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| -rw-r--r-- | 13-2.hs | 79 |
1 files changed, 79 insertions, 0 deletions
@@ -0,0 +1,79 @@ +import Data.Array +import Data.Ratio (denominator, numerator) +import Text.Parsec + +type Matrix = Array (Int,Int) Rational + +type Pair = (Rational,Rational) + +det :: Matrix -> Rational +det m = a*d - b*c + where + a = m ! (1,1) + b = m ! (2,1) + c = m ! (1,2) + d = m ! (2,2) + +matrix :: Pair -> Pair -> Matrix +matrix (a,c) (b,d) = + array ((1,1),(2,2)) [((1,1),a), ((2,1),b), ((1,2),c), ((2,2),d)] + +solve :: Pair -> Pair -> Pair -> Pair +solve target a b = (solA, solB) + where + coefficients = matrix a b + solA = det (matrix target b) / det coefficients + solB = det (matrix a target) / det coefficients + +int :: Rational -> Bool +int = (== 1) . denominator + +maybeSolve :: Pair -> Pair -> Pair -> Maybe Pair +maybeSolve target a b = + let sol@(a',b') = solve target a b + in if int a' && int b' + then Just sol + else Nothing + +cost :: Pair -> Pair -> Pair -> Int +cost target a b = case maybeSolve target a b of + Nothing -> 0 + Just (a',b') -> fromIntegral . numerator $ 3*a' + b' + +cost' :: (Pair,Pair,Pair) -> Int +cost' (a, b, target) = cost target a b + +number :: Parsec String () Rational +number = fromInteger . read <$> many digit + +button :: Parsec String () Pair +button = (,) + <$ string "Button " + <* anyChar + <* string ": X+" + <*> number + <* string ", Y+" + <*> number + <* newline + +prize :: Parsec String () Pair +prize = (,) + <$ string "Prize: X=" + <*> ((+ 10000000000000) <$> number) + <* string ", Y=" + <*> ((+ 10000000000000) <$> number) + <* newline + +parseOne :: Parsec String () (Pair,Pair,Pair) +parseOne = (,,) <$> button <*> button <*> prize + +parseInput :: Parsec String () [(Pair,Pair,Pair)] +parseInput = sepBy parseOne newline + +doParse :: String -> [(Pair,Pair,Pair)] +doParse s = case parse parseInput "" s of + Left e -> error $ show e + Right a -> a + +main :: IO () +main = getContents >>= print . sum . map cost' . doParse |