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-- compile with -O2 to take advantage of memoization!
import Data.Array
import Data.List (nub)
data Pos = Pos Int Int deriving (Eq,Ix,Ord,Show)
type Map = Array Pos Int
type Memo = Array Pos [Pos]
memo :: Map -> Memo
memo m = array (bounds m) [ (p, reachable m p) | p <- indices m ]
step :: Map -> Pos -> [Pos]
step m p@(Pos x y) = filter ((== 1) . subtract (m ! p) . (m !))
. filter (`elem` indices m)
$ steps
where
steps = [ Pos (x+1) y
, Pos (x-1) y
, Pos x (y+1)
, Pos x (y-1)
]
width,height :: [[a]] -> Int
width = length . head
height = length
reachable :: Map -> Pos -> [Pos]
reachable m p | m ! p == 9 = [p]
| otherwise = nub . concatMap (memo m !) $ step m p
trailheads :: Map -> [Pos]
trailheads = map fst . filter ((== 0) . snd) . assocs
parse :: [[Char]] -> Map
parse ls = listArray
(Pos 0 0, Pos (width ls - 1) (height ls - 1))
(map (read . pure) $ concat ls)
main :: IO ()
main = do
m <- parse . lines <$> getContents
print . sum . map (length . (memo m !)) . trailheads $ m
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