109 lines
3.3 KiB
Haskell
109 lines
3.3 KiB
Haskell
{-# LANGUAGE OverloadedStrings #-}
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module Day24 (parse, solveA, solveB) where
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import Data.Void (Void)
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import Data.Text (Text)
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import Data.Maybe (mapMaybe)
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import Data.Bifunctor (first, bimap)
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import Control.Monad ((<=<))
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import Text.Megaparsec (Parsec, errorBundlePretty, runParser, eof, many)
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import Text.Megaparsec.Char (char, space)
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import Text.Megaparsec.Char.Lexer (signed, decimal)
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import Numeric.LinearAlgebra (R, linearSolve, flatten, toList, fromLists, col)
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import Misc (paired)
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type R3 = (R, R, R)
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type Ray = (R3, R3)
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type Parser = Parsec Void Text
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parse :: Text -> Either String [Ray]
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parse = first errorBundlePretty . runParser rays ""
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where
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r :: Parser R
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r = signed space decimal
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r3 :: Parser R3
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r3 = do
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a <- r <* char ',' <* space
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b <- r <* char ',' <* space
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c <- r
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return (a, b, c)
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ray :: Parser (R3, R3)
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ray = do
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t1 <- r3 <* space
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char '@' *> space
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t2 <- r3 <* space
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return (t1, t2)
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rays :: Parser [Ray]
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rays = many ray <* eof
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intersect2D :: Ray -> Ray -> Maybe ([R], (R, R))
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intersect2D r1 r2 =
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let ((sx1, sy1, _), (vx1, vy1, _)) = r1
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((sx2, sy2, _), (vx2, vy2, _)) = r2
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coeffs = fromLists
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[ [vx2, -vx1]
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, [vy2, -vy1]
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]
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rhs = col
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[ sx1 - sx2
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, sy1 - sy2
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]
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times = toList . flatten <$> linearSolve coeffs rhs
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in case times of
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Just ts@(tb:_) -> Just (ts, toPoint tb r2)
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_otherwise -> Nothing
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where
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toPoint :: R -> Ray -> (R, R)
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toPoint t ((sx, sy, _), (vx, vy, _)) = (sx + t * vx, sy + t * vy)
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solveAFor :: R -> R -> [Ray] -> Int
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solveAFor s e = length . filter isBoth . mapMaybe (uncurry intersect2D) . paired
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where
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isFuture :: [R] -> Bool
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isFuture = all (0<=)
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isWithin :: (R, R) -> Bool
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isWithin (x, y) = s <= x && x <= e && s <= y && y <= e
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isBoth :: ([R], (R, R)) -> Bool
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isBoth = uncurry (&&) . bimap isFuture isWithin
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solveA :: [Ray] -> Int
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solveA = solveAFor 200000000000000 400000000000000
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findThrow :: (Ray, Ray, Ray) -> Maybe [Int]
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findThrow (r1, r2, r3) =
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let
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((sx1, sy1, sz1), (vx1, vy1, vz1)) = r1
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((sx2, sy2, sz2), (vx2, vy2, vz2)) = r2
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((sx3, sy3, sz3), (vx3, vy3, vz3)) = r3
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coeffs = fromLists
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[ [0, vz2 - vz1, vy1 - vy2, 0, sz1 - sz2, sy2 - sy1]
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, [0, vz3 - vz1, vy1 - vy3, 0, sz1 - sz3, sy3 - sy1]
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, [vz1 - vz2, 0, vx2 - vx1, sz2 - sz1, 0, sx1 - sx2]
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, [vz1 - vz3, 0, vx3 - vx1, sz3 - sz1, 0, sx1 - sx3]
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, [vy2 - vy1, vx1 - vx2, 0, sy1 - sy2, sx2 - sx1, 0]
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, [vy3 - vy1, vx1 - vx3, 0, sy1 - sy3, sx3 - sx1, 0]
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]
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rhs = col
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[ vy1 * sz1 - sy1 * vz1 + sy2 * vz2 - vy2 * sz2
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, vy1 * sz1 - sy1 * vz1 + sy3 * vz3 - vy3 * sz3
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, sx1 * vz1 - vx1 * sz1 + vx2 * sz2 - sx2 * vz2
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, sx1 * vz1 - vx1 * sz1 + vx3 * sz3 - sx3 * vz3
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, vx1 * sy1 - sx1 * vy1 + sx2 * vy2 - vx2 * sy2
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, vx1 * sy1 - sx1 * vy1 + sx3 * vy3 - vx3 * sy3
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]
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in map round . toList . flatten <$> linearSolve coeffs rhs
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solveB :: [Ray] -> Int
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solveB = maybe 0 (sum . take 3) . findThrow'
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where
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bundle :: [Ray] -> Maybe (Ray, Ray, Ray)
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bundle rays = case rays of
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r1:r2:r3:_ -> Just (r1, r2, r3)
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_otherwise -> Nothing
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findThrow' :: [Ray] -> Maybe [Int]
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findThrow' = findThrow <=< bundle
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