src/advent21/advent21.hs

   1 {-# LANGUAGE NegativeLiterals #-}
   2 {-# LANGUAGE FlexibleContexts #-}
   3 {-# LANGUAGE OverloadedStrings #-}
   4 {-# LANGUAGE TypeFamilies #-}
   5 {-# LANGUAGE BangPatterns #-}
   6
   7 import Data.Text (Text)
   8 import qualified Data.Text as T
   9 import qualified Data.Text.IO as TIO
  10
  11 import Text.Megaparsec hiding (State)
  12 import qualified Text.Megaparsec.Lexer as L
  13 import Text.Megaparsec.Text (Parser)
  14 import qualified Control.Applicative as CA
  15 -- import qualified Data.Functor as F
  16
  17 import qualified Data.Map.Strict as M
  18 import Data.Map.Strict ((!))
  19
  20 import Data.List
  21
  22
  23 type Grid = M.Map (Int, Int) Bool
  24 type ExplodedGrid = M.Map (Int, Int) Grid
  25
  26 data Rule = Rule Grid Grid deriving (Eq, Show)
  27
  28 rulePre (Rule g _) = g
  29 rulePost (Rule _ g) = g
  30
  31
  32 initialGrid = case parse gridP "" ".#./..#/###" of
  33                 Left _ -> M.empty
  34                 Right g -> g
  35
  36
  37 main :: IO ()
  38 main = do
  39         text <- TIO.readFile "data/advent21.txt"
  40         let rules = readRules text
  41         print $ countLit $ nthApplication rules 5
  42         print $ countLit $ nthApplication rules 18
  43
  44
  45 -- Read the rules, and expand them to all equivalent left hand sides
  46 readRules :: Text -> [Rule]
  47 readRules = expandRules . successfulParse
  48
  49
  50 expandRules :: [Rule] -> [Rule]
  51 expandRules = concatMap expandRule
  52
  53 expandRule :: Rule -> [Rule]
  54 expandRule rule = [Rule l (rulePost rule) | l <- allArrangements (rulePre rule)]
  55
  56
  57 reflectH :: Grid -> Grid
  58 reflectH g = M.fromList [((r, c) , M.findWithDefault False (rm - r, c) g) | r <- [0..rm], c <- [0..cm] ]
  59     where (rm, cm) = bounds g
  60
  61 reflectV :: Grid -> Grid
  62 reflectV g = M.fromList [((r, c) , M.findWithDefault False (r, cm - c) g) | r <- [0..rm], c <- [0..cm] ]
  63     where (rm, cm) = bounds g
  64
  65 -- awkward naming to avoid clashing with Prelude
  66 transposeG :: Grid -> Grid
  67 transposeG g = M.fromList [((c, r) , M.findWithDefault False (r, c) g) | r <- [0..rm], c <- [0..cm] ]
  68     where (rm, cm) = bounds g
  69
  70
  71 -- Find all the arrangments of a grid, including reflection and rotation.
