From: Neil Smith Date: Fri, 29 Dec 2023 14:45:51 +0000 (+0000) Subject: Geometic solution to part 2 X-Git-Url: https://git.njae.me.uk/?a=commitdiff_plain;h=a9d950d527ed44dd307f50969b0b67061c84f72b;p=advent-of-code-23.git Geometic solution to part 2 --- diff --git a/advent-of-code23.cabal b/advent-of-code23.cabal index 08ab63c..0eda336 100644 --- a/advent-of-code23.cabal +++ b/advent-of-code23.cabal @@ -216,3 +216,8 @@ executable advent20 import: common-extensions, build-directives main-is: advent20/Main.hs build-depends: containers, text, attoparsec, lens, mtl + +executable advent21 + import: common-extensions, build-directives + main-is: advent21/Main.hs + build-depends: linear, containers, split diff --git a/advent21/Main.hs b/advent21/Main.hs new file mode 100644 index 0000000..ac3b637 --- /dev/null +++ b/advent21/Main.hs @@ -0,0 +1,121 @@ +-- Writeup at https://work.njae.me.uk/2023/12/29/advent-of-code-2023-day-21/ + +import AoC +import Linear (V2(..), (^+^)) +import qualified Data.Set as S +import Data.Ix +import Data.List +import Data.List.Split + +type Position = V2 Int -- r, c +type Grid = S.Set Position + +main :: IO () +main = + do dataFileName <- getDataFileName + text <- readFile dataFileName + let (rocks, bounds) = mkGrid text + let start = findStart text + -- print rocks + -- print bounds + -- print start + print $ part1 rocks bounds start + -- print $ part2Quadratic rocks bounds start + print $ part2 rocks bounds start -- ((26501365 - 65) `div` (131 * 2)) + +part1, part2, part2Quadratic :: Grid -> (Position, Position) -> Grid -> Int +part1 rocks bounds start = S.size $ (!! 64) $ iterate (takeSteps rocks bounds) start + +part2Quadratic rocks bounds start = a * x ^ 2 + b * x + c -- (p, q, r, a * x ^ 2 + b * x + c) + where ps = (!! 65) $ iterate (takeSteps rocks bounds) start + qs = (!! 131) $ iterate (takeSteps rocks bounds) ps + rs = (!! 131) $ iterate (takeSteps rocks bounds) qs + p = S.size ps + q = S.size qs + r = S.size rs + c = p + b = (4*q - 3*p - r) `div` 2 + a = q - p - b + s = 26501365 + x = (s - 65) `div` 131 + +part2 rocks bounds start = + nEvenFilled + nOddFilled + nEdges + upperPoint + lowerPoint + rCap + lCap + where (V2 minR _, V2 maxR _) = bounds + tileWidth = maxR - minR + 1 + (doubleTileSteps, extraSteps) = divMod 26501365 (tileWidth * 2) + positions = (!! (tileWidth * 2 + extraSteps)) $ iterate (takeSteps rocks bounds) start + + evenFilled = countInRange bounds (V2 0 0) positions + oddFilled = countInRange bounds (V2 tileWidth 0) positions + upperPoint = countInRange bounds (V2 (tileWidth * -2) 0) positions + lowerPoint = countInRange bounds (V2 (tileWidth * 2) 0) positions + urEdge = countInRange bounds (V2 (- tileWidth) tileWidth) positions + + countInRange bounds (V2 (- tileWidth * 2) tileWidth) positions + lrEdge = countInRange bounds (V2 tileWidth tileWidth) positions + + countInRange bounds (V2 ( tileWidth * 2) tileWidth) positions + ulEdge = countInRange bounds (V2 (- tileWidth) (- tileWidth)) positions + + countInRange bounds (V2 (- tileWidth * 2) (- tileWidth)) positions + llEdge = countInRange bounds (V2 tileWidth (- tileWidth)) positions + + countInRange bounds (V2 ( tileWidth * 2) (- tileWidth)) positions + rCap = countInRange bounds (V2 (- tileWidth) ( tileWidth * 2)) positions + + countInRange bounds (V2 0 ( tileWidth * 2)) positions + + countInRange bounds (V2 tileWidth ( tileWidth * 2)) positions + lCap = countInRange bounds (V2 (- tileWidth) (- tileWidth * 2)) positions + + countInRange bounds (V2 0 (- tileWidth * 2)) positions + + countInRange bounds (V2 tileWidth (- tileWidth * 2)) positions + edges = urEdge + lrEdge + ulEdge + llEdge + + nEvenFilled = (doubleTileSteps * 2 - 1) ^ 2 * evenFilled + nOddFilled = (doubleTileSteps * 2) ^ 2 * oddFilled + nEdges = (doubleTileSteps * 2 - 1) * edges + + +countInRange :: (Position, Position) -> Position -> Grid -> Int +countInRange bounds delta cells = + S.size $ S.filter (inRange (shiftBounds bounds delta)) cells + +shiftBounds :: (Position, Position) -> Position -> (Position, Position) +shiftBounds (a, b) d = (a ^+^ d, b ^+^ d) + +takeSteps :: Grid -> (Position, Position) -> Grid -> Grid +takeSteps rocks bounds places = + S.filter (notAtRock rocks bounds) $ S.unions $ S.map adjacents places + +notAtRock :: Grid -> (Position, Position) -> Position -> Bool +notAtRock rocks (_, V2 maxR maxC) (V2 r c) = here' `S.notMember` rocks + where here' = V2 (r `mod` (maxR + 1)) (c `mod` (maxC + 1)) + +adjacents :: Position -> Grid +adjacents here = S.map (here ^+^) $ S.fromList [ V2 0 1, V2 1 0, V2 0 (-1), V2 (-1) 0 ] + + +showGrid :: Grid -> (Position, Position) -> Grid -> String +showGrid rocks bounds cells = unlines $ intercalate [" "] $ chunksOf 7 $ fmap (showRow rocks bounds cells) [-28..34] + where showRow rocks bounds cells r = intercalate " " $ chunksOf 7 $ fmap ((showCell rocks bounds cells) . V2 r) [-28..34] + showCell rocks bounds cells here + | not $ notAtRock rocks bounds here = '#' + | here `S.member` cells = 'O' + | otherwise = '.' +-- showCell :: Grid -> (Position, Position) -> Grid -> Position -> Char + +-- reading the map + +mkGrid :: String -> (Grid, (Position, Position)) +mkGrid text = ( S.fromList [ V2 r c | r <- [0..maxR], c <- [0..maxC] + , rows !! r !! c == '#' + ] + , (V2 0 0, V2 maxR maxC) + ) + where rows = lines text + maxR = length rows - 1 + maxC = (length $ head rows) - 1 + +findStart :: String -> Grid +findStart text = S.fromList [ V2 r c | r <- [0..maxR], c <- [0..maxC] + , rows !! r !! c == 'S' + ] + where rows = lines text + maxR = length rows - 1 + maxC = (length $ head rows) - 1 +