{-# LANGUAGE ImplicitParams, ConstraintKinds #-}
-- ABC logic puzzle
module Main where
import Control.Monad
import Data.List
import qualified Data.Vector as Vector
import Data.Vector (Vector, (!))
import MiniSat
import Safe
import System.Environment
import System.Random
type Puzzle = Vector (Vector Field) -- rows of columns
type Field = Vector Lit
data Hints = Hints {
top, right, bottom, left :: Vector Field}
data Full = Full { puzzle :: Puzzle, hints :: Hints}
type Env = (?size :: Int, ?letters :: Int, ?solver :: Solver)
genLit :: Env => IO Lit
genLit = newLit ?solver
genField :: Env => IO Field
genField = Vector.replicateM (?letters+1) genLit
genPuzzle :: Env => IO Puzzle
genPuzzle = Vector.replicateM ?size $ Vector.replicateM ?size genField
genHints :: Env => IO Hints
genHints = liftM4 Hints side side side side
where side = Vector.replicateM ?size genField
genFull :: Env => IO Full
genFull = liftM2 Full genPuzzle genHints
addClause' :: Env => [Lit] -> IO Bool
addClause' = addClause ?solver
addClauses :: Env => [[Lit]] -> IO ()
addClauses = mapM_ addClause'
lx :: Env => [Int]
lx = [1 .. ?letters]
fx :: Env => [Int]
fx = [0 .. ?letters]
sx :: Env => [Int]
sx = [0 .. ?size - 1]
conHint :: Env => 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 :: Env => Vector Field -> Puzzle -> IO ()
conBottomHints h p = sequence_ [conHint (h!i) [(p!j)!i|j<-[(?letters-1) .. (?size-1)]]| i <- sx]
>> mapM_ conField (Vector.toList h)
conRightHints :: Env => Vector Field -> Puzzle -> IO ()
conRightHints h p = sequence_ [conHint (h!i) [(p!i)!j|j<-[(?letters-1) .. (?size-1)]]| i <- sx]
>> mapM_ conField (Vector.toList h)
conTopHints :: Env => Vector Field -> Puzzle -> IO ()
conTopHints h p = sequence_ [conHint (h!i) [(p!j)!i|j<-[(?size - ?letters),(?size - ?letters - 1) .. 0]]| i <- sx]
>> mapM_ conField (Vector.toList h)
conLeftHints :: Env => Vector Field -> Puzzle -> IO ()
conLeftHints h p = sequence_ [conHint (h!i) [(p!i)!j|j<-[(?size - ?letters),(?size - ?letters - 1) .. 0]]| i <- sx]
>> mapM_ conField (Vector.toList h)
conHints :: Env => Full -> IO ()
conHints (Full p h) = conBottomHints (bottom h) p >> conRightHints (right h) p
>> conTopHints (top h) p >> conLeftHints (left h) p
conFull :: Env => Full -> IO ()
conFull full = conPuzzle (puzzle full) >> conHints full
conField :: Env => Field -> IO ()
conField l = do addClause' $ Vector.toList l
addClauses [ [neg (l!i), neg (l!j)] | i <- fx, j <- [0 .. i-1]]
conFields :: Env => Puzzle -> IO ()
conFields p = sequence_ [conField ((p!i)!j) | i <- sx, j <- sx]
-- fields must be different letters (however, both can be blank)
conDiffFields :: Env => Field -> Field -> IO ()
conDiffFields l1 l2 = do
addClauses [[neg (l1!i), neg (l2!i)] | i <- lx]
conRows :: Env => Puzzle -> IO ()
conRows p = do
-- fields must be different letters
sequence_ [conDiffFields (r!i) (r!j) | r <- Vector.toList p, i <- sx, j <- [0..i-1]]
-- each letter must appear
addClauses [[(r!i)!l | i <- sx] | r <- Vector.toList p, l <- lx]
conColumns :: Env => 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 :: Env => 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 :: [[Entry]]}
instance Show Solution where
show = unlines . map (unwords . map show) . unSolution
getSolution :: Env => Puzzle -> IO Solution
getSolution p = liftM Solution $ sequence [ sequence [ getEntry f | f <- Vector.toList r] | r <- Vector.toList p ]
getHints :: Env => Vector Field -> IO [Entry]
getHints h = sequence [ getEntry f | f <- Vector.toList h]
getAllHints :: Env => Hints -> IO AllHints
getAllHints (Hints t r b l) = liftM4 AllHints (getHints t) (getHints r) (getHints b) (getHints l)
data AllHints = AllHints {atop, aright, abottom, aleft :: [Entry]} deriving Show
getEntry :: Env => 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
-- To be called after a successful 'solve'. It tries to find another
-- solution.
solveAgain :: Solver -> [Lit] -> IO Bool
solveAgain solver set =
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)]]
solve solver set
prettyHints :: AllHints -> String
prettyHints (AllHints t r b l) = " | " ++ (intercalate " | " $ map show t) ++ " | \n"
++ rule
++ intercalate rule rows
++ rule
++ " | " ++ (intercalate " | " $ map show b) ++ " | \n"
where rule = "-" ++ concat (replicate size "+---") ++ "+-\n"
divider = concat (replicate size "| ") ++ "|"
rows = zipWith (\l r -> show l ++ divider ++ show r ++ "\n") l r
size = length t
type Env' = (Env, ?space :: ([(Int,Int)]),
?hints :: [((Int,Int),Int)], ?full :: Full)
-- complete list of hint positions
hintPositions :: Env => [(Int,Int)]
hintPositions = [ (side,i) | side <- [0..3], i<- sx] :: [(Int,Int)]
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
?space = hintPositions
?hints = []
growHints
growHints :: Env' => IO AllHints
growHints = do case ?space of
-- reset search if we hit a hint selection with
-- multiple solutions
[] -> let ?space = hintPositions
?hints = []
in growHints
_ -> do
(choice, space') <- pick ?space
letter <- randomRIO (1,?letters)
let hints' = (choice,letter): ?hints
sat <- solve ?solver (map hintValue hints')
if sat then let ?space = space'
?hints = hints'
in growHints
else do
-- We found an unsatisfiable set of hints. We
-- backtrack and check whether we found a set of
-- hints with a unique solution.
let set = map hintValue ?hints
solve ?solver set
sat <- solveAgain ?solver set
if sat then do
-- Solution is not unique. Reset the
-- solver and start growing the hints.
deleteSolver ?solver
solver <- newSolver
let ?solver = solver
f <- genFull
conFull f
let ?full = f
growHints
else minimize ?hints []
-- turn a hint position and letter into a literal
hintValue :: Env' => ((Int, Int), Int) -> Lit
hintValue ((h,i),l) = (([top, right, bottom , left]!! h) (hints ?full) ! i) ! l
pick l = do i <- randomRIO (0,length l -1)
let (l1, choice:l2) = splitAt i l
return (choice, l1++l2)
minimize :: Env' => [((Int, Int), Int)] -> [((Int, Int), Int)] -> IO AllHints
minimize [] acc = 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 acc
sat <- solve ?solver set
sat' <- solveAgain ?solver set
when (not sat || sat') (error "solution is wrong")
getAllHints (hints f)
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 ->
search size letters >>= (putStr . prettyHints)
_ -> usage
_ -> usage
where usage = do name <- getProgName
putStrLn $ "usage: " ++ name ++ " <puzzle size> <number of letters>"
++ "\n\nThe the number of letters may not be larger than the puzzle size."