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+---
+title: "Disk Defragmentation — Haskell — #adventofcode Day 14"
+description: "In which I learn how that old flood fill tool in Microsoft Paint works."
+slug: day-14
+date: 2017-12-15T17:52:46+00:00
+tags:
+- Technology
+- Learning
+- Advent of Code
+- Haskell
+series: aoc2017
+---
+
+[Today's challenge](http://adventofcode.com/2017/day/14) has us helping a disk defragmentation program by identifying contiguous regions of used sectors on a 2D disk.
+
+[→ Full code on GitHub](https://github.com/jezcope/aoc2017/blob/master/14-disk-defragmentation.hs)
+
+!!! commentary
+    Wow, today's challenge had a pretty steep learning curve. Day 14 was the first to directly reuse code from a previous day: [the "knot hash" from day 10][day 10]. I [solved day 10 in Haskell](../day-10/), so I thought it would be easier to stick with Haskell for today as well. The first part was straightforward, but the second was pretty mind-bending in a pure functional language!
+
+    I ended up solving it by implementing a [flood fill algorithm][flood]. It's recursive, which is right in Haskell's wheelhouse, but I ended up using `Data.Sequence` instead of the standard list type as its API for indexing is better. I haven't tried it, but I think it will also be a little faster than a naive list-based version.
+    
+    It took a looong time to figure everything out, but I had a day off work to be able to concentrate on it!
+
+[day 10]: http://adventofcode.com/2017/day/10
+[flood]: https://en.wikipedia.org/wiki/Flood_fill
+
+A lot more imports for this solution, as we're exercising a lot more of the standard library.
+
+```haskell
+module Main where
+
+import Prelude hiding (length, filter, take)
+import Data.Char (ord)
+import Data.Sequence
+import Data.Foldable hiding (length)
+import Data.Ix (inRange)
+import Data.Function ((&))
+import Data.Maybe (fromJust, mapMaybe, isJust)
+import qualified Data.Set as Set
+import Text.Printf (printf)
+import System.Environment (getArgs)
+```
+
+Also we'll extract the key bits from day 10 into a module and import that.
+
+```haskell
+import KnotHash
+```
+
+Now we define a few data types to make the code a bit more readable. `Sector` represent the state of a particular disk sector, either free, used (but unmarked) or used and marked as belonging to a given integer-labelled group. `Grid` is a 2D matrix of `Sector`, as a sequence of sequences.
+
+```haskell
+data Sector = Free | Used | Mark Int
+  deriving (Eq)
+
+instance Show Sector where
+  show Free = "   ."
+  show Used = "   #"
+  show (Mark i) = printf "%4d" i
+
+type GridRow = Seq Sector
+type Grid = Seq (GridRow)
+```
+
+Some utility functions to make it easier to view the grids (which can be quite large): used for debugging but not in the finished solution.
+
+```haskell
+subGrid :: Int -> Grid -> Grid
+subGrid n = fmap (take n) . take n
+
+printRow :: GridRow -> IO ()
+printRow row = do
+  mapM_ (putStr . show) row
+  putStr "\n"
+
+printGrid :: Grid -> IO ()
+printGrid = mapM_ printRow
+```
+
+`makeKey` generates the hash key for a given row.
+
+```haskell
+makeKey :: String -> Int -> String
+makeKey input n = input ++ "-" ++ show n
+```
+
+`stringToGridRow` converts a binary string of '1' and '0' characters to a sequence of `Sector` values.
+
+```haskell
+stringToGridRow :: String -> GridRow
+stringToGridRow = fromList . map convert
+  where convert x
+          | x == '1' = Used
+          | x == '0' = Free
+```
+
+`makeRow` and `makeGrid` build up the grid to use based on the provided input string.
+
+```haskell
+makeRow :: String -> Int -> GridRow
+makeRow input n = stringToGridRow $ concatMap (printf "%08b")
+  $ dense $ fullKnotHash 256
+  $ map ord $ makeKey input n
+
+makeGrid :: String -> Grid
+makeGrid input = fromList $ map (makeRow input) [0..127]
+```
+
+Utility functions to count the number of used and free sectors, to give the solution to part 1.
+
+```haskell
+countEqual :: Sector -> Grid -> Int
+countEqual x = sum . fmap (length . filter (==x))
+
+countUsed = countEqual Used
+countFree = countEqual Free
+```
+
+Now the real meat begins! `fundUnmarked` finds the location of the next used sector that we haven't yet marked. It returns a `Maybe` value, which is `Just (x, y)` if there is still an unmarked block or `Nothing` if there's nothing left to mark.
+
+```haskell
+findUnmarked :: Grid -> Maybe (Int, Int)
+findUnmarked g
+  | y == Nothing = Nothing
+  | otherwise = Just (fromJust x, fromJust y)
+  where
+    hasUnmarked row = isJust $ elemIndexL Used row
+    x = findIndexL hasUnmarked g
+    y = case x of
+      Nothing -> Nothing
+      Just x' -> elemIndexL Used $ index g x'
+```
+
+`floodFill` implements a very simple recursive flood fill. It takes a target and replacement value and a starting location, and fills in the replacement value for every *connected* location that currently has the target value. We use it below to replace a connected used region with a marked region.
+
+```haskell
+floodFill :: Sector -> Sector -> (Int, Int) -> Grid -> Grid
+floodFill t r (x, y) g
+  | inRange (0, length g - 1) x
+    && inRange (0, length g - 1) y
+    && elem == t =
+      let newRow = update y r row
+          newGrid = update x newRow g
+      in newGrid
+         & floodFill t r (x+1, y)
+         & floodFill t r (x-1, y)
+         & floodFill t r (x, y+1)
+         & floodFill t r (x, y-1)
+  | otherwise = g
+  where
+    row = g `index` x
+    elem = row `index` y
+```
+
+`markNextGroup` looks for an unmarked group and marks it if found. If no more groups are found it returns `Nothing`. `markAllGroups` then repeatedly applies `markNextGroup` until `Nothing` is returned.
+
+```haskell
+markNextGroup :: Int -> Grid -> Maybe Grid
+markNextGroup i g = case findUnmarked g of
+                      Nothing -> Nothing
+                      Just loc -> Just $ floodFill Used (Mark i) loc g
+
+markAllGroups :: Grid -> Grid
+markAllGroups g = markAllGroups' 1 g
+  where
+    markAllGroups' i g = case markNextGroup i g of
+      Nothing -> g
+      Just g' -> markAllGroups' (i+1) g'
+```
+
+`onlyMarks` filters a grid row and returns a list of (possibly duplicated) group numbers in the row.
+
+```haskell
+onlyMarks :: GridRow -> [Int]
+onlyMarks = mapMaybe getMark . toList
+  where
+    getMark Free = Nothing
+    getMark Used = Nothing
+    getMark (Mark i) = Just i
+```
+
+Finally, `countGroups` puts all the group numbers into a set to get rid of duplicates and returns the size of the set, i.e. the total number of separate groups.
+
+```haskell
+countGroups :: Grid -> Int
+countGroups g = Set.size groupSet
+  where
+    groupSet = foldl' Set.union Set.empty $ fmap rowToSet g
+    rowToSet = Set.fromList . toList . onlyMarks
+```
+
+As always, every Haskell program needs a main function to drive the I/O and produce the actual result.
+  
+```haskell
+main = do
+  input <- fmap head getArgs
+  let grid = makeGrid input
+      used = countUsed grid
+      marked = countGroups $ markAllGroups grid
+
+  putStrLn $ "Used sectors: " ++ show used
+  putStrLn $ "Groups: " ++ show marked
+```