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