  72 allArrangements :: Grid -> [Grid]
  73 allArrangements grid = map (\f -> f grid) [ id
  74                                           , reflectH
  75                                           , reflectV
  76                                           , transposeG
  77                                           , reflectH . transposeG
  78                                           , reflectV . transposeG
  79                                           , reflectH . reflectV . transposeG
  80                                           , reflectV . reflectH
  81                                           ]
  82
  83
  84
  85 -- Count number of lit pixels
  86 countLit :: Grid -> Int
  87 countLit = M.size . M.filter id
  88
  89 -- apply the rules _n_ times
  90 nthApplication :: [Rule] -> Int -> Grid
  91 nthApplication rules n = (!! n) $ iterate (applyOnce rules) initialGrid
  92
  93 -- Apply one step of the expansion
  94 applyOnce :: [Rule] -> Grid -> Grid
  95 applyOnce rules g = contractExploded $ M.map (apply rules) $ explodeGrid g
  96
  97 -- find the appropriate rule and apply it to a grid
  98 apply :: [Rule] -> Grid -> Grid
  99 apply rules grid = rulePost thisRule
 100     where ri = head $ findIndices (\r -> rulePre r == grid) rules
 101           thisRule = rules!!ri
 102
 103
 104 -- create the appropriate subgrids of a grid
 105 explodeGrid :: Grid -> ExplodedGrid
 106 explodeGrid g = if (rm + 1) `rem` 2 == 0
 107                 then explodeGrid' 2 g
 108                 else explodeGrid' 3 g
 109     where (rm, cm) = bounds g
 110
 111 explodeGrid' :: Int -> Grid -> ExplodedGrid
 112 explodeGrid' n g = M.fromList [((bigR, bigC), subGrid n g bigR bigC) | bigR <- [0..bigRm], bigC <- [0..bigCm]]
 113     where (rm, cm) = bounds g
 114           bigRm = (rm + 1) `div` n - 1
 115           bigCm = (cm + 1) `div` n - 1
 116
 117
 118 subGrid :: Int -> Grid -> Int -> Int -> Grid
 119 subGrid n g bigR bigC = M.fromList [ ((r, c),
 120                                       M.findWithDefault False (r + rStep, c + cStep) g)
 121                                    | r <- [0..(n - 1)], c <- [0..(n - 1)]
 122                                    ]
 123     where rStep = bigR * n
 124           cStep = bigC * n
 125
 126 -- merge a set of subgrids into one
 127 contractExploded :: ExplodedGrid -> Grid
 128 contractExploded gs = foldl1 (>|<) $ map (foldl1 (>-<)) rows
 129     where rows = explodedRows gs
 130
 131 -- find the rows of an exploded grid
 132 explodedRows :: ExplodedGrid -> [ExplodedGrid]
 133 explodedRows eg = [M.filterWithKey (\(r, _) _ -> r == row) eg | row <- [0..rowMax] ]
 134     where (rowMax, _) = bounds eg
 135
 136 -- merge two grids horizontally
 137 (>-<) :: Grid -> Grid -> Grid
 138 (>-<) g1 g2 = M.union g1 g2'
 139     where (_, cm) = bounds g1
 140           g2' = M.mapKeys (\(r, c) -> (r, c + cm + 1)) g2
 141
 142 -- merge two grids vertically
 143 (>|<) :: Grid -> Grid -> Grid
 144 (>|<) g1 g2 = M.union g1 g2'
 145     where (rm, _) = bounds g1
 146           g2' = M.mapKeys (\(r, c) -> (r + rm + 1, c)) g2
 147
 148
 149
 150
 151 bounds :: M.Map (Int, Int) a -> (Int, Int)
 152 bounds grid = (maximum $ map fst $ M.keys grid, maximum $ map snd $ M.keys grid)
 153
 154
 155 showGrid :: Grid -> String
 156 showGrid g = unlines [[showGChar $ M.findWithDefault False (r, c) g |
 157                 c <- [0..cm] ] | r <- [0..rm] ]
 158     where (rm, cm) = bounds g
 159           showGChar True = '#'
 160           showGChar False = '.'
 161
 162
 163
 164 -- really persuade Megaparsec not to include newlines in how it consume spaces.
 165 onlySpace = (char ' ') <|> (char '\t')
 166
 167 sc :: Parser ()
 168 sc = L.space (skipSome onlySpace) CA.empty CA.empty
 169
 170 lexeme  = L.lexeme sc
 171
 172 symbol = L.symbol sc
 173 rowSep = symbol "/"
 174 ruleJoin = symbol "=>"
 175
 176 present = id True <$ symbol "#"
 177 absent = id False <$ symbol "."
 178
 179 rulesP = ruleP `sepBy` space
 180 ruleP = Rule <$> gridP <* ruleJoin <*> gridP
 181
 182 gridP = gridify <$> rowP `sepBy` rowSep
 183     where gridify g = M.fromList $ concat
 184                                     [map (\(c, v) -> ((r, c), v)) nr |
 185                                              (r, nr) <- zip [0..]
 186                                                             [zip [0..] r | r <- g]]
 187
 188
 189 rowP = some (present <|> absent)
 190
 191 successfulParse :: Text -> [Rule]
 192 successfulParse input =
 193         case parse rulesP "input" input of
 194                 Left  _error -> []
 195                 Right instructions  -> instructions