{-# LANGUAGE ImplicitParams #-}
-- ABC logic puzzle
module Main where
import Control.Monad
import Data.List
import Data.Array.IArray
import MiniSat
import Safe
import System.Environment
import System.Random.Shuffle
import System.Random
type Puzzle = Array Int (Array Int Field) -- rows of columns
type Field = Array Int Lit
data Hints = Hints {
top, right, bottom, left :: Array Int Field}
data Full = Full { puzzle :: Puzzle, hints :: Hints}
genLit :: (?solver :: Solver) => IO Lit
genLit = newLit ?solver
replicateAM :: Monad m => Int -> m a -> m (Array Int a)
replicateAM l m = liftM (listArray (0,l-1)) (replicateM l m)
replicateA :: Int -> a -> Array Int a
replicateA l m = listArray (0,l-1) (replicate l m)
genField :: (?letters :: Int, ?solver :: Solver) => IO Field
genField = replicateAM (?letters+1) genLit
genPuzzle :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => IO Puzzle
genPuzzle = replicateAM ?size $ replicateAM ?size genField
genHints :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => IO Hints
genHints = liftM4 Hints side side side side
where side = replicateAM ?size genField
genFull :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => IO Full
genFull = liftM2 Full genPuzzle genHints
addClause' :: (?solver :: Solver) => [Lit] -> IO ()
addClause' c = addClause ?solver c >> return ()
addClauses :: (?solver :: Solver) => [[Lit]] -> IO ()
addClauses = mapM_ addClause'
lx :: (?letters :: Int) => [Int]
lx = [1 .. ?letters]
fx :: (?letters :: Int) => [Int]
fx = [0 .. ?letters]
sx :: (?size :: Int) => [Int]
sx = [0 .. ?size - 1]
sx_reverse :: (?size :: Int) => [Int]
sx_reverse = [?size - 1, (?size - 2).. 0]
conHint :: (?letters :: Int, ?solver :: Solver) => Field -- ^ hint field
-> [Field] -- ^ neighbouring fields, the closest field is last
-- in the list
-> IO ()
conHint hint neigh = addClauses[ hint ! l : hint ! 0 : neg (f ! l) : blanks r
| l <- lx, (f:r)<- init $ tails neigh]
where blanks = map (\f -> neg (f!0))
conBottomHints :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Array Int Field -> Puzzle -> IO ()
conBottomHints h p = sequence_ [conHint (h!i) [(p!j)!i|j<-[(?letters-1) .. (?size-1)]]| i <- sx]
>> mapM_ conField (elems h)
conRightHints :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Array Int Field -> Puzzle -> IO ()
conRightHints h p = sequence_ [conHint (h!i) [(p!i)!j|j<-[(?letters-1) .. (?size-1)]]| i <- sx]
>> mapM_ conField (elems h)
conTopHints :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Array Int Field -> Puzzle -> IO ()
conTopHints h p = sequence_ [conHint (h!i) [(p!j)!i|j<-[(?size - ?letters),(?size - ?letters - 1) .. 0]]| i <- sx]
>> mapM_ conField (elems h)
conLeftHints :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Array Int Field -> Puzzle -> IO ()
conLeftHints h p = sequence_ [conHint (h!i) [(p!i)!j|j<-[(?size - ?letters),(?size - ?letters - 1) .. 0]]| i <- sx]
>> mapM_ conField (elems h)
conHints :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Full -> IO ()
conHints (Full p h) = conBottomHints (bottom h) p >> conRightHints (right h) p
>> conTopHints (top h) p >> conLeftHints (left h) p
conFull :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Full -> IO ()
conFull full = conPuzzle (puzzle full) >> conHints full
conField :: (?letters :: Int, ?solver :: Solver) => Field -> IO ()
conField l = do addClause' $ elems l
addClauses [ [neg (l!i), neg (l!j)] | i <- fx, j <- [0 .. i-1]]
conFields :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Puzzle -> IO ()
conFields p = sequence_ [conField ((p!i)!j) | i <- sx, j <- sx]
-- fields must be different letters (however, both can be blank)
conDiffFields :: (?letters :: Int, ?solver :: Solver) => Field -> Field -> IO ()
conDiffFields l1 l2 = do
addClauses [[neg (l1!i), neg (l2!i)] | i <- lx]
conRows :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Puzzle -> IO ()
conRows p = do
-- fields must be different letters
sequence_ [conDiffFields (r!i) (r!j) | r <- elems p, i <- sx, j <- [0..i-1]]
