Your solution works only because the list isn't too long, and the initial
13| (same as 13 |/) made them all small enough that you can do the */
without losing precision. But if the list were longer:
13 | */ 13 | 10 # 19 29 59 79 89 109 119 139 149 179 199
0
If it makes it more understandable, use explicit defn:
(4 : '13|x*y') / 19 29 59 79 89 109 119 139 149 179 199
4
"Multiplication mod m" means m|x*y, multiply, then take the remainder of
division by m.
On Mon, Sep 18, 2017 at 11:37 AM, Skip Cave <s...@caveconsulting.com> wrote:
> Yes, one of the Quora answer posts for this challenge pointed this out as
> well, so I tried that approach. Not being too competent with the use of &
> @, I tried:
>
> 13|*/13|/19 29 59 79 89 109 119 139 149 179 199
>
> 4
>
>
> I got the answer, but I need a course on the use of @ and & in order to
> tighten up my code.
>
>
> Skip
>
>
> Skip Cave
> Cave Consulting LLC
>
> On Mon, Sep 18, 2017 at 12:47 PM, Roger Hui <rogerhui.can...@gmail.com>
> wrote:
>
> > 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
> >
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
