n =: 5
Neighbors=: 3 3 ((>:i.n,n) e. (9$_1 1 _1 1 1 1) * ,);._3 >:m
,(m,.(i.n,n),.m),m=: *:n
out =: [ ~: Neighbors {~ <@]
----- Original Message -----
From: Roger Hui <[email protected]>
Date: Thursday, February 4, 2010 16:34
Subject: Re: [Jprogramming] Lights Out!
To: Programming forum <[email protected]>
> n =: 5
> Neighbors=: 3 3 ((9$_1 1 _1 1 1 1) * ,);._3 n ,(n,.(i.n,n),.n),n
>
> out =: [ ~: i...@$@[ e. Neighbors {~
> <@]
> BOARD0 out 3 2
> 0 0 0 0 0
> 0 0 0 0 0
> 1 0 0 0 1
> 0 1 1 1 0
> 0 0 1 0 0
>
>
>
> ----- Original Message -----
> From: Dan Bron <[email protected]>
> Date: Thursday, February 4, 2010 14:08
> Subject: [Jprogramming] Lights Out!
> To: 'Programming forum' <[email protected]>
>
> > When I was a kid I had a handheld version of the game "lights
> > out" [1,2], and I was addicted. The game is
> > played on a 5-by-5
> > board of lights, and starts with some of the lights on and all
> > the others off; the goal is to turn off all the lights.
> > You can
> > toggle the state of a light and its 4 neighbors (NSEW) by
> > pressing on it.
> >
> > For example, here is the classic starter board:
> >
> > 00000
> > 00000
> > 10101
> > 00*00
> > 00000
> >
> > Where 0 is an off light, 1 is an on light, and * is a light
> I'm
> > about to press (which happens to be off, but you can't see
> that in
> > this notation). After I press that light, the board looks
> > like this:
> >
> > 00000
> > 00000
> > 10001
> > 0111*
> > 00100
> >
> > Where again the light I'm about to press happens to be off
> (i.e.
> > there's a 0 under that *). Having pressed that, the board now
> > looks like this:
> >
> > 00000
> > 00000
> > 10000
> > 01101
> > 00101
> >
> > and so on until I turn off all the lights.
> >
> > I have an implementation of this in J that I wrote when I was
> > first learning the language (I frequently use this game as my
> > language-familiarization problem, following "Hello,world!" --
> I
> > have one in x86 assembler, somewhere). When I
> > wrote it, one of
> > the things that bothered me was that I couldn't come up with
> an
> > elegant, array-ish way to toggle the lights, given the light the
> > user pressed.
> >
> > So, given J's array mastery, can you? That is, given the inputs:
> >
> > ]
> > BOARD0 =: 5 5 $ 0 0 0 0 0 0 0 0 0 0 1 0 1 0
> > 1 0 0 0 0 0 0 0 0 0 0
> > 0 0 0 0 0
> > 0 0 0 0 0
> > 1 0 1 0 1
> > 0 0 0 0 0
> > 0 0 0 0 0
> >
> >
> > PUSH =: 3 2
> >
> > can you write a dyad out such that:
> >
> > ]
> > BOARD1 =: BOARD0 out PUSH
> > 0 0 0 0 0
> > 0 0 0 0 0
> > 1 0 0 0 1
> > 0 1 1 1 0
> > 0 0 1 0 0
> >
> >
> > in an elegant, array-oriented way? I'm thinking about
> > maybe an inner product of some sort, as opposed to calculating
> > the index
> > array and manually amending the board (e.g. BOARD0 4 : '(-. z
> {
> > x ) (z=.<"1 y <@+"1 _2 ]\ _1 0 0 _1 0 0
> > 0 1 1 0)} x' PUSH). I'd
> > also like to see solutions which avoid handling the edge- and
> > corner-cases specially, especially if this can be done *without*
> > changing the representation of the as a boolean table (but if
> > necessary, feel free to select your own representations for
> > BOARD or
> > PUSH).
> >
> > -Dan
> >
> > [1]: You can play the game online here:
> > http://www.whitman.edu/mathematics/lights_out/
> > and also see its Java
> > source.
> > [2] Wikipedia nicely describes the mathematics of Lights Out:
> > http://en.wikipedia.org/wiki/Lights_Out_(game)
> > including spoilers on how
> > to win (or write a program to determine if a given board is
> winnable).>
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