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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>
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