Raul wrote:
> out=: [ ~: 1 1}. _1 _1}. -...@] |. (0 1 0,1,:0 1 0) {.~ 2 + $...@[
Roger wrote:
> N=: 3 3 (j e. (9$0 1 0 1 1 1) # ,);._3 ] _,(_,.j,._),_: j=. i.n,n
> out =: [ ~: N {~ <@]
Raul calculates the neighborhood at runtime. Roger generates the entire
catalog of neighborhoods in advance. We could take a hybrid approach; we
don't have to generate the entire catalog of neighborhoods, but if we store
just enough, we can still use cut and avoid explicit mention of the edge-
and corner-cases:
Nd =. (,~>:n) |. (,~>:+:n) {. #: 2 7 2
out =: ~: Nd ];.0~ n&([ ,:~ 1 + -)
Neighbors -: ($&0 out "_ 1 ] #: i.) ,~n
1
I haven't checked, but of the three, I'd assume Roger's to be fastest,
because having generated and cached the neighborhood catalog, when applied,
his out needs only to do one { and (and then the ~: which all the verbs
must do). This is in contrast to the other approaches which do more
calculations per application.
Another contrast is between the "structural" and "mathematical" approaches,
where the arrays are represented and manipulated differently (e.g. in terms
of shapes vs in terms of values). I'm going to see if I can make another
hybrid, this time mixing Raul's runtime approach with the mathematical 2&^.
representation I touched on yesterday (which took Roger's catalog approach).
-Dan
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