--- Writeup at https://work.njae.me.uk/2023/12/29/advent-of-code-2023-day-21/
+-- Writeup at https://work.njae.me.uk/2024/01/02/advent-of-code-2023-day-23/
+
+import qualified Debug.Trace as DT
import AoC
-import Linear (V2(..), (^+^))
+import Linear -- (V2(..), (^+^))
import qualified Data.Set as S
-import qualified Data.Map as M
+import qualified Data.Map.Strict as M
+import qualified Data.Sequence as Q
+import Data.Sequence (Seq( (:|>), (:<|) ) )
+import Control.Lens
+import Data.List (foldl')
+import Control.Monad.Reader
+import qualified Data.PQueue.Prio.Max as P
+import Data.Foldable
+import Data.Maybe
data Slide = SlideLeft | SlideRight | SlideUp | SlideDown
deriving (Show, Eq)
type Position = V2 Int -- r, c
+
+_r, _c :: Lens' (V2 Int) Int
+_r = _x
+_c = _y
+
type Grid = S.Set Position
type Slides = M.Map Position Slide
+data CompressedPath = CPath { _nextPos :: Position, _pathLen :: Int }
+ deriving (Show, Eq)
+makeLenses ''CompressedPath
+
+type CompressedMap = M.Map Position [CompressedPath]
+data Mountain = Mountain
+ { _paths :: CompressedMap
+ , _start :: Position
+ , _goal :: Position
+ } deriving (Eq, Show)
+makeLenses ''Mountain
+
+type MountainContext = Reader Mountain
+
+data Agendum =
+ Agendum { _current :: Position
+ , _trail :: Q.Seq Position
+ , _trailCost :: Int
+ , _cost :: Int
+ } deriving (Show, Eq)
+makeLenses ''Agendum
+
+type Agenda = P.MaxPQueue Int Agendum
+
+type ExploredStates = M.Map Position Int
+
+
main :: IO ()
-main =
+main =
do dataFileName <- getDataFileName
text <- readFile dataFileName
let (forest, slides, start, end) = mkGrid text
- -- print forest
- -- print slides
- -- print start
- -- print end
- -- print $ searchStep slides forest [start ^+^ (V2 1 0), start]
- -- let paths = search slides forest end [] [[start ^+^ (V2 1 0), start]]
- -- print $ fmap length paths
+ -- print $ compress slides forest start end
print $ part1 slides forest start end
+ print $ part2 slides forest start end
-part1 slides forest start end = (maximum $ fmap length paths) - 1
- where paths = search slides forest end [] [[start ^+^ (V2 1 0), start]]
+part1, part2 :: Slides -> Grid -> Position -> Position -> Int
+part1 slides forest start end = searchCompressed $ Mountain cMap start end
+ where cMap = compress slides forest start end
+part2 slides forest start end = searchCompressed $ Mountain cMap start end
+ where cMap = compress M.empty forest start end
+-- part2 _ forest start end = maximum $ fmap (pathLength cMap) paths
+-- where cMap = compress M.empty forest start end
+-- paths = searchCompressed cMap start end
adjacents :: Position -> Slides -> Grid -> [Position]
-adjacents here slides walls = filter (`S.notMember` walls) $ fmap (^+^ here) deltas
+adjacents here slides forest = filter (`S.notMember` forest) $ fmap (here ^+^) deltas
where deltas = case M.lookup here slides of
Nothing -> [ V2 0 1, V2 1 0, V2 0 (-1), V2 (-1) 0 ]
Just SlideLeft -> [ V2 0 (-1) ]
Just SlideRight -> [ V2 0 1 ]
Just SlideUp -> [ V2 (-1) 0 ]
Just SlideDown -> [ V2 1 0 ]
-
+
searchStep :: Slides -> Grid -> [Position] -> [[Position]]
searchStep _ _ [] = []
searchStep slides forest path@(here:rest) = fmap (:path) valids
where nexts = adjacents here slides forest
valids = filter (`notElem` rest) nexts
-
-search :: Slides -> Grid -> Position -> [[Position]] -> [[Position]] -> [[Position]]
+search :: Slides -> Grid -> [Position] -> CompressedMap -> [[Position]] -> CompressedMap
search _ _ _ foundPaths [] = foundPaths
-search slides forest goal foundPaths (current:agenda)
- | head current == goal = search slides forest goal (current:foundPaths) agenda
