My previous post was about a Python program to calculate the moves to guarantee a win in the puzzle word game ‘Ghost’. The algorithm was naturally recursive and felt ‘LISPy’. @pdlug has been telling me how writing in Clojure will expand my mind, make me more productive and hem my pants so this week I learned just enough Clojure (I already knew LISP) to re-write the Ghost game solver in Clojure.

See the previous post for details on the Ghost game and the python code. The algorithm is exactly the same, the implementation slightly different. Because Clojure is strongly functional I couldn’t update the Trie in place but instead had to return updated sub-tries as I went. As a traditionally imperative programmer I felt the efficiency hairs rise on the back of my neck thinking about all the extra data manipulation this would cause, but I was pleasantly surprised at how efficient Clojure is. Under the hood Clojure has very efficient re-use of data, just rebuilding tree structures to use existing data in different ways.

The Clojure Program

Here is the code in Clojure. I’ve put it up alongside the Python code on GitHub at ghostSolver

; ghost-solver.clj
; 2016
; Ghost is a word game in which players take turns adding letters to a growing
; word fragment, trying not to be the one to complete a valid word. Each
; fragment must be the beginning of an actual word, there is a minimum of four
; letters of a word that counts. The player who completes a word loses the round.
; This program reads a dictionary and figures out words that will guarantee
; a win both for the player who plays first and the player who plays second.
; Input: ghostSolver.clj (reads "wordlist.txt")
; Output: Player goes first: list of winning words.
;         Player goes second: list of winning words.

(ns ghost-solver.core
(require '[ :as io])

(defmacro dbg    ; handy debugging tool
  ([x]     `(let [x# ~x] (println "dbg:" '~x "=" x#) x#))
  ([label x] `(let [x# ~x] (println "dbg"(quote ~label) ":" '~x "=" x#) x#)))

;; Our trie is a tree of letters forming words.
;; Implemented as a map with letters as keys; values are sub-tries or nil
;; In the ghost game no words are allowed with complete words as prefixes
;;   eg: if we have "cart" we can never reach "cartridge"
;; In the trie during processing for winning moves,
;;   the entries {letter {}} and {letter nil} have different meanings
;;   nil means end-of-word, {} means no winning sub-tries under this node

(defmacro trie-letters [t] `(keys ~t))
(defmacro subtrie [t l] `(~t ~l))
(defn empty-map? [m]
  (and (empty? m) (not (nil? m))))

(defn add-word [trie word]
  (let [letter (first word)
        sub-trie (subtrie trie letter)]
    (if (contains? trie letter) ; letter already in trie, extend it
      (if (nil? sub-trie)
        trie ; letter is end-of-word, dont add superset words!
      ;else add rest of word to sub-trie
        (assoc trie letter (add-word sub-trie (rest word))))
      ; if the letter is not already in the trie put the word in
      ; use a Clojure shortcut to build the whole nested sub-trie all at once
      (assoc-in trie (seq word) nil))))

(defn add-words [words]
  (reduce add-word {} words))

; throw away words less than 4 letters
; clean out some cruft from online dictionaries,
;   anything with Capitals or punctuation
(defn clean-words [words]
  (filter #(and (> (count %) 3) (re-matches #"[a-z]+" %)) words))
(defn build-trie [filename]
  (with-open [rdr ( filename)]
    (add-words (clean-words (map clojure.string/trim (line-seq rdr))))))

(defn players-move? [partial-word player-goes-first]
  (or (and  player-goes-first
            (even? (count partial-word)))
      (and  (not player-goes-first)
            (odd? (count partial-word)))))

(defn all-words
  ; returns list of all words branching from this trie
  ; can also be used for all words branching from a sub-trie and a partial word
   (all-words trie nil)) ; default arg
  ([trie partial-word]
     (for [l (trie-letters trie)]
       (if (nil? (subtrie trie l))
         (str partial-word l)
         (all-words (subtrie trie l) (str partial-word l)))))))
(defn best-sort-decorator [t partial-word]
  ; in: sub-trie in the form of a tuple vector [letter sub-trie], partial-word
  ; return decorated tuple for sorting:
  ;        ([count-words len-shortest-word alpha-first-word] [letter sub-trie])
  (if (nil? (second t))
    ; nil means this branch is the end of a word
    (list [1 (count partial-word) partial-word] t)
  ; else
    (let [words (all-words (second t) (str partial-word (first t)))]
      (list [(count words) (apply min (map count words)) (first (sort words))]
(defn best-words [trie partial-word] ; I have words. I have the best words.
  ; in: a partial word, and a trie of completions of that word
  ; out: a sub-trie with only the best top level branch in it, the rest pruned
  ; best is defined subjectively as:
  ; 1. the branch with the fewest sub-branches (words)
  ; 2. the branch with the shortest word
  ; 3. the branch with alphabetically first word
  ; eg: 1 long word is 'better' than 2 short words
  ;     3 short words and 3 long words are 'better' than 6 medium words
  (->> trie
    ; decorate with ([count-words len-shortest-word alpha-first-word] [letter sub-trie])
    (map #(best-sort-decorator % partial-word))
    (sort-by first)    ; sort by the decorated value
    (map second)       ; undecorate
    first              ; just the best (first sorted) sub-trie
    (apply hash-map)))  ; return a map {letter sub-trie} not a tuple-vector [letter sub-trie]

