Adds parallelism

src/Sudoku.hs

@@ -1,8 +1,8 @@
+{-# LANGUAGE LambdaCase #-}
 module Main where
 
 import Control.Applicative ((<|>))
 import Data.Function ((&))
-import Data.Vector ((!))
 import qualified Control.Monad
 import qualified Control.Monad.ST
 import qualified Data.Char
@@ -11,12 +11,10 @@ import qualified Data.List
 import qualified Data.Map.Strict as Map
 import qualified Data.Word
 import qualified Data.Bits
-import qualified Data.Vector
-import qualified Data.Vector.Unboxed
+import Data.Vector.Unboxed ((!))
 import qualified Data.Vector.Unboxed.Mutable
-import qualified Data.STRef
+import qualified Data.Vector.Unboxed
 import qualified Data.Maybe
-import qualified Control.DeepSeq
 import Control.Parallel.Strategies (withStrategy, rdeepseq, parBuffer)
 
 fixM :: (Eq t, Monad m) => (t -> m t) -> t -> m t
@@ -25,37 +23,35 @@ fixM f x = f x >>= \x' -> if x' == x then return x else fixM f x'
 setBits :: Data.Word.Word16 -> [Data.Word.Word16] -> Data.Word.Word16
 setBits = Data.List.foldl' (Data.Bits..|.)
 
-data Cell = Fixed Data.Word.Word16
-          | Possible Data.Word.Word16
-          deriving (Show, Eq)
-
-instance Control.DeepSeq.NFData Cell where
-  rnf (Fixed w)    = Control.DeepSeq.rnf w
-  rnf (Possible w) = Control.DeepSeq.rnf w
-
-type Grid = Data.Vector.Vector Cell
+type Cell = Data.Word.Word16
+type Grid = Data.Vector.Unboxed.Vector Cell
+type MGrid s = Data.Vector.Unboxed.Mutable.STVector s Cell
 type CellIxs = [Int]
 
-isPossible :: Cell -> Bool
-isPossible (Possible _) = True
-isPossible _            = False
+isPossible, isFixed :: Cell -> Bool
+isPossible = flip Data.Bits.testBit 15
+isFixed = not . isPossible
+
+makePossible, makeFixed :: Data.Word.Word16 -> Cell
+makePossible = flip Data.Bits.setBit 15
+makeFixed = flip Data.Bits.clearBit 15
 
 readGrid :: String -> Maybe Grid
 readGrid s
-  | length s == 81 = Data.Vector.fromList <$> traverse readCell s
+  | length s == 81 = Data.Vector.Unboxed.fromList <$> traverse readCell s
   | otherwise      = Nothing
   where
     allBitsSet = 1022
 
-    readCell '.' = Just $ Possible allBitsSet
+    readCell '.' = Just $ makePossible allBitsSet
     readCell c
-      | Data.Char.isDigit c && c > '0' = Just . Fixed . Data.Bits.bit . Data.Char.digitToInt $ c
+      | Data.Char.isDigit c && c > '0' = Just . Data.Bits.bit . Data.Char.digitToInt $ c
       | otherwise = Nothing
 
 fromXY :: (Int, Int) -> Int
 fromXY (x, y) = x * 9 + y
 
-allRowIxs, allColIxs, allSubGridIxs :: [CellIxs]
+allRowIxs, allColIxs, allSubGridIxs, allIxs :: [CellIxs]
 allRowIxs = [getRow i | i <- [0..8]]
   where getRow n = [ fromXY (n, i) | i <- [0..8] ]
 
@@ -66,45 +62,64 @@ allSubGridIxs = [getSubGrid i | i <- [0..8]]
   where getSubGrid n = let (r, c) = (n `quot` 3, n `mod` 3)
                        in [ fromXY (3 * r + i, 3 * c + j) | i <- [0..2], j <- [0..2] ]
 
