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