I don't think your S3 is overkill, actually it simplifies the prefixes-suffixes
machinery.
;<@(2018 (#-1+I.)@e.~ (-~{:))\ 6%~ (* (>: * >:@+:)) i.>.%:2018
12
/:~;(3 : '<@(y |:@(](#~,: (#-1+I.)@])e.~) (-~{:))\ 6%~ (* (>:* >:@+:))
i.>.%:>./y')2019+i:50
1969 11
1985 2
2010 5
2018 12
2025 1
2030 3
2030 4
2051 7
2054 13
R.E. Boss
> -----Oorspronkelijk bericht-----
> Van: Programming <[email protected]>
> Namens 'Mike Day' via Programming
> Verzonden: donderdag 24 oktober 2019 11:08
> Aan: [email protected]
> Onderwerp: Re: [Jprogramming] Quora problem
>
> (I see RE Boss has just posted, while I was drafting - sorry if it's the
> same!)
>
> I thought to exploit the property that
> S3(n) = sum i^2, i <: n, is n(n+1)(2n+1)%6 but solving S(n) - S(m) = 2018
> isn't
> that easy!
> Anyway, we could define
> S3 =: 6 <.@%~ (* (>: * >:@+:))
> but as we need a string of squares it's overkill.
> Either way, it's useful to be able to identify the indices of ones in a
> boolean
> matrix:
> ixbin =: $#.inv I.@,
>
> So we get, accprding to taste:
>
> -/"1 ixbin 2018 = -/~ +/\ *: i. >: 20
> 12
> -/"1 ixbin 2018 = -/~ S3 i. 20 NB. not as efficient as it looks!
> 12
>
>
> ts'-/"1 ixbin 2018 = -/~ S3 i. 20'
> 1.53e_5 8768
> ts'-/"1 ixbin 2018 = -/~ +/\ *: i. >: 20'
> 8.7e_6 9856
>
> MIke
>
>
>
>
> On 24/10/2019 07:36, Skip Cave wrote:
> > I occasionally try to solve Quora math problems to polish my J skills.
> > Here's a problem that
> >
> > * "The integer 2018 can be written uniquely as the sum of consecutive
> > squared integers. How many squares does the sum contain?"*
> >
> > a=.2^~i.100
> >
> > NB. Find how many consecutive squared integers it takes to sum to
> > 2018. Try each length until I get a hit.
> >
> > +/2018=+/"1]5,\a
> >
> > 0
> >
> > +/2018=+/"1]6,\a
> >
> > 0
> >
> > +/2018=+/"1]7,\a
> >
> > 0
> >
> > +/2018=+/"1]8,\a
> >
> > 0
> >
> > +/2018=+/"1]9,\a
> >
> > 0
> >
> > +/2018=+/"1]10,\a
> >
> > 0
> >
> > +/2018=+/"1]11,\a
> >
> > 0
> >
> > +/2018=+/"1]12,\a
> >
> > 1 NB. A hit!
> >
> > +/2018=+/"1]13,\a
> >
> > 0
> >
> >
> > So the answer is 12
> >
> > List them:
> >
> > b#~2018=+/"1 b=.12,\a
> >
> > 49 64 81 100 121 144 169 196 225 256 289 324
> >
> >
> > Is there a way to do this search without explicit looping?
> >
> >
> > Skip
> >
> >
> > Skip Cave
> > Cave Consulting LLC
> > ----------------------------------------------------------------------
> > For information about J forums see
> http://www.jsoftware.com/forums.htm
>
>
>
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