+allIxs = concat [allRowIxs, allColIxs, allSubGridIxs]
+
 replaceCell :: Int -> Cell -> Grid -> Grid
-replaceCell i c g = g Data.Vector.// [(i, c)]
+replaceCell i c = Data.Vector.Unboxed.modify (\v -> Data.Vector.Unboxed.Mutable.unsafeWrite v i c)
 
 showGrid :: Grid -> String
 showGrid grid = unlines . map (unwords . map (showCell . (grid !))) $ allRowIxs
   where
-    showCell (Fixed x) = show . Data.Bits.countTrailingZeros $ x
-    showCell _         = "."
+    showCell xs
+      | isPossible xs = "."
+      | otherwise     = show . Data.Bits.countTrailingZeros $ xs
 
 showGridWithPossibilities :: Grid -> String
 showGridWithPossibilities grid = unlines . map (unwords . map (showCell . (grid !))) $ allRowIxs
   where
-    showCell (Fixed x)     = (show . Data.Bits.countTrailingZeros $ x) ++ "          "
-    showCell (Possible xs) =
+    showCell xs
+      | isPossible xs =
       "[" ++ map (\i -> if Data.Bits.testBit xs i then Data.Char.intToDigit i else ' ') [1..9] ++ "]"
+      | otherwise     = (show . Data.Bits.countTrailingZeros $ xs) ++ "          "
 
-cellIndicesList :: [Cell] -> [Data.Word.Word16]
-cellIndicesList cells =
-  Data.Vector.Unboxed.toList $ Control.Monad.ST.runST $ do
-    vec <- Data.Vector.Unboxed.Mutable.replicate 9 Data.Bits.zeroBits
-    ref <- Data.STRef.newSTRef (1 :: Int)
-    Control.Monad.forM_ cells $ \cell -> do
-      i <- Data.STRef.readSTRef ref
-      case cell of
-        Fixed _ -> return ()
-        Possible xs -> Control.Monad.forM_ [0..8] $ \d ->
-          Control.Monad.when (Data.Bits.testBit xs (d+1)) $
-            Data.Vector.Unboxed.Mutable.unsafeModify vec (`Data.Bits.setBit` i) d
-      Data.STRef.writeSTRef ref (i+1)
-    Data.Vector.Unboxed.unsafeFreeze vec
+-- Exclusive Possibilities Accumulator
+data ExPosAcc = ExPosAcc ![Int] ![Int] ![Int] ![Int] ![Int] ![Int] ![Int] ![Int] ![Int]
+
+exPosAccEmpty :: ExPosAcc
+exPosAccEmpty = ExPosAcc [] [] [] [] [] [] [] [] []
+
+exPosAccInsert :: Int -> Int -> ExPosAcc -> ExPosAcc
+exPosAccInsert 1 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc (i:v1) v2 v3 v4 v5 v6 v7 v8 v9
+exPosAccInsert 2 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc v1 (i:v2) v3 v4 v5 v6 v7 v8 v9
+exPosAccInsert 3 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc v1 v2 (i:v3) v4 v5 v6 v7 v8 v9
+exPosAccInsert 4 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc v1 v2 v3 (i:v4) v5 v6 v7 v8 v9
+exPosAccInsert 5 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc v1 v2 v3 v4 (i:v5) v6 v7 v8 v9
+exPosAccInsert 6 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc v1 v2 v3 v4 v5 (i:v6) v7 v8 v9
+exPosAccInsert 7 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc v1 v2 v3 v4 v5 v6 (i:v7) v8 v9
+exPosAccInsert 8 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc v1 v2 v3 v4 v5 v6 v7 (i:v8) v9
+exPosAccInsert 9 i (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) = ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 (i:v9)
+exPosAccInsert _ _ _                                     = error "Impossible"
+
+exPosAccToList :: ExPosAcc -> [(Int, [Int])]
+exPosAccToList (ExPosAcc v1 v2 v3 v4 v5 v6 v7 v8 v9) =
+  [(1, v1), (2, v2), (3, v3), (4, v4), (5, v5), (6, v6), (7, v7), (8, v8), (9, v9)]
 
