Over lunch, I just realized that my second implementation using integer digits
could be expressed a lot more directly:
, 10#. ,"1/^:3~ ,. 0 1 2 6
0 1 2 6 10 11 12 16 20 21 22 26 60 61 62 66 100 101 102 106 110 111 ...
Which nicely mirrors the implementation using strings.
On Mon, Oct 21, 2019 at 11:32:54AM +0900, 'B. Wilson' via Programming wrote:
> I was a bit eager on the send button with that last message.
>
> Here is the previous approach, removing some superfluous stuff:
>
> , ". ,"1/^:3~ ,. '0126'
> 0 1 2 6 10 11 12 16 20 21 22 26 60 61 62 66 100 101 102 106 110 111 ...
>
> And here is essentially the same approach, but treating digits as actual
> numbers:
>
> ({~ /:) , 10&#.@,"0/~^:3~ 0 1 2 6
> 0 1 2 6 10 11 12 16 20 21 22 26 60 61 62 66 100 101 102 106 110 111 ...
>
> In either case, we are just taking the Cartesian product S^n X S, i.e. the
> ,"0/~ part. This then reduces the problem to finding a function from said
> product down to the integers. I the first case, ". reads our strings of
> digits into numbers, while in the second case 10&#. effectively converts our
> list of digits into their base-10 integers.
>
> Feel free to ask if anything is unclear! I'm just beginning with J myself,
> too, so there might be some way better approach that I missed.
>
> On Mon, Oct 21, 2019 at 10:38:10AM +0900, 'B. Wilson' via Programming wrote:
> > What about something like this?
> >
> > , ". (,/@:,"1/)^:3~ ,.'0126'
> > 0 1 2 6 10 11 12 16 20 21 22 26 60 61 62 66 100 101 102 106 110 111 ...
> >
> > If S is the set of our digits, then the above essentially is just the
> > Cartesian product S^4.
> >
> > On Sun, Oct 20, 2019 at 06:08:48PM -0500, Skip Cave wrote:
> > > Is there a less-verbose way to list all the integers (one-digit,
> > > two-digit,
> > > three-digit, four-digit) can be formed by using the characters 0, 1, 2,
> > > and
> > > 6 once? I used multiple takes:
> > >
> > > *#b=.~.>10#.ea({1{."1 a),({2{."1 a),({3{."1 a),{a=.(perm 4){0 1 2 6*
> > >
> > > *49*
> > >
> > > *b*
> > >
> > > *0 1 2 6 10 12 16 20 21 26 60 61 62 102 106 120 126 160 162 201 206 210
> > > 216
> > > 260 261 601 602 610 612 620 621 1026 1062 1206 1260 1602 1620 2016 2061
> > > 2106 2160 2601 2610 6012 6021 6102 6120 6201 6210*
> > >
> > >
> > > Skip Cave
> > > Cave Consulting LLC
> > > ----------------------------------------------------------------------
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> > ----------------------------------------------------------------------
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