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 allArrangements grid = map ($ grid) [ id
  73                                     , reflectH
  74                                     , reflectV
  75                                     , transposeG
  76                                     , reflectH . transposeG
  77                                     , reflectV . transposeG
  78                                     , reflectH . reflectV . transposeG
  79                                     , reflectV . reflectH
  80                                     ]
  81
  82
  83
  84 -- Count number of lit pixels
  85 countLit :: Grid -> Int
  86 countLit = M.size . M.filter id
  87
  88 -- apply the rules _n_ times
  89 nthApplication :: [Rule] -> Int -> Grid
  90 nthApplication rules n = (!! n) $ iterate (applyOnce rules) initialGrid
  91
  92 -- Apply one step of the expansion
  93 applyOnce :: [Rule] -> Grid -> Grid
  94 applyOnce rules g = contractExploded $ M.map (apply rules) $ explodeGrid g
  95
  96 -- find the appropriate rule and apply it to a grid
  97 apply :: [Rule] -> Grid -> Grid
  98 apply rules grid = rulePost thisRule
  99     where ri = head $ findIndices (\r -> rulePre r == grid) rules
 100           thisRule = rules!!ri
 101
 102
 103 -- create the appropriate subgrids of a grid
 104 explodeGrid :: Grid -> ExplodedGrid
 105 explodeGrid g = if (rm + 1) `rem` 2 == 0
 106                 then explodeGrid' 2 g
 107                 else explodeGrid' 3 g
 108     where (rm, _cm) = bounds g
 109
 110 explodeGrid' :: Int -> Grid -> ExplodedGrid
 111 explodeGrid' n g = M.fromList [((bigR, bigC), subGrid n g bigR bigC) | bigR <- [0..bigRm], bigC <- [0..bigCm]]
 112     where (rm, cm) = bounds g
 113           bigRm = (rm + 1) `div` n - 1
 114           bigCm = (cm + 1) `div` n - 1
 115
 116
 117 subGrid :: Int -> Grid -> Int -> Int -> Grid
 118 subGrid n g bigR bigC = M.fromList [ ((r, c),
 119                                       M.findWithDefault False (r + rStep, c + cStep) g)
 120                                    | r <- [0..(n - 1)], c <- [0..(n - 1)]
 121                                    ]
 122     where rStep = bigR * n
 123           cStep = bigC * n
 124
 125 -- merge a set of subgrids into one
 126 contractExploded :: ExplodedGrid -> Grid
 127 contractExploded gs = foldl1 (>|<) $ map (foldl1 (>-<)) rows
 128     where rows = explodedRows gs
 129
 130 -- find the rows of an exploded grid
 131 explodedRows :: ExplodedGrid -> [ExplodedGrid]
 132 explodedRows eg = [M.filterWithKey (\(r, _) _ -> r == row) eg | row <- [0..rowMax] ]
 133     where (rowMax, _) = bounds eg
 134
 135 -- merge two grids horizontally
 136 (>-<) :: Grid -> Grid -> Grid
 137 (>-<) g1 g2 = M.union g1 g2'
 138     where (_, cm) = bounds g1
 139           g2' = M.mapKeys (\(r, c) -> (r, c + cm + 1)) g2
 140
 141 -- merge two grids vertically
 142 (>|<) :: Grid -> Grid -> Grid
 143 (>|<) g1 g2 = M.union g1 g2'
 144     where (rm, _) = bounds g1
 145           g2' = M.mapKeys (\(r, c) -> (r + rm + 1, c)) g2
 146
 147
 148
 149
 150 bounds :: M.Map (Int, Int) a -> (Int, Int)
 151 bounds grid = (maximum $ map fst $ M.keys grid, maximum $ map snd $ M.keys grid)
 152
 153
 154 showGrid :: Grid -> String
 155 showGrid g = unlines [[showGChar $ M.findWithDefault False (r, c) g |
 156                 c <- [0..cm] ] | r <- [0..rm] ]
 157     where (rm, cm) = bounds g
 158           showGChar True = '#'
 159           showGChar False = '.'
 160
 161
 162
 163 -- really persuade Megaparsec not to include newlines in how it consume spaces.
 164 onlySpace = (char ' ') <|> (char '\t')
 165
 166 sc :: Parser ()
 167 sc = L.space (skipSome onlySpace) CA.empty CA.empty
 168
 169 symbol = L.symbol sc
 170 rowSep = symbol "/"
 171 ruleJoin = symbol "=>"
 172
 173 present = id True <$ symbol "#"
 174 absent = id False <$ symbol "."
 175
 176 rulesP = ruleP `sepBy` space
 177 ruleP = Rule <$> gridP <* ruleJoin <*> gridP
 178
 179 gridP = gridify <$> rowP `sepBy` rowSep
 180     where gridify g = M.fromList $ concat
 181                                     [map (\(c, v) -> ((r, c), v)) nr |
 182                                              (r, nr) <- zip [0..]
 183                                                             [zip [0..] r | r <- g]]
 184
 185
 186 rowP = some (present <|> absent)
 187
 188 successfulParse :: Text -> [Rule]
 189 successfulParse input =
 190         case parse rulesP "input" input of
 191                 Left  _error -> []
 192                 Right instructions  -> instructions