This particular problem can be solved without resort to extended
precision. Use multiplication mod 13, that is, find the remainder at each
step rather than waiting until the end:
13&|@* / 19 29 59 79 89 109 119 139 149 179 199
4
On Mon, Sep 18, 2017 at 10:00 AM, Skip Cave <s...@caveconsulting.com> wrote:
> People posting problems on Quora are typically expecting an explicit
> algebraic formula solution to their problem, though they never explicitly
> state that requirement. The posted Quora problems often involve very large
> numbers, which the poster expects will prevent solutions from using a
> calculator or computer program to solve. In most cases, J's extended
> precision arithmetic can handle those large numbers quite handily.
>
> Typical Quora problem:
> How would you calculate the remainder of {19 × 29 × 59 × 79 × 89 × 109 ×
> 119 × 139 × 149 × 179 × 199} divided by 13?
> <https://www.quora.com/How-would-you-calculate-the-
> remainder-of-19-%C3%97-29-%C3%97-59-%C3%97-79-%C3%97-89-%C3%
> 97-109-%C3%97-119-%C3%97-139-%C3%97-149-%C3%97-179-%C3%97-
> 199-divided-by-13>
>
> My answer:
>
> Using the J programming language (Jsoftware.com)
>
> 13|*/19 29 59 79 89 109 119 139 149 179 199x
>
> 4
>
> So the answer is 4
>
>
> Skip Cave
> Cave Consulting LLC
>
> On Mon, Sep 18, 2017 at 6:17 AM, Raul Miller <rauldmil...@gmail.com>
> wrote:
>
> > That has been characteristic of Project Euler but Quora Challenges are
> > new to me.
> >
> > Anyways, if the problem expects to answers work with precisions well
> > beyond measurable limits, that should be stated as a part of the
> > problem.
> >
> > Thanks,
> >
> > --
> > Raul
> >
> >
> > On Sun, Sep 17, 2017 at 2:05 PM, Skip Cave <s...@caveconsulting.com>
> > wrote:
> > > The fact that the problem is a Quora challenge is exactly the point.
> It's
> > > like if someone asks your for the square root of 75976307044. Yes,
> there
> > is
> > > a manual process that one can use to compute the square root. But why
> > spend
> > > all that time when one can type %:75976307044 or use a hand-held
> > > calculator, and get the answer instantly. As an engineer, speed and
> > > accuracy are more important than going through a complicated manual
> > process
> > > to get that same answer.
> > >
> > > I post lots of these J solutions on Quora to remind folks of that fact.
> > > It's not that I'm against knowing the manual approach to the solutions.
> > > It's just that the more tools we have to make hard problems easier, the
> > > better we can solve even harder problems.
> > >
> > > Skip Cave
> > > Cave Consulting LLC
> > >
> > > On Sun, Sep 17, 2017 at 12:28 PM, Erling Hellenäs <
> > erl...@erlinghellenas.se>
> > > wrote:
> > >
> > >> Strange things happen here. It works but give incorrect results. I
> just
> > >> changed F to lower case to put it through my tests. Not sure what
> might
> > >> happen here. I have J 8.04 on this machine. 64 bit.
> > >> I never doubted that p: was good. I just thought that since it was a
> > Quora
> > >> challenge that using p: would not be a good idea, since the algorithm
> > used
> > >> in p: is not known to the audience. It also seemed like some kind of
> > >> cheating, like using a subroutine someone else wrote to solve half the
> > >> problem.
> > >> Well, I also thought p: would have to generate the array of primes for
> > >> each call, but it's obviously not the case. There is a formula which
> > does
> > >> the trick? Or a hash table of primes?
> > >>
> > >> thru=: <. + >:@>. i.@- <.
> > >>
> > >> biggap=: {~ 0 1 - [: (i. <./) 2 -/\ ]
> > >>
> > >> f=: [: thru/ 1 _1 + [: biggap <./ >. >./ <. thru&.(p:inv)
> > >>
> > >> s=: 10 f 100
> > >>
> > >> s
> > >>
> > >> 20 21 22
> > >>
> > >> >./90 91 92 93 94 95 96 = s
> > >>
> > >> |length error: scriptd
> > >>
> > >> | >./90 91 92 93 94 95 96 =s
> > >>
> > >> |[-5] j:\j64-803-user\projects\quoraraul.ijs
> > >>
> > >> inv
> > >>
> > >> ^:_1
> > >>
> > >>
> > >> Cheers,
> > >>
> > >> Erling
> > >>
> > >> On 2017-09-17 17:38, Raul Miller wrote:
> > >>
> > >>> Yes. :)
> > >>>
> > >>> When J provides a mechanism for something it is usually worth trying.
> > >>> Sometimes you can write something faster, but usually J's approach
> > >>> will be useful.
> > >>>
> > >>> For example, in this case, consider this approach:
> > >>>
> > >>> thru=: <. + >:@>. i.@- <.
> > >>> biggap=: {~ 0 1 - [: (i. <./) 2 -/\ ]
> > >>> F=: [: thru/ 1 _1 + [: biggap <./ >. >./ <. thru&.(p:inv)
> > >>>
> > >>> There will be cases where another approach could be more efficient,
> > >>> but it performs reasonably well.
> > >>>
> > >>> Thanks,
> > >>>
> > >>>
> > >> ------------------------------------------------------------
> ----------
> > >> 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
