Haskell

Spent a lot of time trying to find symmetric quadrants. In the end made an interactive visualization and found that a weird pattern appeared on iterations (27 + 101k) and (75 + 103k'). Put those congruences in an online Chinese remainder theorem calculator and go to the answer: x ≡ 8006 (mod 101*103)

import Data.Bifunctor
import Data.Char
import qualified Data.Set as S
import Data.Functor
import Data.List
import Control.Monad
import Text.ParserCombinators.ReadP
import Data.IORef

bounds = (101, 103)

parseInt :: ReadP Int
parseInt = (*) <$> option 1 (char '-' $> (-1)) <*> (read <$> munch1 isDigit)
parseTuple = (,) <$> parseInt <*> (char ',' *> parseInt)
parseRow = (,) <$> (string "p=" *> parseTuple) <*> (string " v=" *> parseTuple)
parse = fst . last . readP_to_S (endBy parseRow (char '\n'))

move t (x, y) (vx, vy) = bimap (mod (x + vx * t)) (mod (y + vy * t)) bounds

getQuadrant :: (Int, Int) -> Int
getQuadrant (x, y)
    | x == mx || y == my = 0
    | otherwise = case (x > mx, y > my) of
        (True, True) -> 1
        (True, False) -> 2
        (False, True) -> 3
        (False, False) -> 4
  where
    (mx, my) = bimap (`div` 2) (`div` 2) bounds

step (x, y) (vx, vy) = (,(vx, vy)) $ bimap (mod (x + vx)) (mod (y + vy)) bounds

main = do
    p <- parse <$> readFile "input14"

    print . product . fmap length . group . sort . filter (/=0) . fmap (getQuadrant . uncurry (move 100)) $ p

    let l = iterate (fmap (uncurry step)) p

    current <- newIORef 0
    actions <- lines <$> getContents
    forM_ actions $ \a -> do
        case a of
            "" -> modifyIORef current (+1)
            "+" -> modifyIORef current (+1)
            "-" -> modifyIORef current (subtract 1)
            n -> writeIORef current (read n)
        pos <- readIORef current
        putStr "\ESC[2J" -- clear screen
        print pos
        visualize $ fst <$> l !! pos

visualize :: [(Int, Int)] -> IO ()
visualize pos = do
    let p = S.fromList pos
    forM_ [1..(snd bounds)] $ \y -> do
        forM_ [1..(fst bounds)] $ \x -> do
            putChar $ if S.member (x, y) p then '*' else '.'
        putChar '\n'