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46 lines
2.0 KiB
Haskell
46 lines
2.0 KiB
Haskell
module Sudoku
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(
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Sudoku,
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solve,
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isSolved,
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pPrint
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) where
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import Data.Maybe
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import Data.List
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import Data.List.Split
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type Sudoku = [Int]
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solve :: Sudoku -> Maybe Sudoku
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solve sudoku
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| isSolved sudoku = Just sudoku
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| otherwise = do
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index <- elemIndex 0 sudoku
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let sudokus = [nextTest sudoku index i | i <- [1..9],
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checkRow (nextTest sudoku index i) index,
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checkColumn (nextTest sudoku index i) index,
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checkBox (nextTest sudoku index i) index]
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listToMaybe $ mapMaybe solve sudokus
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where nextTest sudoku index i = take index sudoku ++ [i] ++ drop (index+1) sudoku
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checkRow sudoku index = (length $ getRow sudoku index) == (length $ nub $ getRow sudoku index)
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checkColumn sudoku index = (length $ getColumn sudoku index) == (length $ nub $ getColumn sudoku index)
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checkBox sudoku index = (length $ getBox sudoku index) == (length $ nub $ getBox sudoku index)
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getRow sudoku index = filter (/=0) $ (chunksOf 9 sudoku) !! (quot index 9)
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getColumn sudoku index = filter (/=0) $ (transpose $ chunksOf 9 sudoku) !! (mod index 9)
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getBox sudoku index = filter (/=0) $ (map concat $ concatMap transpose $ chunksOf 3 $ map (chunksOf 3) $ chunksOf 9 sudoku)
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!! (3 * (quot index 27) + (quot (mod index 9) 3))
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isSolved :: Sudoku -> Bool
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isSolved sudoku
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| product sudoku == 0 = False
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| map (length . nub) sudokuRows /= map length sudokuRows = False
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| map (length . nub) sudokuColumns /= map length sudokuColumns = False
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| map (length . nub) sudokuBoxes /= map length sudokuBoxes = False
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| otherwise = True
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where sudokuRows = chunksOf 9 sudoku
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sudokuColumns = transpose sudokuRows
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sudokuBoxes = map concat $ concatMap transpose $ chunksOf 3 $ map (chunksOf 3) $ chunksOf 9 sudoku
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pPrint :: Sudoku -> String
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pPrint sudoku = intercalate "\n" $ map (intercalate " " . map show) $ chunksOf 9 sudoku |