haskell: 2023 24 refactor

2023/haskell/solutions/Day24.hs

@@ -5,14 +5,16 @@ import Data.Void (Void)
 import Data.Text (Text)
 import Data.Maybe (mapMaybe)
 import Data.Bifunctor (first, bimap)
-import Text.Megaparsec (Parsec, errorBundlePretty, runParser, eof, many, sepBy)
+import Control.Monad ((<=<))
+import Text.Megaparsec (Parsec, errorBundlePretty, runParser, eof, many)
 import Text.Megaparsec.Char (char, space)
 import Text.Megaparsec.Char.Lexer (signed, decimal)
-import Numeric.LinearAlgebra (R, (|>), linearSolve, asColumn, fromColumns, flatten, toList, fromLists, col)
+import Numeric.LinearAlgebra (R, linearSolve, flatten, toList, fromLists, col)
 import Misc (paired)
 
 
-type Ray  = ([R], [R])
+type R3  = (R, R, R)
+type Ray = (R3, R3)
 
 type Parser = Parsec Void Text
 
@@ -20,33 +22,43 @@ type Parser = Parsec Void Text
 parse :: Text -> Either String [Ray]
 parse = first errorBundlePretty . runParser rays ""
   where
-    point :: Parser [R]
-    point = signed space decimal `sepBy` (char ',' <* space)
-    ray :: Parser ([R], [R])
+    r :: Parser R
+    r = signed space decimal
+    r3 :: Parser R3
+    r3 = do
+      a <- r <* char ',' <* space
+      b <- r <* char ',' <* space
+      c <- r
+      return (a, b, c)
+    ray :: Parser (R3, R3)
     ray = do
-      t1 <- point
-      space
-      _  <- char '@'
-      space
-      t2 <- point
-      space
+      t1 <- r3 <* space
+      char '@' *> space
+      t2 <- r3 <* space
       return (t1, t2)
     rays :: Parser [Ray]
     rays = many ray <* eof
 
 
 intersect2D :: Ray -> Ray -> Maybe ([R], (R, R))
-intersect2D (sa, va) (sb, vb) =
-  let consts = 2 |> sa - 2 |> sb
-      coeffs = [2 |> vb, negate $ 2 |> va]
-      times  = toList . flatten <$> linearSolve (fromColumns coeffs) (asColumn consts)
+intersect2D r1 r2 =
+  let ((sx1, sy1, _), (vx1, vy1, _)) = r1
+      ((sx2, sy2, _), (vx2, vy2, _)) = r2
+      coeffs = fromLists
+        [ [vx2, -vx1]
+        , [vy2, -vy1]
+        ]
+      rhs = col
+        [ sx1 - sx2
+        , sy1 - sy2
+        ]
+      times  = toList . flatten <$> linearSolve coeffs rhs
   in case times of
-    Just ts@(tb:_) -> Just (ts, toPoint (sb, vb) tb)
+    Just ts@(tb:_) -> Just (ts, toPoint tb r2)
     _otherwise     -> Nothing
   where
-    toPoint :: Ray -> R -> (R, R)
-    toPoint (sx:sy:_, vx:vy:_) t = (sx + t * vx, sy + t * vy)
-    toPoint _ _ = undefined
+    toPoint :: R -> Ray -> (R, R)
+    toPoint t ((sx, sy, _), (vx, vy, _)) = (sx + t * vx, sy + t * vy)
 
 solveAFor :: R -> R -> [Ray] -> Int
 solveAFor s e = length . filter isBoth . mapMaybe (uncurry intersect2D) . paired
@@ -61,13 +73,13 @@ solveAFor s e = length . filter isBoth . mapMaybe (uncurry intersect2D) . paired
 solveA :: [Ray] -> Int
 solveA = solveAFor 200000000000000 400000000000000
 
-findThrow :: [Ray] -> Maybe [Int]
-findThrow rays =
+findThrow :: (Ray, Ray, Ray) -> Maybe [Int]
+findThrow (r1, r2, r3) =
   let
-    ([sx1, sy1, sz1], [vx1, vy1, vz1]) = rays !! 0
-    ([sx2, sy2, sz2], [vx2, vy2, vz2]) = rays !! 1
-    ([sx3, sy3, sz3], [vx3, vy3, vz3]) = rays !! 2
-    consts = fromLists
+    ((sx1, sy1, sz1), (vx1, vy1, vz1)) = r1
+    ((sx2, sy2, sz2), (vx2, vy2, vz2)) = r2
+    ((sx3, sy3, sz3), (vx3, vy3, vz3)) = r3
+    coeffs = fromLists
       [ [0, vz2 - vz1, vy1 - vy2, 0, sz1 - sz2, sy2 - sy1]
       , [0, vz3 - vz1, vy1 - vy3, 0, sz1 - sz3, sy3 - sy1]
       , [vz1 - vz2, 0, vx2 - vx1, sz2 - sz1, 0, sx1 - sx2]
@@ -75,7 +87,7 @@ findThrow rays =
       , [vy2 - vy1, vx1 - vx2, 0, sy1 - sy2, sx2 - sx1, 0]
       , [vy3 - vy1, vx1 - vx3, 0, sy1 - sy3, sx3 - sx1, 0]
       ]
-    coeffs = col
+    rhs = col
       [ vy1 * sz1 - sy1 * vz1 + sy2 * vz2 - vy2 * sz2
       , vy1 * sz1 - sy1 * vz1 + sy3 * vz3 - vy3 * sz3
       , sx1 * vz1 - vx1 * sz1 + vx2 * sz2 - sx2 * vz2
@@ -83,7 +95,14 @@ findThrow rays =
       , vx1 * sy1 - sx1 * vy1 + sx2 * vy2 - vx2 * sy2
       , vx1 * sy1 - sx1 * vy1 + sx3 * vy3 - vx3 * sy3
       ]
-    in map round . toList . flatten <$> linearSolve consts coeffs
+    in map round . toList . flatten <$> linearSolve coeffs rhs
 
 solveB :: [Ray] -> Int
-solveB = maybe 0 (sum . take 3) . findThrow
+solveB = maybe 0 (sum . take 3) . findThrow'
+  where
+    bundle :: [Ray] -> Maybe (Ray, Ray, Ray)
+    bundle rays = case rays of
+      r1:r2:r3:_ -> Just (r1, r2, r3)
+      _otherwise -> Nothing
+    findThrow' :: [Ray] -> Maybe [Int]
+    findThrow' = findThrow <=< bundle