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-- requires cabal install --lib megaparsec parser-combinators heap vector
module Main (main) where
import Control.Applicative.Permutations
import Control.Monad (void, when)
import qualified Data.Char as C
import Data.Either
import Data.Functor
import qualified Data.Heap as H
import qualified Data.List as L
import qualified Data.Map as M
import Data.Maybe
import qualified Data.Set as S
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import Data.Void (Void)
import Text.Megaparsec
import Text.Megaparsec.Char
import Debug.Trace
data Tile = Start | Plot | Rock deriving Eq
instance Show Tile where
show Start = "S"
show Plot = "."
show Rock = "#"
type Line = V.Vector Tile
type Input = V.Vector Line
type Parser = Parsec Void String
parseTile :: Parser Tile
parseTile = char 'S' $> Start
<|> char '.' $> Plot
<|> char '#' $> Rock
parseLine :: Parser Line
parseLine = do
line <- some parseTile <* eol
return $ V.generate (length line) (line !!)
parseInput' :: Parser Input
parseInput' = do
line <- some parseLine <* eof
return $ V.generate (length line) (line !!)
parseInput :: String -> IO Input
parseInput filename = do
input <- readFile filename
case runParser parseInput' filename input of
Left bundle -> error $ errorBundlePretty bundle
Right input' -> return input'
type Steps = M.Map (Int, Int) ()
-- 26501365 = 202300 * 131 + 65
compute :: Input -> Integer
compute input = let steps = compute' 65 start
steps' = compute' 131 steps
steps'' = compute' 131 steps'
steps''' = compute' 131 steps''
-- lagrange polynomial interpolation for the quadratic function
f :: Integer -> Integer
f x = let lamb xi = product (map (\xj -> (x-xj)) (L.delete xi xs)) `div` product (map (\xj -> (xi-xj)) (L.delete xi xs))
in sum $ zipWith (*) ys (map lamb xs)
xs = toInteger <$> [x*131+65|x<-[0..3]]
ys = toInteger . M.size <$> [steps, steps', steps'', steps''']
in f 26501365
where
compute' :: Int -> Steps -> Steps
compute' 0 steps = steps
compute' i steps = compute' (i-1) next
where
next :: Steps
next = M.foldrWithKey nextSteps M.empty steps
nextSteps :: (Int, Int) -> () -> Steps -> Steps
nextSteps (x, y) _ = nextOne (x-1, y) . nextOne (x+1, y) . nextOne (x, y-1) . nextOne (x, y+1)
nextOne :: (Int, Int) -> Steps -> Steps
nextOne (x, y) acc = case input V.!? (y `mod` len) of
Just line -> case line V.!? (x `mod` len) of
Just Rock -> acc
Just _ -> M.insert (x, y) () acc
_ -> acc
Nothing -> acc
start = M.singleton (mid, mid) ()
mid = len `div` 2
len = V.length input
main :: IO ()
main = do
input <- parseInput "input"
print $ compute input
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