Day 24: Never Tell Me The Odds (part 2)

README.md

@@ -28,5 +28,5 @@ Development occurs in language-specific directories:
 |[Day21.hs](hs/src/Day21.hs)|[Day21.kt](kt/aoc2023-lib/src/commonMain/kotlin/com/github/ephemient/aoc2023/Day21.kt)|[day21.py](py/aoc2023/day21.py)|[day21.rs](rs/src/day21.rs)|
 |[Day22.hs](hs/src/Day22.hs)|[Day22.kt](kt/aoc2023-lib/src/commonMain/kotlin/com/github/ephemient/aoc2023/Day22.kt)|[day22.py](py/aoc2023/day22.py)|[day22.rs](rs/src/day22.rs)|
 ||[Day23.kt](kt/aoc2023-lib/src/commonMain/kotlin/com/github/ephemient/aoc2023/Day23.kt)||[day23.rs](rs/src/day23.rs)|
-|[Day24.hs](hs/src/Day24.hs) ½|[Day24.kt](kt/aoc2023-lib/src/commonMain/kotlin/com/github/ephemient/aoc2023/Day24.kt) ½|[day24.py](py/aoc2023/day24.py) ½|[day24.rs](rs/src/day24.rs) ½|
+|[Day24.hs](hs/src/Day24.hs)|[Day24.kt](kt/aoc2023-lib/src/commonMain/kotlin/com/github/ephemient/aoc2023/Day24.kt) ½|[day24.py](py/aoc2023/day24.py) ½|[day24.rs](rs/src/day24.rs) ½|
 |[Day25.hs](hs/src/Day25.hs)|[Day25.kt](kt/aoc2023-lib/src/commonMain/kotlin/com/github/ephemient/aoc2023/Day25.kt)|[day25.py](py/aoc2023/day25.py)|[day25.rs](rs/src/day25.rs)|

hs/src/Day24.hs

@@ -10,15 +10,19 @@ import Control.Monad ((>=>), filterM, guard, when)
 import Data.Char (isSpace)
 import Data.Functor (($>))
 import Data.List (tails)
+import Data.Maybe (catMaybes)
+import Data.Ratio ((%), denominator, numerator)
 import Data.Text (Text)
 import qualified Data.Text as T (dropWhile, lines, singleton, stripPrefix)
-import Data.Text.Read (Reader)
 import qualified Data.Text.Read as T (decimal, signed)
+import Data.Text.Read (Reader)
+import GHC.Exts (the)
 
 parseLine :: (Num a) => Reader ((a, a, a), (a, a, a))
 parseLine text = do
     let decimal' = fmap (first fromIntegral) . T.signed T.decimal . T.dropWhile isSpace
-        skip token = maybe (Left $ "expected " ++ [token]) Right . T.stripPrefix (T.singleton token) . T.dropWhile isSpace
+        skip token = maybe (Left $ "expected " ++ [token]) Right .
+            T.stripPrefix (T.singleton token) . T.dropWhile isSpace
     (x, text) <- decimal' text
     (y, text) <- skip ',' text >>= decimal'
     (z, text) <- skip ',' text >>= decimal'
@@ -41,7 +45,34 @@ part1 lo hi input = do
             y = m0 * x + b0
     length <$> filterM ok [(line0, line1) | line0:lines' <- tails lines, line1 <- lines']
 
-part2 :: Text -> Either String Int
+part2 :: (Integral a) => Text -> Either String a
 part2 input = do
     points <- mapM (readEntire parseLine) $ T.lines input
-    Left "unimplemented"
+    foldr (<>) (Left "no solution") $ do
+        ((x0, y0, z0), (vx0, vy0, vz0)):points <- tails points
+        let offset ((x, y, z), (vx, vy, vz)) =
+                ((x - x0, y - y0, z - z0), (vx - vx0, vy - vy0, vz - vz0))
+        ((x1, y1, z1), (vx1, vy1, vz1)):points <- tails $ offset <$> points
+        let px1 = y1 * vz1 - z1 * vy1
+            py1 = z1 * vx1 - x1 * vz1
+            pz1 = x1 * vy1 - y1 * vx1
+        guard $ px1 /= 0 || py1 /= 0 || pz1 /= 0 -- 0 and 1 are skew
+        ((x2, y2, z2), (vx2, vy2, vz2)):points <- tails points
+        let px2 = y2 * vz2 - z2 * vy2
+            py2 = z2 * vx2 - x2 * vz2
+            pz2 = x2 * vy2 - y2 * vx2
+        guard $ px2 /= 0 || py2 /= 0 || pz2 /= 0 -- 0 and 2 are skew
+        let mx = py1 * pz2 - pz1 * py2
+            my = pz1 * px2 - px1 * pz2
+            mz = px1 * py2 - py1 * px2
+        guard $ mx /= 0 || my /= 0 || mz /= 0 -- 1 and 2 are skew
+        let u1 = (y1 * vx1 - x1 * vy1) % (my * vx1 - mx * vy1)
+            u2 = (y2 * vx2 - x2 * vy2) % (my * vx2 - mx * vy2)
+            f _ _ _ 0 = Nothing
+            f m u p v = Just $ 1 % v * (m % 1 * u - p % 1)
+            t1 = the $ catMaybes [f mx u1 x1 vx1, f my u1 y1 vy1, f mz u1 z1 vz1]
+            t2 = the $ catMaybes [f mx u2 x2 vx2, f my u2 y2 vy2, f mz u2 z2 vz2]
+        let offset = (mx + my + mz) % 1 * (u1 * t2 - u2 * t1) / (t2 - t1)
+        pure $ if denominator offset /= 1
+            then Left "non-integral solution"
+            else Right $ x0 + y0 + z0 + numerator offset

hs/test/Day24Spec.hs

@@ -4,7 +4,7 @@ module Day24Spec (spec) where
 import Data.Text (Text)
 import qualified Data.Text as T (unlines)
 import Day24 (part1, part2)
-import Test.Hspec (Spec, describe, it, shouldBe, xit)
+import Test.Hspec (Spec, describe, it, shouldBe)
 
 example :: Text
 example = T.unlines
@@ -21,5 +21,5 @@ spec = do
         it "examples" $ do
             part1 7 27 example `shouldBe` Right 2
     describe "part 2" $ do
-        xit "examples" $ do
+        it "examples" $ do
             part2 example `shouldBe` Right 47