- | otherwise = search slides forest goal foundPaths (agenda ++ extendeds)
+search slides forest goals foundPaths (current:agenda)
+ | head current `elem` goals = search slides forest goals foundPaths' agenda
+ | otherwise = search slides forest goals foundPaths (agenda ++ extendeds)
where extendeds = searchStep slides forest current
+ origin = last current
+ foundPaths' = if origin == head current then foundPaths
+ else M.adjust (cp :) origin foundPaths
+ cp = CPath (head current) (length current - 1)
+
+-- collapsing the map
+
+interestingPoints :: Slides -> Grid -> Position -> Position -> CompressedMap
+interestingPoints slides forest start end = M.fromList [(p, []) | p <- pointsSE]
+ where Just minR = minimumOf (folded . _r) forest
+ Just maxR = maximumOf (folded . _r) forest
+ Just minC = minimumOf (folded . _c) forest
+ Just maxC = maximumOf (folded . _c) forest
+ points = [ V2 r c | r <- [(minR + 2)..(maxR - 2)]
+ , c <- [(minC + 1)..(maxC - 1)]
+ , (V2 r c) `S.notMember` forest
+ , (length $ adjacents (V2 r c) slides forest) > 2
+ ]
+ pointsSE = start : end : points
+
+compress :: Slides -> Grid -> Position -> Position -> CompressedMap
+compress slides forest start end = foldl' go compressed0 iPoints
+ where compressed0 = interestingPoints slides forest start end
+ iPoints = M.keys compressed0
+ go com here = search slides forest iPoints com $ fmap (: [here]) $ adjacents here slides forest
+
+
+-- searchCompressed :: CompressedMap -> Position -> [[Position]] -> [[Position]] -> [[Position]]
+-- -- searchCompressed _ _ _ (c:_) _ | DT.trace (show c) False = undefined
+-- searchCompressed _ _ found [] = found
+-- searchCompressed map goal found (current:agenda)
+-- | head current == goal = searchCompressed map goal (current:found) agenda
+-- | otherwise = searchCompressed map goal found (nextPositions ++ agenda)
+-- where neighbours0 = map M.! (head current)
+-- neighbours = neighbours0 ^.. folded . filtered ((`notElem` current) . _nextPos)
+-- nextPositions = fmap ((: current) . _nextPos) neighbours
+
+searchCompressed :: Mountain -> Int
+searchCompressed mountain = maybe 0 _trailCost result
+ where result = runReader searchMountain mountain
+
+searchMountain :: MountainContext (Maybe Agendum)
+searchMountain =
+ do agenda <- initAgenda
+ aStar agenda Nothing
+
+initAgenda :: MountainContext Agenda
+initAgenda =
+ do s <- asks _start
+ c <- estimateCost Q.Empty s
+ let agendum = Agendum { _current = s, _trail = Q.empty, _trailCost = 0, _cost = c}
+ let agenda = P.singleton c agendum
+ return agenda
+
+aStar :: Agenda -> (Maybe Agendum) -> MountainContext (Maybe Agendum)
+aStar agenda best
+ -- | trace ("Peeping " ++ (show $ fst $ P.findMin agenda) ++ ": " ++ (show reached) ++ " <- " ++ (show $ toList $ Q.take 1 $ _trail $ currentAgendum) ++ " :: " ++ (show newAgenda)) False = undefined
+ -- | DT.trace ("Peeping " ++ (show $ _current $ snd $ P.findMax agenda) ) False = undefined
+ -- | DT.trace ("Peeping " ++ (show $ snd $ P.findMax agenda) ) False = undefined
+ -- | DT.trace ("Peeping " ++ (show agenda) ) False = undefined
+ | P.null agenda = return best
+ | (fst $ P.findMax agenda) < maybe 0 _trailCost best = return best
+ | otherwise =
+ do let (_, currentAgendum) = P.findMax agenda
+ let reached = currentAgendum ^. current
+ nexts <- candidates currentAgendum
+ let newAgenda = foldl' (\q a -> P.insert (_cost a) a q) (P.deleteMax agenda) nexts
+ reachedGoal <- isGoal reached
+ let best' = updateBest reachedGoal best currentAgendum
+ -- let closed' = M.insert reached (currentAgendum ^. trailCost) closed
