So far, Roger's solution for counting the divisors of any integer using __
q: seems the most efficient.
* div=:3 :'*/>:{:__ q:y'*
Test it:
* >div each 10 47 360 2357047123200*
*4 2 24 1620*
* ts '>div each 10 47 360 2357047123200' *
*2.89e_5 10944*
Finding and listing the actual divisors is much more resource-intensive in
both time and space.
Skip Cave
Cave Consulting LLC
On Sat, Apr 25, 2020 at 5:47 AM 'Michael Day' via Programming <
[email protected]> wrote:
> Yes, that works as expected.
>
> BUT consider:
>
> __ q: 360 NB. generate a table of primes and powers:
> 2 3 5
> 3 2 1
> ((3+3*>:i._10),:~p:i.10) NB. set up a bigger table
> 2 3 5 7 11 13 17 19 23 29
> 33 30 27 24 21 18 15 12 9 6
> NB. generate a number from it:
> __ q: N NB. __ q: factors it quite fast
> 2 3 5 7 11 13 17 19 23 29
> 33 30 27 24 21 18 15 12 9 6
> _ q: N NB. so does _ q:
> 33 30 27 24 21 18 15 12 9 6
>
> ts'__ q: N'
> 0.0001254 45504
> ts'_ q: N'
> 0.0001236 61696
> */>:_ q: N NB. the number of divisors is quite large!
> 4490309824000
>
> */>: 33 30 27 24 21 18 15 12 9 6 NB. checking result
> 4490309824000
>
> The performance of q: in its various guises will of course deteriorate
> with the
>
> presence of large prime factors!
>
> Anyway, it's advisable not to generate all divisors here unless you
> really need them!
>
> Cheers,
>
> Mike
>
> Note - I've trimmed the history below here...
>
> On 25/04/2020 03:47, Devon McCormick wrote:
> > I found this one in my bag of tricks:
> > allFactors=: */&>@{@((^ i.@>:)&.>/)@q:~&__
> > #,allFactors */p:i.10
> > 1024
> >
> >
> > On Fri, Apr 24, 2020 at 7:15 PM 'Mike Day' via Programming <
> > [email protected]> wrote:
> >
> >> Numbers of divisors below, not the divisors themselves... the thread had
> >> split! I was attempting to comment on Hauke Rehr’s post.
> >> M
> >>
> >> Sent from my iPad
> >>
> >>> On 24 Apr 2020, at 23:52, 'Jon' via Programming <
> >> [email protected]> wrote:
> >>> This is missing a few divisors. It seems Skip's original method would
> be
> >> difficult to beat. It's O(n) in time and space. You could improve space
> >> complexity by doing a simple loop, but as far as I can see there are no
> >> shortcuts, and the best way is to just "brute force" it.
> >>> Sent from BlueMail
> >>>
> >>>> On Apr 25, 2020, 5:35 AM, at 5:35 AM, 'Mike Day' via Programming <
> >> [email protected]> wrote:
> >>>> I think this is near to the approved way:
> >>>>
> >>>> (*/"1@:>:@(_& q:))24 360 4711
> >>>> 8 24 4
> >>>>
> >>>> Mike
> >>>>
> >>>> Sent from my iPad
> >>>>
> >>>>> On 24 Apr 2020, at 21:13, Hauke Rehr <[email protected]> wrote:
> >>>>>
> >>>>> I now have an answer for the number of results:
> >>>>>
> >>>>> */ >: +/"1 (=/~ ~.) q: 4711
> >>>>> 4
> >>>>> */ >: +/"1 (=/~ ~.) q: 42
> >>>>> 8
> >>>>>
> >>>>> I hesitate using =/~ (it’s actually deprecated)
> >>>>> but I wouldn’t know a better way in this case
> >>>>>
> >>>>>
> >>>>>
>
> --
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