 exclusivePossibilities :: [Cell] -> [Data.Word.Word16]
-exclusivePossibilities row =
-  row
-  & cellIndicesList
-  & zip [1..9]
-  & filter (\(_, xs) -> let p = Data.Bits.popCount xs in p > 0 && p < 4)
+exclusivePossibilities cells =
+  cells
+  & zip ([1..9] :: [Int])
+  & filter (isPossible . snd)
+  & Data.List.foldl'
+      (\acc (i, xs) ->
+        Data.List.foldl'
+          (\acc' n -> if Data.Bits.testBit xs n then exPosAccInsert n i acc' else acc')
+          acc
+          [1..9])
+      exPosAccEmpty
+  & exPosAccToList
+  & filter ((< 4) . length . snd)
   & Data.List.foldl' (\acc (x, is) -> Map.insertWith prepend is [x] acc) Map.empty
-  & Map.filterWithKey (\is xs -> Data.Bits.popCount is == length xs)
+  & Map.filterWithKey (\is xs -> length is == length xs)
   & Map.elems
   & map (Data.List.foldl' Data.Bits.setBit Data.Bits.zeroBits)
   where
@@ -112,49 +127,81 @@ exclusivePossibilities row =
 
 makeCell :: Data.Word.Word16 -> Maybe Cell
 makeCell ys
-  | ys == Data.Bits.zeroBits   = Nothing
-  | Data.Bits.popCount ys == 1 = Just $ Fixed ys
-  | otherwise                  = Just $ Possible ys
+  | ys == Data.Bits.zeroBits               = Nothing
+  | Data.Bits.popCount (makeFixed ys) == 1 = Just $ makeFixed ys
+  | otherwise                              = Just $ makePossible ys
 
-pruneCells :: Grid -> CellIxs -> Maybe Grid
-pruneCells grid cellIxs = Control.Monad.foldM pruneCell grid cellIxs
+pruneCells :: MGrid s -> CellIxs -> Control.Monad.ST.ST s (Maybe Bool)
+pruneCells grid cellIxs = do
+  cells <- traverse (Data.Vector.Unboxed.Mutable.unsafeRead grid) cellIxs
+  pruneCells' grid cells cellIxs
+
+pruneCells' :: MGrid s -> [Cell] -> CellIxs -> Control.Monad.ST.ST s (Maybe Bool)
+pruneCells' grid cells = Control.Monad.foldM pruneCell' (Just False)
   where
-    cells         = map (grid !) cellIxs
+    pruneCell' Nothing _ = return Nothing
+    pruneCell' (Just changed) i = pruneCell i >>= \case
+      Nothing -> return Nothing
+      Just changed' -> return $ Just (changed || changed')
+
     exclusives    = exclusivePossibilities cells
     allExclusives = setBits Data.Bits.zeroBits exclusives
-    fixeds        = setBits Data.Bits.zeroBits [x | Fixed x <- cells]
+    fixeds        = setBits Data.Bits.zeroBits . filter isFixed $ cells
 
-    pruneCell g i =
-      pruneCellByFixed g (i, g ! i) >>= \g' -> pruneCellByExclusives g' (i, g' ! i)
+    pruneCell i = do
+      cell <- Data.Vector.Unboxed.Mutable.unsafeRead grid i
+      pruneCellByFixed (i, cell) >>= \case
+        Nothing -> return Nothing
+        Just changed -> do
+          cell' <- Data.Vector.Unboxed.Mutable.unsafeRead grid i
+          pruneCellByExclusives (i, cell') >>= \case
+            Nothing       -> return Nothing
+            Just changed' -> return $ Just (changed || changed')
 
-    pruneCellByFixed g (_, Fixed _) = Just g
-    pruneCellByFixed g (i, Possible xs)
-      | xs' == xs = Just g
-      | otherwise = flip (replaceCell i) g <$> makeCell xs'
+    pruneCellByFixed (i, xs)
+      | isFixed xs = return $ Just False
+      | xs' == xs  = return $ Just False
+      | otherwise  = case makeCell xs' of
+          Nothing -> return Nothing
+          Just cell' -> do
+            Data.Vector.Unboxed.Mutable.unsafeWrite grid i cell'
+            return $ Just True
       where
         xs' = xs Data.Bits..&. Data.Bits.complement fixeds
 
