Your solution is as elegant as brilliant in its simplicity. And your
explanation is admirable.
I noticed the similarity with nested parenthesized expressions and even
remembered these were solved, but could not find the appropriate post(s).
I did not however, realize that 'top level items' were the odd and 'nested
items' were the even ones. Smart observation.
Nor did I know (or was forgotten, but what's the difference?) about the
gerundial form of cut.
Even though I do not like $: , I see no way to improve your solution (be it
that I prefer 2 >/\ {.<] above 2 ~:/\ ]={. ).
Thanks for jumping in when you are needed.
R.E. Boss
-----Oorspronkelijk bericht-----
Van: [email protected]
[mailto:[email protected]] Namens Dan Bron
Verzonden: vrijdag 25 november 2011 4:43
Aan: 'Programming forum'
Onderwerp: Re: [Jprogramming] multiple boxing
This looks similar to boxing a recursively nested parenthesized expression
(or XML, or whatever). So, we can use recursion:
foo =: ] <`(<@$:);.1~ 1 , 2 ~:/\ ]={.
foo 1 1 2 2 3 3 4 2 3 4 4 1 2 2 2 1
+---+---------------------------+-+-------+-+
|1 1|+---+---------+-+---------+|1|+-----+|1|
| ||2 2|+---+---+|2|+-+-----+|| ||2 2 2|| |
| || ||3 3|+-+|| ||3|+---+||| |+-----+| |
| || || ||4||| || ||4 4|||| | | |
| || || |+-+|| || |+---+||| | | |
| || |+---+---+| |+-+-----+|| | | |
| |+---+---------+-+---------+| | | |
+---+---------------------------+-+-------+-+
We start by cutting the list into "top level" items, and "nested" items.
Having done this, we only need to recurse into the nested items and process
them similarly.
Of course, since series of top-level items are grouped together until
interrupted a nested item, the list will end up alternating between groups
(boxes) of top-level items and groups of nested items, like A B A B A B. So
we only need to recurse into the odd boxes, and leave the even boxes alone.
The verb's relative simplicity arises from this observation, and the cute
gerundial form of ;. which allows us to say f`g;.1 where f and g will be
applied cyclically to the partitions of the argument (but if we didn't have
that feature, we could emulate it with ^: ).
-Dan
PS:
This assumes you trust $: not to abort with a stack error, which it does
sometimes. Though I'd only expect that with long and deeply-nested
arguments.
But if you wanted to be certain ab initio (or you just have time to kill and
find J amusing), you could try rewriting the verb using a bottom-up approach
based on ^: . You even could start with the code you (REB) provided to me
in a similar thread back in 2009 [1].
[1] Thread "Recursive nesting, avoiding recursion"
http://www.jsoftware.com/pipermail/programming/2009-August/016181.html
PPS: Happy Thanksgiving!
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of R.E. Boss
Sent: Thursday, November 24, 2011 9:27 AM
To: Programming forum
Subject: [Jprogramming] multiple boxing
Given an array of positive integers A starting with 1 and such that 2 > >./
2 -~/\ A
(a next atom in A is at most 1 larger than the preceding one).
Now I want the items to be boxed according to this example
foo 1 1 2 2 3 3 4 2 3 4 4 1 2 2 2 1
+---+---------------------------+-+-------+-+
|1 1|+---+---------+-+---------+|1|+-----+|1|
| ||2 2|+---+---+|2|+-+-----+|| ||2 2 2|| |
| || ||3 3|+-+|| ||3|+---+||| |+-----+| |
| || || ||4||| || ||4 4|||| | | |
| || || |+-+|| || |+---+||| | | |
| || |+---+---+| |+-+-----+|| | | |
| |+---+---------+-+---------+| | | |
+---+---------------------------+-+-------+-+
Any suggestions for foo?
R.E. Boss
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