[Jprogramming] Interesting Quora Problem:
Quora Question: Can you arrange the digits 1-9 to make a nine-digit number
such that the first digit is divisible by one, the first two digits are
divisible by two, the first three divisible by three and so on?
My solution:
ea=.&.>
at=.>10#.ea(a=.362880 9$1 to 9){.ea{n=.>:perm 9
{:"1 at#~*./"1[0=a|"1 at
381654729
The answer is 381654729.
Check:
]m=.>10#.ea(;/1 to 9){.ea{sep 381654729
3 38 381 3816 38165 381654 3816547 38165472 381654729
(1 to 9)| m
0 0 0 0 0 0 0 0 0
There is only one answer. Is there a way to simplify or minimize the big
repetitive array 'a' to make the two J code lines more memory efficient &
succinct?
Skip Cave
Cave Consulting LLC
--
For information about J forums see http://www.jsoftware.com/forums.htm
Re: [Jprogramming] Interesting Quora Problem:
I guess to simplify it, I would filter the possibilities at each step.
first digit divisible by 1:
N1=: 1+i.9
Second digit divisible by 2:
N2=: ;(10*N1)+each (<2*1+i.4)-.each N
Third digit divisible by 3:
digits=: 10&#.inv
N3=: (#~ 0=3|]);(10*N2)+each (<1+i.9) (-. digits) each N2
And, so on... and since we're basically doing the same thing at each
step, we could encapsulate and parameterize this step as a function.
F=: {{(#~ 0=x|]);(10*y)+each ( wrote:
>
> Quora Question: Can you arrange the digits 1-9 to make a nine-digit number
> such that the first digit is divisible by one, the first two digits are
> divisible by two, the first three divisible by three and so on?
>
> My solution:
> ea=.&.>
>
> at=.>10#.ea(a=.362880 9$1 to 9){.ea{n=.>:perm 9
>
> {:"1 at#~*./"1[0=a|"1 at
>
> 381654729
>
>
> The answer is 381654729.
>
>
> Check:
>
> ]m=.>10#.ea(;/1 to 9){.ea{sep 381654729
>
> 3 38 381 3816 38165 381654 3816547 38165472 381654729
>
> (1 to 9)| m
>
> 0 0 0 0 0 0 0 0 0
>
>
> There is only one answer. Is there a way to simplify or minimize the big
> repetitive array 'a' to make the two J code lines more memory efficient &
> succinct?
>
>
> Skip Cave
> Cave Consulting LLC
> --
> For information about J forums see http://www.jsoftware.com/forums.htm
--
For information about J forums see http://www.jsoftware.com/forums.htm
Re: [Jprogramming] Interesting Quora Problem:
If we do a bit of work by ourselves? Consider that the 5 has to be in fifth
position (starting from 1), and that there must be even digits (four of
them) on the even positions. The other four odd digits go to the remaining
odd positions. Then there are only 576 possibilities left.
odds =: (i.24) A. '1379' NB. there's a better trick, is there?
evens =: (i.24) A. '2468'
all =: ,/ odds {{ }. x 1 3 7 9 } y 2 4 6 8 } '0oeoe5eoeo' }}"1/ evens
all #~ (1+i.9) {{*./ 0 = x | ". x {."0 1 y }}"1 all
381654729
Direct Definition rules!
Greetings,
Ben
On Mon, 11 Sept 2023 at 08:09, Raul Miller wrote:
> I guess to simplify it, I would filter the possibilities at each step.
>
> first digit divisible by 1:
>N1=: 1+i.9
>
> Second digit divisible by 2:
>N2=: ;(10*N1)+each (<2*1+i.4)-.each N
>
> Third digit divisible by 3:
>digits=: 10&#.inv
>N3=: (#~ 0=3|]);(10*N2)+each (<1+i.9) (-. digits) each N2
>
> And, so on... and since we're basically doing the same thing at each
> step, we could encapsulate and parameterize this step as a function.
