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sudoku solver haskell implementation
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| {- SUDOKU SOLVER -} | |
| module Sudoku | |
| ( | |
| solve | |
| ) where | |
| import Data.List | |
| board = [ [5,1,7,6,0,0,0,3,4] | |
| , [2,8,9,0,0,4,0,0,0] | |
| , [3,4,6,2,0,5,0,9,0] | |
| , [6,0,2,0,0,0,0,1,0] | |
| , [0,3,8,0,0,6,0,4,7] | |
| , [0,0,0,0,0,0,0,0,0] | |
| , [0,9,0,0,0,0,0,7,8] | |
| , [7,0,3,4,0,0,5,6,0] | |
| , [0,0,0,0,0,0,0,0,0] | |
| ] | |
| type Colx = Int | |
| type Rowx = Int | |
| type Posx = Int | |
| type Board = [[Integer]] | |
| getCol :: Board -> Colx -> [Integer] | |
| getCol board colx = map (!! colx) board | |
| getRow :: Board -> Rowx -> [Integer] | |
| getRow board rowx = board !! rowx | |
| getRange :: Posx -> [Posx] | |
| getRange pos | |
| | pos < 3 = [0,1,2] | |
| | pos < 6 = [3,4,5] | |
| | pos < 9 = [6,7,8] | |
| getBox :: Board -> Colx -> Rowx -> [Integer] | |
| getBox board colx rowx = concat [map (row !!) colRange | row <- rows] | |
| where | |
| rowRange = getRange rowx | |
| colRange = getRange colx | |
| rows = map (board !!) rowRange | |
| -- Find possible values [1..9] on a board | |
| -- at given position (colx,rowx) | |
| possible :: Board -> Colx -> Rowx -> [Integer] | |
| possible board colx rowx = | |
| let col = getCol board colx | |
| row = getRow board rowx | |
| box = getBox board colx rowx | |
| taken = nub $ filter (/= 0) $ col ++ row ++ box | |
| in [x | x <- [1..9], x `notElem` taken] | |
| -- Find possible values [1..9] on a board | |
| -- at all unfilled position (==0) | |
| allPossible :: Board -> [(Colx, Rowx, [Integer])] | |
| allPossible board = [(colx, rowx, possible board colx rowx) | |
| | colx <- [0..8] | |
| , rowx <- [0..8] | |
| , board !! rowx !! colx == 0] | |
| -- Find all position on board where there is only one | |
| -- exact possible value [1..9] | |
| onePossible :: Board -> [(Colx, Rowx, [Integer])] | |
| onePossible board = filter (\(_,_,options) -> length options == 1) | |
| $ allPossible board | |
| -- True if board is already solved | |
| isSolved :: Board -> Bool | |
| isSolved = not . any (==0) . concat | |
| -- Solve Sudoku board | |
| solve :: Board -> Board | |
| solve board = if isSolved board | |
| then board | |
| else solve $ foldl (\board (c,r,[x]) -> update board c r x) board $ onePossible board | |
| -- Update element of board at given position (colx,rowx) | |
| update :: Board -> Colx -> Rowx -> Integer -> Board | |
| update board colx rowx x = changeItem board rowx newRow | |
| where newRow = changeItem (board !! rowx) colx x | |
| -- Change element (x) in list (xs) at given position (n) | |
| changeItem :: [a] -> Int -> a -> [a] | |
| changeItem xs n x = take n xs ++ [x] ++ drop (n + 1) xs | |
| -- TODO: | |
| -- Pretty print Sudoku board | |
| pretty :: Board -> IO () | |
| pretty board = undefined |
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