Haskell

First parse and floodfill from start, each position then holds the distance from the start

For part 1, I check all neighbor tiles of neighbor tiles that are walls and calculate the distance that would've been in-between.

In part 2 I check all tiles within a manhattan distance <= 20 and calculate the distance in-between on the path. Then filter out all cheats <100 and count

Takes 1.4s sadly, I believe there is still potential for optimization.

Edit: coding style

import Control.Arrow

import qualified Data.List as List
import qualified Data.Set as Set
import qualified Data.Map as Map
import qualified Data.Maybe as Maybe

parse s = Map.fromList [ ((y, x), c) | (l, y) <- zip ls [0..], (c, x) <- zip l [0..]]
        where
        ls = lines s

floodFill m = floodFill' m startPosition (Map.singleton startPosition 0)
        where
                startPosition = Map.assocs
                        >>> filter ((== 'S') . snd)
                        >>> head
                        >>> fst
                        $ m

neighbors (p1, p2) = [(p1-1, p2), (p1, p2-1), (p1, p2+1), (p1+1, p2)]

floodFill' m p f
        | m Map.! p == 'E' = f
        | otherwise = floodFill' m n f'
        where
                seconds = f Map.! p
                ns = neighbors p
                n = List.filter ((m Map.!) >>> (`Set.member` (Set.fromList ".E")))
                        >>> List.filter ((f Map.!?) >>> Maybe.isNothing)
                        >>> head
                        $ ns
                f' = Map.insert n (succ seconds) f

taxiCabDistance (a1, a2) (b1, b2) = abs (a1 - b1) + abs (a2 - b2)

calculateCheatAdvantage f (p1, p2) = c2 - c1 - taxiCabDistance p1 p2
        where
                c1 = f Map.! p1
                c2 = f Map.! p2

cheatDeltas :: Int -> Int -> [(Int, Int)]
cheatDeltas l h = [(y, x) | x <- [-h..h], y <- [-h..h], let d = abs x + abs y, d <= h, d >= l]

(a1, a2) .+. (b1, b2) = (a1 + b1, a2 + b2)

solve l h (f, ps) = Set.toList
        >>> List.map ( repeat
                >>> zip (cheatDeltas l h)
                >>> List.map (snd &&& uncurry (.+.))
                >>> List.filter (snd >>> (`Set.member` ps))
                >>> List.map (calculateCheatAdvantage f)
                >>> List.filter (>= 100)
                >>> List.length
                )
        >>> List.sum
        $ ps
part1 = solve 2 2
part2 = solve 1 20

main = getContents
        >>= print
        . (part1 &&& part2)
        . (id &&& Map.keysSet)
        . floodFill
        . parse