2023-21 part 2 in haskell
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2023/21-Step_Counter/second.hs
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92
2023/21-Step_Counter/second.hs
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-- requires cabal install --lib megaparsec parser-combinators heap vector
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module Main (main) where
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import Control.Applicative.Permutations
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import Control.Monad (void, when)
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import qualified Data.Char as C
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import Data.Either
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import Data.Functor
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import qualified Data.Heap as H
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import qualified Data.List as L
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import qualified Data.Map as M
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import Data.Maybe
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import qualified Data.Set as S
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import qualified Data.Vector as V
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import qualified Data.Vector.Unboxed as VU
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import Data.Void (Void)
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import Text.Megaparsec
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import Text.Megaparsec.Char
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import Debug.Trace
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data Tile = Start | Plot | Rock deriving Eq
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instance Show Tile where
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show Start = "S"
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show Plot = "."
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show Rock = "#"
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type Line = V.Vector Tile
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type Input = V.Vector Line
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type Parser = Parsec Void String
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parseTile :: Parser Tile
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parseTile = char 'S' $> Start
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<|> char '.' $> Plot
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<|> char '#' $> Rock
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parseLine :: Parser Line
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parseLine = do
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line <- some parseTile <* eol
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return $ V.generate (length line) (line !!)
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parseInput' :: Parser Input
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parseInput' = do
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line <- some parseLine <* eof
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return $ V.generate (length line) (line !!)
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parseInput :: String -> IO Input
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parseInput filename = do
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input <- readFile filename
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case runParser parseInput' filename input of
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Left bundle -> error $ errorBundlePretty bundle
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Right input' -> return input'
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type Steps = M.Map (Int, Int) ()
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-- 26501365 = 202300 * 131 + 65
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compute :: Input -> Integer
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compute input = let steps = compute' 65 start
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steps' = compute' 131 steps
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steps'' = compute' 131 steps'
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steps''' = compute' 131 steps''
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-- lagrange polynomial interpolation for the quadratic function
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f :: Integer -> Integer
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f x = let lamb xi = product (map (\xj -> (x-xj)) (L.delete xi xs)) `div` product (map (\xj -> (xi-xj)) (L.delete xi xs))
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in sum $ zipWith (*) ys (map lamb xs)
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xs = toInteger <$> [x*131+65|x<-[0..3]]
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ys = toInteger . M.size <$> [steps, steps', steps'', steps''']
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in f 26501365
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where
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compute' :: Int -> Steps -> Steps
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compute' 0 steps = steps
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compute' i steps = compute' (i-1) next
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where
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next :: Steps
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next = M.foldrWithKey nextSteps M.empty steps
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nextSteps :: (Int, Int) -> () -> Steps -> Steps
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nextSteps (x, y) _ = nextOne (x-1, y) . nextOne (x+1, y) . nextOne (x, y-1) . nextOne (x, y+1)
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nextOne :: (Int, Int) -> Steps -> Steps
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nextOne (x, y) acc = case input V.!? (y `mod` len) of
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Just line -> case line V.!? (x `mod` len) of
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Just Rock -> acc
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Just _ -> M.insert (x, y) () acc
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_ -> acc
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Nothing -> acc
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start = M.singleton (mid, mid) ()
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mid = len `div` 2
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len = V.length input
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main :: IO ()
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main = do
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input <- parseInput "input"
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print $ compute input
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