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-- requires cabal install --lib megaparsec parser-combinators heap vector
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 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 = 2
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'
compute :: Rational -> Rational -> Input -> Int
compute mini maxi = compute'
where
compute' :: Input -> Int
compute' (_:[]) = 0
compute' ((x1, y1, _, a1, b1, _):hs) = L.foldl' computeOne 0 hs + compute' hs
where
(x2, y2) = (x1 + a1, y1 + b1)
computeOne :: Int -> Hail -> Int
computeOne acc (x3, y3, _, a3, b3, _) | valid = acc + 1
| otherwise = acc
where
valid | denominator == 0 || t < 0 || u < 0 = False
| x >= mini && x <= maxi && y >= mini && y <= maxi = True
| otherwise = False
(x4, y4) = (x3 + a3, y3 + b3)
denominator = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
a = x1 * y2 - y1 * x2
b = x3 * y4 - y3 * x4
numeratorX = b * a1 - a * a3
numeratorY = b * b1 - a * b3
(x, y) = (numeratorX / denominator, numeratorY / denominator)
(t, u) = ((x - x1) / a1, (x - x3) / a3)
main :: IO ()
main = do
example <- parseInput "example"
let exampleOutput = compute 7 27 example
when (exampleOutput /= exampleExpectedOutput) (error $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput)
input <- parseInput "input"
print $ compute 200000000000000 400000000000000 input
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