Code Golf: Lights out

Answer 1

Haskell, 263 characters (277 and 285 before edit) (according to wc)

import List
o x=zipWith4(\a b c i->foldr1(/=)[a,b,c,i])x(f:x)$tail x++[f]
f=0>0
d t=mapM(\_->[f,1>0])t>>=c t
c(l:m:n)x=map(x:)$c(zipWith(/=)m x:n)$o x l
c[k]x=[a|a<-[[x]],not$or$o x k]
main=interact$unlines.u((['.','X']!!).fromEnum).head.d.u(<'.').lines
u=map.map

This includes IO code : you can simply compile it and it works. This method use the fact that once the first line of the solution is determined, it is easy to determine what the other lines should look like. So we try every solution for the first line, and verify that the all lights are off on the last line, and this algorithm is O(n²*2^n)

Edit : here is an un-shrunk version :

import Data.List

-- xor on a list. /= works like binary xor, so we just need a fold
xor = foldr (/=) False

-- what will be changed on a line when we push the buttons :
changeLine orig chg = zipWith4 (\a b c d -> xor [a,b,c,d]) chg (False:chg) (tail chg ++ [False]) orig

-- change a line according to the buttons pushed one line higher :
changeLine2 orig chg = zipWith (/=) orig chg

-- compute a solution given a first line.
-- if no solution is given, return []

solution (l1:l2:ls) chg = map (chg:) $ solution (changeLine2 l2 chg:ls) (changeLine l1 chg)
solution [l] chg = if or (changeLine l chg) then [] else [[chg]]


firstLines n = mapM (const [False,True]) [1..n]

-- original uses something equivalent to "firstLines (length gris)", which only
-- works on square grids.
solutions grid = firstLines (length $ head grid) >>= solution grid

main = interact $ unlines . disp . head . solutions . parse . lines
    where parse = map (map (\c ->
                                case c of
                                  '.' -> False
                                  '*' -> True))
          disp = map (map (\b -> if b then 'X' else '.'))