-- each letter must appear
addClauses [[(r!i)!l | i <- sx] | r <- elems p, l <- lx]
conColumns :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Puzzle -> IO ()
conColumns p = do
-- letters must be different letters
sequence_ [conDiffFields ((p!i)!c) ((p!j)!c) | c <- sx, i <- sx, j <- [0..i-1]]
-- each letter must appear
addClauses [[((p!i!)c)!l | i <- sx] | c <- sx, l <- lx]
conPuzzle :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Puzzle -> IO ()
conPuzzle p = conRows p >> conColumns p >> conFields p
data Entry = Blank
| Letter Int
instance Show Entry where
show Blank = " "
show (Letter l) = [iterate succ 'A' !! l]
newtype Solution = Solution {unSolution :: Array Int (Array Int (Entry))}
instance Show Solution where
show = unlines . map (unwords . map show . elems) . elems . unSolution
getSolution :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Puzzle -> IO Solution
getSolution p = liftM Solution $ liftM (listArray (0,?size-1)) $
sequence [ liftM (listArray (0,?size-1)) $
sequence [ getEntry f | f <- elems r] | r <- elems p ]
getHints :: (?size :: Int, ?letters :: Int, ?solver :: Solver) => Array Int Field -> IO [Entry]
getHints h = sequence [ getEntry f | f <- elems h]
getAllHints :: Int -> [((Int,Int),Int)] -> AllHints
getAllHints size hints = (AllHints t r b l (length hints))
where [t,r,b,l] = [ emp // [ (i,Letter (letter-1)) | ((s',i),letter) <- hints, s' == s] | s <- [0..3]]
emp = replicateA size Blank
data AllHints = AllHints {atop, aright, abottom, aleft :: Array Int Entry, hintSize :: Int} deriving Show
getEntry :: (?letters :: Int, ?solver :: Solver) => Field -> IO Entry
getEntry l = do Just b <- modelValue ?solver (l!0)
if b then return Blank else getLetter
where getLetter :: IO Entry
getLetter = do res <- mapM (\i -> modelValue ?solver (l!i)) lx
let Just n = findIndex (== Just True) res
return $ Letter n
-- Adds clause to avoid the currently found solution.
removeCurrentSolution :: (?solver :: Solver) => IO Bool
removeCurrentSolution = do
n <- minisat_num_vars ?solver
addClause ?solver =<<
sequence [(modelValue ?solver lit >>= (\ (Just b) ->
return (if b then neg lit else lit)))
| lit <- map (MkLit . fromInteger . toInteger) [0..(n-1)]]
entryToInt :: Entry -> Int
entryToInt Blank = 0
entryToInt (Letter i) = i + 1
removeSolution :: (?size :: Int, ?letters :: Int, ?solver :: Solver, ?full :: Full) => Solution -> IO ()
removeSolution (Solution sol) = addClause' [neg (entryValue ((i,j),entryToInt $ (sol!i)!j))| i<-sx,j<-sx]
prettyHints :: AllHints -> String
prettyHints (AllHints t r b l s) =
" | " ++ (intercalate " | " $ map show $ elems t) ++ " | \n"
++ rule
++ intercalate rule rows
++ rule
++ " | " ++ (intercalate " | " $ map show $ elems b) ++ " | \n\n"
++ "number of hints: " ++ show s ++ "\n"
where rule = "--" ++ concat (replicate size "+---") ++ "+--\n"
divider = concat (replicate size " | ") ++ " | "
rows = zipWith (\l r -> show l ++ divider ++ show r ++ "\n") (elems l) (elems r)
size = length $ indices t
-- complete list of entry positions
search :: Int -> Int -> IO AllHints
search size letters = do
solver <- newSolver
let ?solver = solver
?size = size
?letters = letters
f <- genFull
conFull f
let ?full = f
generateConfiguration
generateConfiguration :: (?size :: Int, ?letters :: Int, ?solver :: Solver, ?full :: Full)
=> IO AllHints
generateConfiguration = do space <- shuffleM [ (i,j) | i <- sx, j<- sx]
growPuzzle space []
growPuzzle :: (?size :: Int, ?letters :: Int, ?solver :: Solver, ?full :: Full)
=> [(Int,Int)] -> [((Int,Int),Int)] -> IO AllHints
-- reset search if we hit a hint selection with
-- multiple solutions
growPuzzle [] _ = putStrLn "did not find a puzzle" >> generateConfiguration
growPuzzle (choice:space') entries = do
letter <- randomRIO (0,?letters)
let entries' = (choice,letter): entries
sat <- solve ?solver (map entryValue entries')
if sat then growPuzzle space' entries'
else do
-- We found an unsatisfiable set of hints.
