day13: add haskell solution

2020/README.md

@@ -17,5 +17,6 @@ https://adventofcode.com/2020/
 | 9 |        |  `**`   |      |
 |10 |        |  `**`   |      |
 |11 |  `**`  |         |      |
+|13 |        |  `**`   |      |
 
 `test.sh` can be used to run all solutions and automatically compares them to (my) puzzle inputs and the expected outputs.

2020/data/day13.expected

@@ -0,0 +1,2 @@
+2215
+1058443396696792

2020/data/day13.input

@@ -0,0 +1,2 @@
+1005162
+19,x,x,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,823,x,x,x,x,x,x,x,23,x,x,x,x,x,x,x,x,17,x,x,x,x,x,x,x,x,x,x,x,29,x,443,x,x,x,x,x,37,x,x,x,x,x,x,13

2020/day13/day13.hs

@@ -0,0 +1,47 @@
+module Day13 where
+
+import AoC
+
+import Data.List
+import Data.List.Split
+import Data.Maybe
+import Data.Ord
+import Data.Tuple
+
+-- | inverse integer modulus, "remainder until the next multiple of d"
+--
+-- @(n + n `'invMod'` d) `'mod'` d == 0@
+invMod :: Integral a => a -> a -> a
+invMod n d | r == 0 = 0
+           | otherwise = d - r
+           where r = n `mod` d
+
+-- | @'combineRemainders' (r1, d1) (r2, d2) = (r3, d3)@ combines a relation of the form
+--
+-- @
+-- x = r1 (mod d1)
+-- x = r2 (mod d2)
+-- @
+--
+-- into a single relation
+--
+-- @
+-- x = r3 (mod d3)
+-- @
+--
+-- @d1@ should be larger than @d2@ for better performance.
+combineRemainders :: (Integral a) => (a, a) -> (a, a) -> (a, a)
+combineRemainders (r1, d1) (r2, d2) = (fromJust . find (\x -> x `mod` d2 == r2) $ [r1,d1+r1..], d1*d2)
+
+part1 :: Int -> [Int] -> Int
+part1 arr = uncurry (*) . minimumBy (comparing snd) . map (toSnd $ invMod arr)
+    where toSnd f x = (x, f x)
+
+part2 :: [Maybe Int] -> Int
+part2 = fst . foldl1 combineRemainders . map (\(r, d) -> (r `invMod` d, d)) . catMaybes . map sequence . enumerate 0
+    where enumerate start (x:xs) = (start, x) : enumerate (succ start) xs
+          enumerate _ [] = []
+
+main = runAoC (intoTuple . map (map (fmap read . justIf (/="x")) . splitOn ",") . lines) (uncurry part1 . fmap catMaybes) (part2 . snd)
+    where intoTuple [[Just x], y] = (x, y)
+          justIf p x = if p x then Just x else Nothing