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| -rw-r--r-- | 2023/24-Never_Tell_Me_The_Odds/second.hs | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/2023/24-Never_Tell_Me_The_Odds/second.hs b/2023/24-Never_Tell_Me_The_Odds/second.hs new file mode 100644 index 0000000..9ef800a --- /dev/null +++ b/2023/24-Never_Tell_Me_The_Odds/second.hs @@ -0,0 +1,93 @@ +-- requires cabal install --lib megaparsec parser-combinators heap vector matrix +module Main (main) where + +import Control.Applicative.Permutations +import Control.Monad (void, when) +import qualified Data.Char as C +import Data.Either +import Data.Functor +import qualified Data.Heap as H +import qualified Data.List as L +import qualified Data.Map as M +import qualified Data.Matrix as MTX +import Data.Maybe +import Data.Ratio +import qualified Data.Set as S +import qualified Data.Vector as V +import qualified Data.Vector.Unboxed as VU +import Data.Void (Void) +import Text.Megaparsec +import Text.Megaparsec.Char + +import Debug.Trace + +exampleExpectedOutput = 47 + +type Hail = (Rational, Rational, Rational, Rational, Rational, Rational) +type Input = [Hail] + +type Parser = Parsec Void String + +parseNumber :: Parser Integer +parseNumber = read <$> some (char '-' <|> digitChar) <* optional (char ',') <* optional hspace <* optional (char '@' <* hspace) + +parseHail :: Parser Hail +parseHail = (,,,,,) <$> (fromInteger <$> parseNumber) + <*> (fromInteger <$> parseNumber) + <*> (fromInteger <$> parseNumber) + <*> (fromInteger <$> parseNumber) + <*> (fromInteger <$> parseNumber) + <*> (fromInteger <$> parseNumber) + +parseInput' :: Parser Input +parseInput' = some (parseHail <* eol) <* eof + +parseInput :: String -> IO Input +parseInput filename = do + input <- readFile filename + case runParser parseInput' filename input of + Left bundle -> error $ errorBundlePretty bundle + Right input' -> return input' + +-- rock in (x, y, z, a, b, c) +-- with a known hail (x1, y1, z1, a1, b1, x1) we have +-- x + a * t1 = x1 + a1 * t1 +-- => t1 = (x - x1) / (a1 - a) = (y - y1) / (b1 - b) +-- => (x - x1)(b1 - b) = (y - y1)(a1 - a) +-- => xb1 - xb - x1b1 + x1b = ya1 - ya - y1a1 + y1a +-- => ya - xb = ya1 - y1a1 + y1a - xb1 + x1b1 - x1b +-- With a second hail we also get: +-- ya - xb = ya2 - y2a2 + y2a - xb2 + x2b2 - x2b +-- By substracting the two equations, we get: +-- => y(a1-a2) + a(y1-y2) - x(b1-b2) - b(x1-x2) = y1a1 - y2a2 - x1b1 + x2b2 +-- => a(y1-y2) + b(x2-x1) + x(b2-b1) + y(a1-a2) = y1a1 - y2a2 - x1b1 + x2b2 +-- We build 4 equations on this template and populate a matrix to triangularise +-- and solve for x and y, then repeat with z. +compute :: Input -> Rational +compute input = x + y + z + where + (x1, y1, z1, a1, b1, c1) + :(x2, y2, z2, a2, b2, c2) + :(x3, y3, z3, a3, b3, c3) + :(x4, y4, z4, a4, b4, c4) + :(x5, y5, z5, a5, b5, c5) + :_ = input + (Right mxy) = MTX.rref $ MTX.fromList 4 5 [ y1-y2, x2-x1, b2-b1, a1-a2, y1*a1-y2*a2-x1*b1+x2*b2 + , y1-y3, x3-x1, b3-b1, a1-a3, y1*a1-y3*a3-x1*b1+x3*b3 + , y1-y4, x4-x1, b4-b1, a1-a4, y1*a1-y4*a4-x1*b1+x4*b4 + , y1-y5, x5-x1, b5-b1, a1-a5, y1*a1-y5*a5-x1*b1+x5*b5 ] + (Right mxz) = MTX.rref $ MTX.fromList 4 5 [ z1-z2, x2-x1, c2-c1, a1-a2, z1*a1-z2*a2-x1*c1+x2*c2 + , z1-z3, x3-x1, c3-c1, a1-a3, z1*a1-z3*a3-x1*c1+x3*c3 + , z1-z4, x4-x1, c4-c1, a1-a4, z1*a1-z4*a4-x1*c1+x4*c4 + , z1-z5, x5-x1, c5-c1, a1-a5, z1*a1-z5*a5-x1*c1+x5*c5 ] + y = mxy MTX.! (4, 5) + x = mxy MTX.! (3, 5) + z = mxz MTX.! (4, 5) + +main :: IO () +main = do + example <- parseInput "example" + let exampleOutput = compute example + when (exampleOutput /= exampleExpectedOutput) (error $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput) + input <- parseInput "input" + print $ compute input |