+ if reachedGoal -- || (reached `S.member` closed)
+ then aStar (P.deleteMax agenda) best' -- closed'
+ else aStar newAgenda best' -- closed'
+
+updateBest :: Bool -> Maybe Agendum -> Agendum -> Maybe Agendum
+updateBest False current _ = current
+updateBest True Nothing best
+ -- | DT.trace ("Nothing " ++ show best) False = undefined
+ | otherwise = Just best
+updateBest True (Just current) best
+ -- | DT.trace (show current ++ " " ++ show best) False = undefined
+ | (current ^. trailCost) > (best ^. trailCost) = Just current
+ | otherwise = Just best
+
+
+
+
+candidates :: Agendum -> MountainContext (Q.Seq Agendum)
+candidates agendum =
+ do let here = agendum ^. current
+ let previous = agendum ^. trail
+ let prevCost = agendum ^. trailCost
+ ts <- asks _paths
+ let succs = Q.fromList $ ts M.! here
+ -- succs <- successors candidate
+ let nonloops = Q.filter (\s -> (s ^. nextPos) `notElem` previous) succs
+ mapM (makeAgendum previous prevCost here) nonloops
+
+
+makeAgendum :: (Q.Seq Position) -> Int -> Position -> CompressedPath -> MountainContext Agendum
+makeAgendum previous prevCost here step =
+ do let newTrail = previous :|> here
+ predicted <- estimateCost newTrail $ step ^. nextPos
+ -- ts <- asks _trails
+ let incurred = prevCost + step ^. pathLen
+ return Agendum { _current = step ^. nextPos
+ , _trail = newTrail
+ , _trailCost = incurred
+ , _cost = incurred + predicted
+ }
+
+
+isGoal :: Position -> MountainContext Bool
+isGoal here =
+ do goal <- asks _goal
+ return $ here == goal
+
+estimateCost :: Q.Seq Position -> Position -> MountainContext Int
+estimateCost r e =
+ do ts <- asks _paths
+ let endCost = fromMaybe 0 $ maximumOf (folded . filtered ((`notElem` r) . _nextPos) . pathLen) $ ts M.! e
+ let res = S.fromList $ toList (r :|> e)
+ let otherPaths = concat $ M.elems $ ts `M.withoutKeys` res
+ let restCost = sumOf (folded . filtered ((`notElem` r) . _nextPos) . pathLen) otherPaths
+ return $ (restCost `div` 2) + endCost
+-- pathLength :: CompressedMap -> [Position] -> Int
+-- pathLength map ps = sum $ zipWith (stepLength map) ps $ tail ps
--- showGrid :: Grid -> (Position, Position) -> Grid -> String
--- showGrid rocks bounds cells = unlines $ intercalate [" "] $ chunksOf 7 $ fmap (showRow rocks bounds cells) [-28..34]
--- where showRow rocks bounds cells r = intercalate " " $ chunksOf 7 $ fmap ((showCell rocks bounds cells) . V2 r) [-28..34]
--- showCell rocks bounds cells here
--- | not $ notAtRock rocks bounds here = '#'
--- | here `S.member` cells = 'O'
--- | otherwise = '.'
+-- stepLength :: CompressedMap -> Position -> Position -> Int
+-- stepLength map here there =
+-- -- head $ (map M.! there) ^.. folded . filtered ((== here) . _nextPos) . pathLen
+-- head $ (map M.! there) ^.. folded . filteredBy (nextPos . only here) . pathLen
-- reading the map
mkGrid :: String -> (Grid, Slides, Position, Position)
-mkGrid text = (forest, slides, start, end)
+mkGrid text = ((S.union forest caps), slides, start, end)
where rows = lines text
maxR = length rows - 1
maxC = (length $ head rows) - 1
forest = S.fromList [ V2 r c | r <- [0..maxR], c <- [0..maxC]
, rows !! r !! c == '#'
]
- slides = M.fromList [ (V2 r c, readSlide (rows !! r !! c))
+ slides = M.fromList [ (V2 r c, readSlide (rows !! r !! c))
| r <- [0..maxR], c <- [0..maxC]
, elem (rows !! r !! c) ("<>^v" :: String)
]
end = head $ [ V2 maxR c | c <- [0..maxC]
, rows !! maxR !! c == '.'
]
+ caps = S.fromList [start ^+^ (V2 -1 0), end ^+^ (V2 1 0)]
readSlide :: Char -> Slide
readSlide '<' = SlideLeft
projects / advent-of-code-23.git / blobdiff