Haskell

Cool task, nothing to optimize

import Control.Arrow

import Data.Array.Unboxed (UArray)
import Data.Set (Set)

import qualified Data.Char as Char
import qualified Data.List as List
import qualified Data.Set as Set
import qualified Data.Array.Unboxed as UArray

parse :: String -> UArray (Int, Int) Int
parse s = UArray.listArray ((1, 1), (n, m)) . map Char.digitToInt . filter (/= '\n') $ s
        where
                n = takeWhile (/= '\n') >>> length $ s
                m = filter (== '\n') >>> length >>> pred $ s

reachableNeighbors :: (Int, Int) -> UArray (Int, Int) Int -> [(Int, Int)]
reachableNeighbors p@(py, px) a = List.filter (UArray.inRange (UArray.bounds a))
        >>> List.filter ((a UArray.!) >>> pred >>> (== (a UArray.! p)))
        $ [(py-1, px), (py+1, px), (py, px-1), (py, px+1)]

distinctTrails :: (Int, Int) -> UArray (Int, Int) Int -> Int
distinctTrails p a
        | a UArray.! p == 9 = 1
        | otherwise = flip reachableNeighbors a
                >>> List.map (flip distinctTrails a)
                >>> sum
                $ p

reachableNines :: (Int, Int) -> UArray (Int, Int) Int -> Set (Int, Int)
reachableNines p a
        | a UArray.! p == 9 = Set.singleton p
        | otherwise = flip reachableNeighbors a
                >>> List.map (flip reachableNines a)
                >>> Set.unions
                $ p

findZeros = UArray.assocs
        >>> filter (snd >>> (== 0))
        >>> map fst

part1 a = findZeros
        >>> map (flip reachableNines a)
        >>> map Set.size
        >>> sum
        $ a
part2 a = findZeros
        >>> map (flip distinctTrails a)
        >>> sum
        $ a

main = getContents
        >>= print
        . (part1 &&& part2)
        . parse