comments

solutions/src/2023/12.hs

@@ -1,4 +1,4 @@
-{-# Language QuasiQuotes, NPlusKPatterns #-}
+{-# Language QuasiQuotes #-}
 {-|
 Module      : Main
 Description : Day 12 solution
@@ -8,6 +8,25 @@ Maintainer  : emertens@gmail.com
 
 <https://adventofcode.com/2023/day/12>
 
+This problem asks us to find the number of unqiue
+rows that satisfy the grouping constraint. The question
+mark characters are wildcards.
+
+A naive enumeration solution won't work here, there are
+far too many possible assignments in part 2. This solution
+uses a boxed array to implement a dynamic programing solution
+to the problem.
+
+Because the array is boxed we can lean on laziness to resolve
+all of the data dependencies entailed by the dynamic programming
+approach implicitly. By indexing on Ints representing the
+suffix instead of suffixes as Map keys we get a performance
+speedup.
+
+To break the problem into increasingly smaller components
+we solve it for all the suffixes of the input pattern and
+group constraint.
+
 >>> :{
 :main +
 "???.### 1,1,3
@@ -28,7 +47,7 @@ import Advent (format, arrIx)
 import Data.Array (range, (!), listArray)
 import Data.List (intercalate)
 
--- |
+-- | Parse the input sequences and print out answers to both parts.
 --
 -- >>> :main
 -- 6871
@@ -39,9 +58,18 @@ main =
     print (sum [ways g s | (s,g) <- input])
     print (sum [ways (concat (replicate 5 g)) (unfoldSprings s) | (s,g) <- input])
 
+-- | Expand the input row as specified for part 2
+--
+-- >>> unfoldSprings ".#"
+-- ".#?.#?.#?.#?.#"
 unfoldSprings :: String -> String
 unfoldSprings = intercalate "?" . replicate 5
 
+-- | Given a group clue and an spring sequence, compute the number
+-- of unique rows that match the clue.
+--
+-- >>> ways [3,2,1] "?###????????"
+-- 10
 ways :: [Int] -> String -> Int
 ways groups springs = answersA ! (0,0)
   where
@@ -57,29 +85,31 @@ ways groups springs = answersA ! (0,0)
     -- recusive calls to go are memoized via the array
     rec groupI springI = answersA ! (groupI, springI)
 
+    -- compute the number of matches at suffixes starting at these indexes
     go groupI springI =
       let dotCase  = rec groupI (springI + 1)
           hashCase = startGroup groupI (springI + 1)
-          {-# Inline hashCase #-} in
+          {-# Inline hashCase #-} in -- improved benchmark results
       case arrIx springsA springI of
         Just '.'   -> dotCase
         Just '#'   -> hashCase
         Just '?'   -> hashCase + dotCase
         _          -> if groupI == groupsN then 1 else 0
 
+    -- compute the number of ways assuming the next group starts here
     startGroup groupI springI =
       case arrIx groupsA groupI of
         Just n     -> loopGroup (groupI + 1) springI (n - 1)
         Nothing    -> 0 -- no group available to start
 
-    loopGroup groupI springI (n + 1) = -- middle of group
-      case arrIx springsA springI of
-        Just '.'   -> 0 -- group too short
-        Nothing    -> 0 -- group too short
-        _          -> loopGroup groupI (springI + 1) n
-
     loopGroup groupI springI 0 = -- end of group
       case arrIx springsA springI of
         Nothing    -> if groupI == groupsN then 1 else 0
         Just '#'   -> 0 -- group too long
         _          -> rec groupI (springI + 1)
+
+    loopGroup groupI springI n = -- middle of group
+      case arrIx springsA springI of
+        Just '.'   -> 0 -- group too short
+        Nothing    -> 0 -- group too short
+        _          -> loopGroup groupI (springI + 1) (n - 1)