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{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE TupleSections #-}
module Main (main, showLayout) where
import Data.List (sortBy, transpose, intercalate, tails)
import Data.Foldable (toList)
import qualified Data.Map.Strict as Map
import Data.Map.Strict (Map)
import Data.Maybe (catMaybes, listToMaybe, fromJust)
import Data.Ord (Down(..), comparing)
import qualified Data.Set as Set
import Data.Set (Set)
import Input
import Util
data V4 a = V4 a a a a
deriving (Show, Functor)
instance Applicative V4 where
pure x = V4 x x x x
V4 f1 f2 f3 f4 <*> V4 x1 x2 x3 x4 = V4 (f1 x1) (f2 x2) (f3 x3) (f4 x4)
instance Foldable V4 where
foldr f z (V4 a b c d) = f a (f b (f c (f d z)))
ifmap :: (Int -> a -> b) -> V4 a -> V4 b
ifmap f (V4 a b c d) = fmap (uncurry f) (V4 (0, a) (1, b) (2, c) (3, d))
(!*) :: V4 a -> Int -> a
V4 a b c d !* i = [a, b, c, d] !! i
data B = F | T
deriving (Eq, Ord)
instance Show B where
show F = "."
show T = "#"
newtype Border' a = Border { unBorder :: [a] }
deriving (Eq, Ord, Functor)
type Border = Border' B
instance Show a => Show (Border' a) where
show (Border l) =
let l' = map show l
in if all ((== 1) . length) l' then concat l' else show l
data Rotation = R Int B -- rotated n, then possibly horizontally flipped
deriving (Show)
data Tile' a = Tile Int Rotation (V4 (Border' a)) [[a]]
deriving (Functor)
type Tile = Tile' B
instance Show a => Show (Tile' a) where
showsPrec p (Tile i r v _) = showParen (p > 10) (showString ("Tile " ++ show i ++ " (" ++ show r ++ ") ") . showsPrec 11 v . showString " {...}")
boolb :: Bool -> B
boolb True = T
boolb False = F
notB :: B -> B
notB F = T
notB T = F
tileID :: Tile -> Int
tileID (Tile i _ _ _) = i
parseTile :: [String] -> Tile
parseTile [] = error "empty tile"
parseTile (hdr:lns) =
fmap (boolb . (== '#')) $
Tile (if take 5 hdr == "Tile " then read (take 4 (drop 5 hdr)) else error ("tile header?" ++ show hdr))
(R 0 F)
(V4 (Border (head lns))
(Border (map last lns))
(Border (reverse (last lns)))
(Border (reverse (map head lns))))
lns
-- Rotates clockwise 90 degrees
rotArray :: [[a]] -> [[a]]
rotArray = map reverse . transpose
-- Flips horizontally
flipArray :: [[a]] -> [[a]]
flipArray = map reverse
-- Rotates clockwise 90 degrees
rotate :: Tile -> Tile
rotate (Tile i (R rotn rotf) (V4 a b c d) e) = Tile i (R (rotn+1) rotf) (V4 d a b c) (rotArray e)
-- Flips horizontally
flipTile :: Tile -> Tile
flipTile (Tile i (R rotn rotf) (V4 (Border a) (Border b) (Border c) (Border d)) e) =
Tile i (R rotn (notB rotf)) (V4 (Border (reverse a)) (Border (reverse d)) (Border (reverse c)) (Border (reverse b))) (flipArray e)
type Cd = (Int, Int) -- coordinate
data Layout = Layout (Map Cd Tile) (Set Cd)
deriving (Show)
lput :: Cd -> Tile -> Layout -> Layout
lput pos tile (Layout mp bd) =
Layout (Map.insertWith (error "lput: taken") pos tile mp)
(Set.delete pos bd <> (Set.fromList (toList (neighbours pos)) Set.\\ Map.keysSet mp))
neighbours :: Cd -> V4 Cd
neighbours (x, y) = V4 (x, y-1) (x+1, y) (x, y+1) (x-1, y)
borderAt :: Cd -> Layout -> V4 (Maybe Border)
borderAt pos (Layout mp _) =
ifmap (\i pos' -> (\(Tile _ _ bd _) -> Border (reverse (unBorder (bd !* mod (i + 2) 4)))) <$> Map.lookup pos' mp) (neighbours pos)
densityAt :: Layout -> Cd -> Int
densityAt ly pos = length (catMaybes (toList (borderAt pos ly)))
