day 6

Signed-off-by: Amneesh Singh <natto@weirdnatto.in>

day06.hs

@@ -0,0 +1,25 @@
+data Race = Race {time :: Int, distance :: Int} deriving (Show)
+
+main :: IO ()
+main = do
+  [_ : time', _ : distance'] <- map words . lines <$> readFile "day06.in"
+  
+  let races = zipWith (\t d -> Race {time = read t, distance = read d}) time' distance'
+  let bigRace = Race {time = read $ concat time', distance = read $ concat distance'}
+  
+  putStr "Q1: "
+  print . product . map race $ races
+  putStr "Q2: "
+  print $ race bigRace
+
+-- we need (T - a) * a > D or a^2 - T*a + D < 0 i.e, a quadratic inequality
+race :: Race -> Int
+race Race {time, distance} =
+  let (x, y) = roots
+   in ceiling (x - 1) - floor (y + 1) + 1
+  where
+    -- roots
+    roots :: (Double, Double)
+    roots =
+      let disc = fromIntegral $ time * time - 4 * distance
+       in ((fromIntegral time + sqrt disc) / 2, (fromIntegral time - sqrt disc) / 2)