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August 13, 2009 19:02
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Peter Norvig's beautiful Python program (http://norvig.com/sudoku.html) now in Haskell!
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-- Peter Norvig's beautiful Python program (http://norvig.com/sudoku.html) | |
-- that uses constraint propagation (and ultimately searching) | |
-- to solve Sudoku instances | |
-- | |
-- Now in everybody's favorite language! | |
-- Haskell coding by Ashutosh Mehra (http://ashutoshmehra.net/blog/) | |
import List (elem, nub, filter, delete, intersperse, replicate) | |
import Data.Map (Map, fromList, (!), insert, keys, elems, toList) | |
import Data.List (intercalate) | |
import Data.Maybe | |
type Val = Char -- Value of a cell | |
type Square = String -- two-character square ID | |
type Board = Maybe (Map Square String) -- The board state | |
cross xs ys = [[x,y] | x <- xs, y <- ys] | |
rows = "ABCDEFGHI" | |
cols = "123456789" | |
digits = "123456789" | |
squares = cross rows cols | |
unitlist = [cross rows [c] | c <- cols] | |
++ [cross [r] cols | r <- rows] | |
++ [cross rs cs | rs <- ["ABC", "DEF", "GHI"], cs <- ["123","456","789"]] | |
units sq = filter (elem sq) unitlist | |
peers sq = delete sq . nub . concat $ units sq | |
-- Check for places where d appears in the units of sq | |
checkplaces :: Board -> Square -> Val -> Board | |
checkplaces b0 sq d = foldl f b0 (units sq) | |
where f b u | |
| isNothing b || len == 0 = Nothing | |
| len == 1 = assign b (head dplaces) d | |
| otherwise = b | |
where dplaces = [s | s <- u, elem d ((fromJust b)!s)] | |
-- dplaces is all squares in the unit u possibly containing d | |
len = length dplaces | |
eliminate :: Board -> Square -> Val -> Board | |
eliminate Nothing _ _ = Nothing | |
eliminate (Just b0) sq d | |
| notElem d v = Just b0 -- Already Eliminated | |
| length v' == 0 = Nothing -- Contradiction: Removed last value | |
| length v' == 1 = checkplaces b'' sq d -- Only 1 left: Remove from peers | |
| otherwise = checkplaces (Just b') sq d | |
where v = b0 ! sq | |
v' = delete d v | |
b' = insert sq v' b0 | |
h = (head v') | |
b'' = foldl (\b p -> eliminate b p h) (Just b') (peers sq) | |
assign :: Board -> Square -> Val -> Board | |
assign Nothing _ _ = Nothing | |
assign b0 sq d0 = foldl f b0 ((fromJust b0) ! sq) | |
where f b d = if d0 == d then b else eliminate b sq d | |
parsegr :: String -> Board | |
parsegr s = foldl f b0 (zip squares s') | |
where s' = filter (\x -> elem x "0.-123456789") s | |
b0 = Just (fromList [(s, digits) | s <- squares]) | |
f b (sq, d) | |
| isNothing b = Nothing | |
| notElem d digits = b | |
| otherwise = assign b sq d | |
search :: Board -> Board | |
search Nothing = Nothing | |
search (Just b) = | |
if all ((==1) . length) $ elems b then Just b else search' (b!s) | |
where minl = minimum [l | v <- elems b, let l = length v, l > 1] | |
s = head [sq | (sq, v) <- toList b, length v == minl] | |
search' [] = Nothing | |
search' (d:ds) = if isJust b' then b' else search' ds | |
where b' = search $ assign (Just b) s d | |
printgr :: Board -> String | |
printgr Nothing = "Unsolvable" | |
printgr (Just b) = concat [(fr r) ++ (if elem r "CF" then line else "") ++ "\n" | r<-rows] | |
where w = 1 + maximum [length (b!sq) | sq <- squares] | |
line = (++) "\n" $ intercalate "+" $ replicate 3 $ replicate (3 * w) '-' | |
fr r = concat [(fmt (b![r,c])) ++ (if elem c "36" then "|" else "") | c<-cols] | |
fmt s = s ++ replicate (w - (length s)) ' ' | |
solve :: String -> IO () | |
solve s = putStrLn $ printgr $ search $ parsegr s | |
-- Instance from http://programmingpraxis.com/2009/02/19/sudoku/2/ | |
grid = "7..1......2.....15.....639.2...18....4..9..7....75...3.785.....56.....4......1..2" | |
main = solve grid | |
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