matchesOutline :: Tile -> V4 (Maybe Border) -> Bool
matchesOutline (Tile _ _ bd _) outl =
all id ((\b -> maybe True (== b)) <$> bd <*> outl)
rotrefls :: Tile -> [Tile]
rotrefls = concatMap (\t -> [t, flipTile t]) . take 4 . iterate rotate
matchesAtPos :: Layout -> [Tile] -> Cd -> [(Tile, [Tile])]
matchesAtPos ly ts pos =
[(t', rest)
| (t, rest) <- splits' ts
, t' <- rotrefls t
, matchesOutline t' (borderAt pos ly)]
allCandidates :: Layout -> [Tile] -> [(Cd, Tile, [Tile])]
allCandidates ly@(Layout _ bd) ts =
catMaybes
[case matchesAtPos ly ts pos of
[(t, ts')] -> Just (pos, t, ts')
_ -> Nothing
| pos <- sortBy (comparing (Down . densityAt ly)) (toList bd)]
findCandidate :: Layout -> [Tile] -> Maybe (Cd, Tile, [Tile])
findCandidate ly ts = listToMaybe (allCandidates ly ts)
placeAll :: Layout -> [Tile] -> (Layout, [Tile])
placeAll ly ts
| Just (pos, t, ts') <- findCandidate ly ts = placeAll (lput pos t ly) ts'
| otherwise = (ly, ts)
extents :: Map Cd a -> ((Int, Int), (Int, Int))
extents mp =
let keys = Map.keys mp
in ((minimum (map fst keys), maximum (map fst keys))
,(minimum (map snd keys), maximum (map snd keys)))
showLayout :: Layout -> String
showLayout (Layout mp bd) =
let mp' = foldr (uncurry Map.insert) (Map.map Just mp) (map (,Nothing) (toList bd))
((xmin, xmax), (ymin, ymax)) = extents mp'
in unlines [intercalate " "
[maybe "...." (maybe "----" (show . tileID)) (Map.lookup (x, y) mp')
| x <- [xmin..xmax]]
| y <- [ymin..ymax]]
cornerProd :: Layout -> Int
cornerProd (Layout mp _) =
let ((xmin, xmax), (ymin, ymax)) = extents mp
in product (map (tileID . fromJust . (`Map.lookup` mp)) [(xmin,ymin), (xmin,ymax), (xmax,ymin), (xmax,ymax)])
squareOfTiles :: Layout -> [[Tile]]
squareOfTiles (Layout mp _) =
let ((xmin, xmax), (ymin, ymax)) = extents mp
in [[mp Map.! (x, y) | x <- [xmin..xmax]] | y <- [ymin..ymax]]
removeEdges :: [[B]] -> [[B]]
removeEdges = map trim . trim
where trim = tail . reverse . tail . reverse
joinEdges :: [[Tile]] -> [[B]]
joinEdges tiles =
concat [map concat (transpose [removeEdges body | Tile _ _ _ body <- tilerow])
| tilerow <- tiles]
monster :: [[B]]
monster = map (map (\case '#' -> T ; ' ' -> F ; _ -> undefined)) pat
where pat = [" # "
,"# ## ## ###"
," # # # # # # "]
fieldParts :: [[a]] -> [[[a]]]
fieldParts bd = concatMap maptails (tails bd)
where maptails [] = []
maptails ([]:_) = []
maptails l = l : maptails (map tail l)
exceedsLength :: [a] -> [a] -> Bool
_ `exceedsLength` [] = True
[] `exceedsLength` _ = False
(_:xs) `exceedsLength` (_:ys) = xs `exceedsLength` ys
matchPattern :: [[B]] -> [[B]] -> Bool
matchPattern bd pat =
bd `exceedsLength` pat &&
all (\(bdrow, patrow) -> bdrow `exceedsLength` patrow &&
all (\(b, p) -> (p == F) || (b == T)) (zip bdrow patrow))
(zip bd pat)
countPattern :: [[B]] -> [[B]] -> Int
countPattern bd pat = length (filter (`matchPattern` pat) (fieldParts bd))
numTrue :: [[B]] -> Int
numTrue = length . concat . map (filter (== T))
main :: IO ()
main = do
tile0:tiles <- map parseTile . filter (not . null) . toList . splitOn null <$> getInput 20
let initLayout = lput (0, 0) tile0 (Layout mempty (Set.singleton (0, 0)))
(ly', _) = placeAll initLayout tiles
print (cornerProd ly')
let image = joinEdges (squareOfTiles ly')
images = concatMap (\b -> [b, flipArray b]) (take 4 (iterate rotArray image))
print (numTrue image - numTrue monster * maximum (map (`countPattern` monster) images))
|
