Island detection / Flood fill with clojure

May 9, 2018

I had already talked about a mutable version of this algorithm for flood filling island detection here. This time I went immutable with clojure The algorithm is a bit different, this we will not have a variable in the outer scope but pass a new instance of a board (which is efficiently managed by clojure) to the function for each iteration/recursion.

The full source is at https://gitlab.com/dendiz/kelimelik-clj/tree/master

there a few helper functions

first-char-on-board scans the board to find the first tile that is not empty split this will split a string such as “abc” into a vector as ["a" "b" "c"]

the basic idea is to keep a list of next slots to visit on the board as we visit slots. the next-frontier function will return a list of next slots. This is basically BFS search on a graph.

(defn flood-fill
  "flood fill the board starting from the first non empty slot.
   the flooded slots will contain '!' empty slots '.'. If there
   are islands they will contain letters.
  "
  [board]
  (let [[y x] (first-char-on-board board)
        board (mapv split board)
        ]
    (loop [board board
           frontier [[x y]]]
      (if (-> frontier count zero?)
        board
        (let [front (first frontier)
              x (first front)
              y (second front)]
          (recur
           (assoc-in board [y x] "!")
           (concat (next frontier) (next-frontier board [x y]))))))))
		   		   

the next-frontier code is also worth mentioning

(defn next-frontier
  "return the coordinates of candidate neighbors for flood filling"
  [board [x y]]
  (for [i [(dec y) y (inc y)]
        j [(dec x) x (inc x)]
        :when (and (>= i 0)
                   (>= j 0)
                   (< i 15)
                   (< j 15)
                   (or (= x j) (= y i))
                   (not (and (= x j) (= y i)))
                   (not= "!" (get-in board [i j]))
                   (not= "." (get-in board [i j])))]
    [j i]))

flood-fill will mark visited slots with ! and next-frontier will return a list of the candidate slot from the 8 neighbors of the current slot. if the neighbor is visited or empty it’s not included in the list.

if the starting board was like this

...a...
...bc..
..de...

the flood would start with a and the next-frontier would return only b from the neighbors and mark a as !. b would return c and e and d. a would be marked as ! so it would not be included. After the fill the board would be like

...!...
...!!..
..!!...

this algorithm is useful when detecting if the scrabble board is connected.