Replaces list with vector, naively
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@ -14,6 +14,7 @@ description: Please see the README on GitHub at <https://github.com/abhi
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dependencies:
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- base >= 4.7 && < 5
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- containers
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- vector
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executables:
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sudoku:
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104
src/Sudoku.hs
104
src/Sudoku.hs
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@ -5,11 +5,12 @@ import Data.Function ((&))
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import qualified Control.Monad
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import qualified Data.Char
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import qualified Data.Function
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import qualified Data.List.Split
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import qualified Data.List
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import qualified Data.Map.Strict as Map
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import qualified Data.Word
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import qualified Data.Bits
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import qualified Data.Vector
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import Data.Vector ((!))
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fixM :: (Eq t, Monad m) => (t -> m t) -> t -> m t
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fixM f x = f x >>= \x' -> if x' == x then return x else fixM f x'
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@ -21,8 +22,8 @@ data Cell = Fixed Data.Word.Word16
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| Possible Data.Word.Word16
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deriving (Show, Eq)
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type Row = [Cell]
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type Grid = [Row]
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type Grid = Data.Vector.Vector Cell
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type CellIxs = [Int]
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isPossible :: Cell -> Bool
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isPossible (Possible _) = True
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@ -30,7 +31,7 @@ isPossible _ = False
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readGrid :: String -> Maybe Grid
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readGrid s
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| length s == 81 = traverse (traverse readCell) . Data.List.Split.chunksOf 9 $ s
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| length s == 81 = Data.Vector.fromList <$> traverse readCell s
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| otherwise = Nothing
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where
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allBitsSet = 1022
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@ -40,14 +41,31 @@ readGrid s
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| Data.Char.isDigit c && c > '0' = Just . Fixed . Data.Bits.bit . Data.Char.digitToInt $ c
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| otherwise = Nothing
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fromXY :: (Int, Int) -> Int
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fromXY (x, y) = x * 9 + y
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allRowIxs, allColIxs, allSubGridIxs :: [CellIxs]
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allRowIxs = [getRow i | i <- [0..8]]
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where getRow n = [ fromXY (n, i) | i <- [0..8] ]
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allColIxs = [getCol i | i <- [0..8]]
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where getCol n = [ fromXY (i, n) | i <- [0..8] ]
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allSubGridIxs = [getSubGrid i | i <- [0..8]]
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where getSubGrid n = let (r, c) = (n `quot` 3, n `mod` 3)
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in [ fromXY (3 * r + i, 3 * c + j) | i <- [0..2], j <- [0..2] ]
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replaceCell :: Int -> Cell -> Grid -> Grid
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replaceCell i c g = g Data.Vector.// [(i, c)]
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showGrid :: Grid -> String
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showGrid = unlines . map (unwords . map showCell)
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showGrid grid = unlines . map (unwords . map (showCell . (grid !))) $ allRowIxs
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where
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showCell (Fixed x) = show . Data.Bits.countTrailingZeros $ x
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showCell _ = "."
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showGridWithPossibilities :: Grid -> String
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showGridWithPossibilities = unlines . map (unwords . map showCell)
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showGridWithPossibilities grid = unlines . map (unwords . map (showCell . (grid !))) $ allRowIxs
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where
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showCell (Fixed x) = (show . Data.Bits.countTrailingZeros $ x) ++ " "
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showCell (Possible xs) =
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@ -79,55 +97,59 @@ makeCell ys
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| Data.Bits.popCount ys == 1 = Just $ Fixed ys
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| otherwise = Just $ Possible ys
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pruneCellsByFixed :: [Cell] -> Maybe [Cell]
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pruneCellsByFixed cells = traverse pruneCell cells
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pruneCellsByFixed :: Grid -> CellIxs -> Maybe Grid
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pruneCellsByFixed grid cellIxs =
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Control.Monad.foldM pruneCell grid . map (\i -> (i, grid ! i)) $ cellIxs
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where
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fixeds = setBits Data.Bits.zeroBits [x | Fixed x <- cells]
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fixeds = setBits Data.Bits.zeroBits [x | Fixed x <- map (grid !) cellIxs]
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pruneCell (Possible xs) = makeCell (xs Data.Bits..&. Data.Bits.complement fixeds)
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pruneCell x = Just x
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pruneCellsByExclusives :: [Cell] -> Maybe [Cell]
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pruneCellsByExclusives cells = case exclusives of
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[] -> Just cells
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_ -> traverse pruneCell cells
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pruneCell g (_, Fixed _) = Just g
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pruneCell g (i, Possible xs)