>
>F=: {{(#~ 0=x|]);(10*y)+each (9 F 8 F 7 F 6 F 5 F 4 F 3 F 2 F N1
> 381654729
>
>timespacex '9 F 8 F 7 F 6 F 5 F 4 F 3 F 2 F N1'
> 0.0006679 38400
>
> So that took about a millisecond of machine time on this little laptop.
>
> Further simplifications are possible, but since this is a one use
> calculation this is probably good enough.
>
> --
> Raul
>
> On Sun, Sep 10, 2023 at 2:02 PM 'Skip Cave' via Programming
> wrote:
> >
> > Quora Question: Can you arrange the digits 1-9 to make a nine-digit
> number
> > such that the first digit is divisible by one, the first two digits are
> > divisible by two, the first three divisible by three and so on?
> >
> > My solution:
> > ea=.&.>
> >
> > at=.>10#.ea(a=.362880 9$1 to 9){.ea{n=.>:perm 9
> >
> > {:"1 at#~*./"1[0=a|"1 at
> >
> > 381654729
> >
> >
> > The answer is 381654729.
> >
> >
> > Check:
> >
> > ]m=.>10#.ea(;/1 to 9){.ea{sep 381654729
> >
> > 3 38 381 3816 38165 381654 3816547 38165472 381654729
> >
> > (1 to 9)| m
> >
> > 0 0 0 0 0 0 0 0 0
> >
> >
> > There is only one answer. Is there a way to simplify or minimize the big
> > repetitive array 'a' to make the two J code lines more memory efficient &
> > succinct?
> >
> >
> > Skip Cave
> > Cave Consulting LLC
> > --
> > 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
Re: [Jprogramming] Interesting Quora Problem:
Wow! Raul & Ben both provided solutions to my Quora problem that were
radically different from my original solution, and radically different from
each other. Both solutions reduced the execution time & space by several
orders of magnitude, when compared with my original solution. Also, both
used different approaches that took advantage of features in J which I knew
about, but had not used very much. A good learning experience.
Raul used a 'chain of dyadic verbs' (x F x F x F y) to solve the problem. I
haven't ever tried this, where right-to-left execution is used to feed the
result of one dyadic verb into the next one on the left. It was a bit
confusing until I realized that the rightmost verb 'eats' its left
argument, so that the verb result is passed to the next verb on the left,
instead of the previous verb's left argument. This problem provides a good
example of the use of this feature. I wonder if this linear 'chain of
verbs' could be replaced with the hatco operator (^:)?
Ben used the Anagram primitive (A.) to generate permutations of digits.
Now I'm still trying to get my head around (parse) the two direct
definitions Ben provided:
all =: ,/ odds {{ }. x 1 3 7 9 } y 2 4 6 8 } '0oeoe5eoeo' }}"1/ evens
all #~ (1+i.9) {{*./ 0 = x | ". x {."0 1 y }}"1 all
If explained in detail, this example would make a good tutorial on how to
use Direct Definition.
This Quora problem shows the versatility of J primitives, and how J can
provide multiple tools for different approaches to solve a specific
problem.
Skip Cave
Cave Consulting LLC
On Sun, Sep 10, 2023 at 1:01 PM Skip Cave wrote:
> Quora Question: Can you arrange the digits 1-9 to make a nine-digit number
> such that the first digit is divisible by one, the first two digits are
> divisible by two, the first three divisible by three and so on?
>
> My solution:
> ea=.&.>
>
> at=.>10#.ea(a=.362880 9$1 to 9){.ea{n=.>:perm 9
>
> {:"1 at#~*./"1[0=a|"1 at
>
> 381654729
>
>
> The answer is 381654729.
>
>
> Check:
>
> ]m=.>10#.ea(;/1 to 9){.ea{sep 381654729
>
> 3 38 381 3816 38165 381654 3816547 38165472 381654729
>
> (1 to 9)| m
>
> 0 0 0 0 0 0 0 0 0
>
>
> There is only one answer. Is there a way to simplify or minimize the big
> repetitive array 'a' to make the two J code lines more memory efficient &
> succinct?
>
>
> Skip Cave
> Cave Consulting LLC
>
--
For information about J forums see http://www.jsoftware.com/forums.htm
