Hi all. Reading this list has been very useful as I've been learning J.
I'd like to ask for help in finding a simple tacit way to express f below,
or at least an appropriate commonly-used tacit J idiom.
Say s is a symmetric boolean matrix with 1's on the diagonal, and define:
f =: 3 : 0
for_k. i.#y do. y =. (<:~ k&{) y end.
*/ y
)
e.g.
] s =: ((= |:) (?. 10 10 $ 2))
1 0 0 0 1 1 0 1 0 0
0 1 0 0 0 1 1 1 1 1
0 0 1 0 1 1 0 0 0 0
0 0 0 1 1 1 1 1 1 0
1 0 1 1 1 0 0 1 1 1
1 1 1 1 0 1 1 0 1 0
0 1 0 1 0 1 1 0 1 0
1 1 0 1 1 0 0 1 0 1
0 1 0 1 1 1 1 0 1 1
0 1 0 0 1 0 0 1 1 1
f s
1 0 0 0 1 0 0 1 0 0
One way to describe f is: given undirected graph s it finds a maximal
clique:
http://mathworld.wolfram.com/MaximalClique.html
(maximal clique, not maximum clique... which would be NP-hard)
The 1's in (f s) mark a clique of nodes linked by edges (marked by 1's in s)
and this clique is maximal in that nothing can be added to it.
One tacit approach is to translate the for loop using a boxed list of
indices:
g =: [: */@>@((]<:~{)&.>/) <"0@|.@i.@# , <
g s
1 0 0 0 1 0 0 1 0 0
Another is to rotate repeatedly so the head is always next to be processed:
h =: */@(([:(1 1)&|.]<:~{.)^:#)
h s
1 0 0 0 1 0 0 1 0 0
But these seem somewhat awkward to me.
The explicit function f has just two verbs inside the body of the for loop,
so I was hoping to find a tacit solution that also needed at most two verbs
inside the / or ^: or whatever else is used to replace the loop.
Any ideas?
Or maybe there is an entirely different approach, more suited to tacit J?
Thanks.
-Chris
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