True <- solve ?solver (map entryValue entries)
s@(Solution sol) <- getSolution (puzzle ?full)
removeSolution s
let getLetters i = let soli = sol ! i
in [((3,i),getLetter [soli!j | j<- sx]),
((0,i),getLetter [(sol!j)!i | j<-sx]),
((1,i),getLetter [soli!j | j<- sx_reverse]),
((2,i),getLetter [(sol!j)!i | j<-sx_reverse])]
space = concatMap getLetters sx
sat <- solve ?solver (map hintValue space)
if sat then generateConfiguration -- not unique, start again
else do -- check whether solution is it really unique
-- (we excluded some previous solutions)
deleteSolver ?solver
solver <- newSolver
let ?solver = solver
f <- genFull
conFull f
removeSolution s
sat <- solve ?solver (map hintValue space)
if sat then generateConfiguration -- not unique, start again
else do
space' <- shuffleM space
minimize space' []
where getLetter = foldr getLetterRun (error "Internal error: cannot find letter in solution!")
getLetterRun Blank r = r
getLetterRun (Letter l) _ = l + 1
-- turn a hint position and letter into a literal
hintValue :: (?full :: Full) => ((Int, Int), Int) -> Lit
hintValue ((h,i),l) = (([top, right, bottom , left]!! h) (hints ?full) ! i) ! l
entryValue :: (?full :: Full) => ((Int, Int), Int) -> Lit
entryValue ((i,j),l) = (((puzzle ?full) ! i) ! j) ! l
minimize :: (?size :: Int, ?letters :: Int, ?solver :: Solver, ?full :: Full)
=> [((Int, Int), Int)] -> [((Int, Int), Int)] -> IO AllHints
minimize [] result = do
-- We minimised the set of hints. Now we just verify that we indeed
-- have a unique solution.
deleteSolver ?solver
solver <- newSolver
let ?solver = solver
f <- genFull
conFull f
let set = map hintValue result
sat <- solve ?solver set
when (not sat) (error "solution is wrong: not satisfiable!")
s <- getSolution (puzzle ?full)
removeSolution s
sat' <- solve ?solver set
when sat' (error "solution is wrong: not unique!")
return(getAllHints ?size result)
minimize (h: r) acc = do sat' <- solve ?solver (map hintValue (r ++ acc))
if sat' then minimize r (h:acc)
else minimize r acc
main = do c <- getArgs
case c of
[size,letters] ->
case (readMay size, readMay letters) of
(Just size, Just letters)
| size < letters -> putStrLn "The the number of letters may not be larger than the puzzle size."
| letters < 1 -> putStrLn "The the number of letters must be a positive integer"
| otherwise -> search size letters >>= (putStr . prettyHints)
_ -> usage
_ -> usage
where usage = do name <- getProgName
putStrLn $ "usage: " ++ name ++ " <puzzle size> <number of letters>"