │1 │2 3│ >> >> └───┴───┴───┘ >> >> >> What would the verb 'sel' look like that would use those indices to select >> from a different set of objects >> >> >> a sel 'abcd' >> >> ┌───┬───┬───┐ >> >> │a b│c │d │ >> >> ├───┼───┼───┤ >> >> │a c│b │d │ >> >> ├───┼───┼───┤ >> >> │a │b c│d │ >> >> ├───┼───┼───┤ >> >> │a d│b │c │ >> >> ├───┼───┼───┤ >> >> │a │b d│c │ >> >> ├───┼───┼───┤ >> >> │a │b │c d│ >> >> └───┴───┴───┘ >> >> >> Skip >> >> >> >> Skip Cave >> Cave Consulting LLC >> >>> On Sat, Nov 4, 2017 at 11:09 AM, Skip Cave <[email protected]> wrote: >>> >>> Raul, >>> Yes, the original Quora question specified positive factors only, but i >>> forgot to include that in the specification. >>> >>> Skip >>> >>> Skip Cave >>> Cave Consulting LLC >>> >>>> On Sat, Nov 4, 2017 at 3:52 AM, Raul Miller <[email protected]> wrote: >>>> >>>> Well, ok, though that was not a part of your re-specification this time. >>>> >>>> Actually, though, re-reading your spec, i left out a factor of 16 of >>>> the solutions: integers can be negative and as long as we include an >>>> even number of negatives they cancel out in a product. >>>> >>>> Thanks, >>>> >>>> -- >>>> Raul >>>> >>>> >>>> On Sat, Nov 4, 2017 at 2:28 AM, 'Skip Cave' via Programming >>>> <[email protected]> wrote: >>>>> Raul, very nice! >>>>> >>>>> Actually I prefer the solution that doesn't allow 1 as a factor of p. Of >>>>> course, that restricts the max number of partitions to the max number of >>>>> prime factors of any p. That also greatly reduces the number of >>>> partition >>>>> instances that will be generated. Then: >>>>> >>>>> 5 par 358258 >>>>> >>>>> ┌─┬─┬──┬──┬───┐ >>>>> >>>>> │2│7│11│13│179│ >>>>> >>>>> └─┴─┴──┴──┴───┘ >>>>> >>>>> Skip >>>>> >>>>> Skip Cave >>>>> Cave Consulting LLC >>>>> >>>>> On Fri, Nov 3, 2017 at 2:40 AM, Raul Miller <[email protected]> >>>> wrote: >>>>>> So... 358358 has five prime factors (32 integer factors). We want to >>>>>> find all sorted sequences (not sets - values can repeat) of five of >>>>>> those factors whose product is 358358. >>>>>> >>>>>> To restrict our search, we can investigate only those sorted sequences >>>>>> of "number of prime factors represented in the variable" whose sum is >>>>>> five: >>>>>> >>>>>> ~./:~"1 (#~ 5=+/"1) 6 #.inv i.6^5 >>>>>> 0 0 0 0 5 >>>>>> 0 0 0 1 4 >>>>>> 0 0 0 2 3 >>>>>> 0 0 1 1 3 >>>>>> 0 0 1 2 2 >>>>>> 0 1 1 1 2 >>>>>> 1 1 1 1 1 >>>>>> >>>>>> In other words, the results of these seven expressions (use >>>>>> require'stats' first to get comb): >>>>>> >>>>>> 1 1 1 1 >>>>>> >>>>>> 358358 >>>>>> (1 1 1,(358358%*/),*/)"1 (4 comb 5){q:358358 >>>>>> /:~"1 (1 1 1,(358358%*/),*/)"1 (3 comb 5){q:358358 >>>>>> /:~"1 (1 1,q:@(358358%*/),*/)"1 (3 comb 5){q:358358 >>>>>> ~./:~"1 (1 1,({.,*/@}.)@q:@(358358%*/),*/)"1 (2 comb 5){q:358358 >>>>>> /:~"1 (1,q:@(358358%*/),*/)"1 (2 comb 5){q:358358 >>>>>> q:358358 >>>>>> >>>>>> That's 44 different solutions: >>>>>> >>>>>> 1 1 1 1 358358 >>>>>> 1 1 1 179 2002 >>>>>> 1 1 1 13 27566 >>>>>> 1 1 1 11 32578 >>>>>> 1 1 1 7 51194 >>>>>> 1 1 1 2 179179 >>>>>> 1 1 1 154 2327 >>>>>> 1 1 1 182 1969 >>>>>> 1 1 1 143 2506 >>>>>> 1 1 1 286 1253 >>>>>> 1 1 1 91 3938 >>>>>> 1 1 1 77 4654 >>>>>> 1 1 1 358 1001 >>>>>> 1 1 1 26 13783 >>>>>> 1 1 1 22 16289 >>>>>> 1 1 1 14 25597 >>>>>> 1 1 13 154 179 >>>>>> 1 1 11 179 182 >>>>>> 1 1 11 13 2506 >>>>>> 1 1 7 179 286 >>>>>> 1 1 7 13 3938 >>>>>> 1 1 7 11 4654 >>>>>> 1 1 2 179 1001 >>>>>> 1 1 2 13 13783 >>>>>> 1 1 2 11 16289 >>>>>> 1 1 2 7 25597 >>>>>> 1 1 11 14 2327 >>>>>> 1 1 7 22 2327 >>>>>> 1 1 7 26 1969 >>>>>> 1 1 7 143 358 >>>>>> 1 1 2 77 2327 >>>>>> 1 1 2 91 1969 >>>>>> 1 1 2 143 1253 >>>>>> 1 11 13 14 179 >>>>>> 1 7 13 22 179 >>>>>> 1 7 11 26 179 >>>>>> 1 7 11 13 358 >>>>>> 1 2 13 77 179 >>>>>> 1 2 11 91 179 >>>>>> 1 2 11 13 1253 >>>>>> 1 2 7 143 179 >>>>>> 1 2 7 13 1969 >>>>>> 1 2 7 11 2327 >>>>>> 2 7 11 13 179 >>>>>> >>>>>> We could of course come up with a routine which does something similar >>>>>> for other examples (but we will run into prohibitive resource >>>>>> limitations if we allow large enough integers). >>>>>> >>>>>> So... just to confirm... this is the problem we are trying to solve? >>>>>> >>>>>> Thanks, >>>>>> >>>>>> -- >>>>>> Raul >>>>>> >>>>>> >>>>>> >>>>> ---------------------------------------------------------------------- >>>>> 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