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| xs' == xs = Just g
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| otherwise = flip (replaceCell i) g <$> makeCell xs'
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where
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xs' = xs Data.Bits..&. Data.Bits.complement fixeds
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pruneCellsByExclusives :: Grid -> CellIxs -> Maybe Grid
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pruneCellsByExclusives grid cellIxs = case exclusives of
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[] -> Just grid
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_ -> Control.Monad.foldM pruneCell grid . zip cellIxs $ cells
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where
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cells = map (grid !) cellIxs
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exclusives = exclusivePossibilities cells
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allExclusives = setBits Data.Bits.zeroBits exclusives
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pruneCell cell@(Fixed _) = Just cell
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pruneCell cell@(Possible xs)
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| intersection `elem` exclusives = makeCell intersection
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| otherwise = Just cell
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pruneCell g (_, Fixed _) = Just g
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pruneCell g (i, Possible xs)
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| intersection == xs = Just g
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| intersection `elem` exclusives =
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flip (replaceCell i) g <$> makeCell intersection
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| otherwise = Just g
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where
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intersection = xs Data.Bits..&. allExclusives
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pruneCells :: [Cell] -> Maybe [Cell]
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pruneCells cells = fixM pruneCellsByFixed cells >>= fixM pruneCellsByExclusives
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subGridsToRows :: Grid -> Grid
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subGridsToRows =
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concatMap (\rows -> let [r1, r2, r3] = map (Data.List.Split.chunksOf 3) rows
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in zipWith3 (\a b c -> a ++ b ++ c) r1 r2 r3)
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. Data.List.Split.chunksOf 3
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pruneCells :: Grid -> CellIxs -> Maybe Grid
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pruneCells grid cellIxs =
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fixM (flip pruneCellsByFixed cellIxs) grid
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>>= fixM (flip pruneCellsByExclusives cellIxs)
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pruneGrid' :: Grid -> Maybe Grid
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pruneGrid' grid =
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traverse pruneCells grid
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>>= fmap Data.List.transpose . traverse pruneCells . Data.List.transpose
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>>= fmap subGridsToRows . traverse pruneCells . subGridsToRows
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Control.Monad.foldM pruneCells grid allRowIxs
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>>= flip (Control.Monad.foldM pruneCells) allColIxs
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>>= flip (Control.Monad.foldM pruneCells) allSubGridIxs
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pruneGrid :: Grid -> Maybe Grid
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pruneGrid = fixM pruneGrid'
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isGridFilled :: Grid -> Bool
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isGridFilled grid = null [ () | Possible _ <- concat grid ]
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isGridFilled = not . Data.Vector.any isPossible
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isGridInvalid :: Grid -> Bool
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isGridInvalid grid =
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any isInvalidRow grid
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|| any isInvalidRow (Data.List.transpose grid)
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|| any isInvalidRow (subGridsToRows grid)
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any isInvalidRow (map (map (grid !)) allRowIxs)
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|| any isInvalidRow (map (map (grid !)) allColIxs)
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|| any isInvalidRow (map (map (grid !)) allSubGridIxs)
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where
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isInvalidRow row =
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let fixeds = [x | Fixed x <- row]
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@ -145,12 +167,10 @@ nextGrids :: Grid -> (Grid, Grid)
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nextGrids grid =
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let (i, first@(Fixed _), rest) =
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fixCell
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. Data.List.minimumBy (compare `Data.Function.on` (possibilityCount . snd))
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. filter (isPossible . snd)
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. zip [0..]
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. concat
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. Data.Vector.minimumBy (compare `Data.Function.on` (possibilityCount . snd))
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. Data.Vector.imapMaybe (\j cell -> if isPossible cell then Just (j, cell) else Nothing)
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$ grid
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in (replace2D i first grid, replace2D i rest grid)
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in (replaceCell i first grid, replaceCell i rest grid)
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where
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possibilityCount (Possible xs) = Data.Bits.popCount xs
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possibilityCount (Fixed _) = 1
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@ -161,10 +181,6 @@ nextGrids grid =
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Nothing -> error "Impossible case"
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Just cell -> (i, Fixed (Data.Bits.bit x), cell)
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replace2D :: Int -> a -> [[a]] -> [[a]]
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replace2D i v = let (x, y) = (i `quot` 9, i `mod` 9) in replace x (replace y (const v))
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replace p f xs = [if i == p then f x else x | (x, i) <- zip xs [0..]]
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solve :: Grid -> Maybe Grid
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solve grid = pruneGrid grid >>= solve'
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where
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