feat: solve part 2 day 3

app/Day3.hs

@@ -2,7 +2,9 @@ module Main where
 
 import Data.Char (digitToInt)
 import Data.Either (rights)
-import Debug.Trace
+import Data.List (foldl')
+import Data.Map (Map)
+import qualified Data.Map as M
 import System.Environment (getArgs)
 
 -- | A candidate is either a left-most number we've just selected, or
@@ -37,8 +39,43 @@ part1 = sum . map (maximum . map combine . rights . foldl go [] . map digitToInt
     combine :: (Int, Int) -> Int
     combine (a, b) = a * 10 + b
 
+type CandidateN = [Int]
+
+-- | Maintain one partial candidates for each length.
+--
+-- Insight: If there are at least N-1 digits left after we've spotted
+-- the greatest digit, that digit needs to be the first digit of our
+-- candidates.
+--
+-- Insight 2: We only ever need to store one candidate per length.
 part2 :: String -> Int
-part2 = error "Not implemented"
+part2 = sum . map (combine . (M.! 12) . foldl' checkPotential mempty . map digitToInt) . lines
+  where
+    checkPotential :: Map Int CandidateN -> Int -> Map Int CandidateN
+    checkPotential cs x =
+      let partials = filter ((< 12) . length) $ M.elems cs
+          partials' = [x] : map (genPartial x) partials
+       in foldl' insertMaxCandidate cs $ filter ((<= 12) . length) partials'
+
+    -- generates new partials by appending x at candidate or after
+    -- replacing a shedding smaller digits.
+    genPartial :: Int -> CandidateN -> CandidateN
+    genPartial x candidate = candidate ++ [x]
+
+    -- replaces a candidate with a better one with the same length
+    insertMaxCandidate :: Map Int CandidateN -> CandidateN -> Map Int CandidateN
+    insertMaxCandidate m c = M.insertWith maxCandidate (length c) c m
+
+    maxCandidate :: CandidateN -> CandidateN -> CandidateN
+    maxCandidate a b
+      | combine a > combine b = a
+      | otherwise = b
+
+    combine :: CandidateN -> Int
+    combine xs = sum $ zipWith power [0 :: Int ..] (reverse xs)
+
+    power :: Int -> Int -> Int
+    power pow b = b * 10 ^ pow
 
 testInput :: String
 testInput =