-    pruneCellByExclusives g (_, Fixed _) = Just g
-    pruneCellByExclusives g (i, Possible xs)
-      | null exclusives                = Just g
-      | intersection == xs             = Just g
-      | intersection `elem` exclusives =
-          flip (replaceCell i) g <$> makeCell intersection
-      | otherwise                      = Just g
+    pruneCellByExclusives (i, xs)
+      | isFixed xs                       = return $ Just False
+      | null exclusives                  = return $ Just False
+      | makePossible intersection == xs  = return $ Just False
+      | intersection `elem` exclusives   = case makeCell intersection of
+          Nothing -> return Nothing
+          Just cell' -> do
+            Data.Vector.Unboxed.Mutable.unsafeWrite grid i cell'
+            return $ Just True
+      | otherwise                        = return $ Just False
       where
         intersection = xs Data.Bits..&. allExclusives
 
-pruneGrid' :: Grid -> Maybe Grid
-pruneGrid' grid =
-  Control.Monad.foldM pruneCells grid allRowIxs
-  >>= flip (Control.Monad.foldM pruneCells) allColIxs
-  >>= flip (Control.Monad.foldM pruneCells) allSubGridIxs
+pruneGrid' :: MGrid s -> Control.Monad.ST.ST s (Maybe Bool)
+pruneGrid' grid = Control.Monad.foldM pruneCells' (Just False) allIxs
+  where
+    pruneCells' Nothing _ = return Nothing
+    pruneCells' (Just changed) ixs = pruneCells grid ixs >>= \case
+      Nothing       -> return Nothing
+      Just changed' -> return $ Just (changed || changed')
 
 pruneGrid :: Grid -> Maybe Grid
-pruneGrid = fixM pruneGrid'
+pruneGrid grid = Control.Monad.ST.runST $ do
+  mGrid <- Data.Vector.Unboxed.unsafeThaw grid
+  fix mGrid
+  where
+    fix mg = pruneGrid' mg >>= \case
+      Nothing -> return Nothing
+      Just True -> fix mg
+      Just False -> Just <$> Data.Vector.Unboxed.unsafeFreeze mg
 
 isGridFilled :: Grid -> Bool
-isGridFilled = not . Data.Vector.any isPossible
+isGridFilled = not . Data.Vector.Unboxed.any isPossible
 
 isGridInvalid :: Grid -> Bool
 isGridInvalid grid =
@@ -163,8 +210,8 @@ isGridInvalid grid =
   || any isInvalidRow (map (map (grid !)) allSubGridIxs)
   where
     isInvalidRow row =
-      let fixeds         = [x  | Fixed x <- row]
-          emptyPossibles = [() | Possible x <- row, x == Data.Bits.zeroBits]
+      let fixeds         = filter isFixed row
+          emptyPossibles = filter (== 32768) . filter isPossible $ row
       in hasDups fixeds || not (null emptyPossibles)
 
     hasDups l = hasDups' l []
@@ -176,21 +223,22 @@ isGridInvalid grid =
 
 nextGrids :: Grid -> (Grid, Grid)
 nextGrids grid =
-  let (i, first@(Fixed _), rest) =
+  let (i, first, rest) =
         fixCell
-        . Data.Vector.minimumBy (compare `Data.Function.on` (possibilityCount . snd))
-        . Data.Vector.imapMaybe (\j cell -> if isPossible cell then Just (j, cell) else Nothing)
+        . Data.Vector.Unboxed.minimumBy (compare `Data.Function.on` (possibilityCount . snd))
+        . Data.Vector.Unboxed.imapMaybe (\j cell -> if isPossible cell then Just (j, cell) else Nothing)
         $ grid
   in (replaceCell i first grid, replaceCell i rest grid)
   where
-    possibilityCount (Possible xs) = Data.Bits.popCount xs
-    possibilityCount (Fixed _)     = 1
+    possibilityCount xs
+      | isPossible xs = Data.Bits.popCount xs - 1
+      | otherwise     = 1
 
-    fixCell ~(i, Possible xs) =
+    fixCell (i, xs) =
       let x = Data.Bits.countTrailingZeros xs
       in case makeCell (Data.Bits.clearBit xs x) of
         Nothing -> error "Impossible case"
-        Just cell -> (i, Fixed (Data.Bits.bit x), cell)
+        Just cell -> (i, Data.Bits.bit x, cell)
 
 solve :: Grid -> Maybe Grid
 solve grid = pruneGrid grid >>= solve'