(defn all-or-nothing [trie]
  ; in: trie hashmap {letter sub-trie ...}
  ; out: if ANY sub-tries are empty {} returns {}, else returns the original trie
  (if (some (fn [t] ((comp empty-map? second) t)) trie) {} trie))
(defn winning-moves [trie partial-word player-goes-first]
  ; in: boolean player player-goes-first?
  ;     trie hash-map {letter sub-trie ...}
  ;     partial-word eg: "aardva"
  ; out: trie hash-map w only player winning branches,
  ;      and only the "best" of these from each node
    (nil? trie) nil
    (players-move? partial-word player-goes-first)
    (as-> trie X
      (into {} (remove (comp nil? second) X)) ; prune end-of-word player lost
      (reduce (fn [t l]
                 (assoc t l
                  (winning-moves (subtrie X l) (str partial-word l) player-goes-first)))
              (trie-letters X))        ; find sub-winners
      (into {} (remove (comp empty-map? second)) X) ; prune {} w/no winning moves
      (best-words X partial-word))      ; choose only the best winning branch
    :else ; opponent's move
      ; find sub-winners, return all winning sub-branches.
      ; but if any branches have no winning moves, thus allowing opponent to
      ; force player-loss this entire branch is dangerous, return none {}
        (reduce (fn [t l]
                  (assoc t l
                    (winning-moves (subtrie trie l) (str partial-word l) player-goes-first)))
                (trie-letters trie)))))
(defn print-winner [trie letter player-goes-first]
  (let [winning-trie (winning-moves trie (str letter) player-goes-first)]
    (if (not (empty-map? winning-trie))
      (println letter ": " (sort (all-words winning-trie letter)))
      (println letter ": No winning words."))))
(defn print-winners [trie player-goes-first]
  (map #(print-winner (subtrie trie %) % player-goes-first) (sort (keys trie))))
(defn -main []
  (let [trie (build-trie (io/resource "ubuntu-wordlist.txt"))]
    (println "Player goes first: winning words")
    (doall (print-winners trie true))
    (println "Adversary goes first: winning words")
    (doall (print-winners trie false))
  ; note: -main doesn't actually consume (use) the return values
  ;       so wrap the functions with doall to force all lazy evaluations to happen
  ;       otherwise Clojure will be happy to return with the silent knowledge
  ;       that it knows how to (print-winners trie true) but since you didn't
  ;       use the result it won't execute all the sub-calculations

The Results

The results were exactly the same, as expected. Both programs runtime was the same order of magnitude (a couple of seconds on a 45,000 word dictionary). Writing it in Clojure took me a little longer than writing it in Python no doubt because I was learning the language at the same time as I wrote the program. Both programs are approximately the same length in lines of code. I found that writing it in Clojure forced me to think more clearly about the problem, ie: what does this sub-trie represent conceptually at each point in the code.

Player goes first: winning words
a :  ()
b :  ()
c :  ()
d :  ()
e :  ()
f :  ()
g :  ()
h :  (hack hegemony hick hoar hues hybrid)
i :  ()
j :  (jack jest jigs jobs just)
k :  ()
l :  ()
m :  (maze meek meet mien mnemonic moan moat muff myth)
n :  ()
o :  ()
p :  ()
q :  ()
r :  (raft relate relating relent relish reload reluctance rely rhapsody rill rock ruin)
s :  ()
t :  ()
u :  ()
v :  ()
w :  ()
y :  ()
z :  (zeal zinc zodiac)
Adversary goes first: winning words
a :  (ahead)
b :  (black bleed blimp bloat bluff)
c :  (clarity cleft cliff cloak cluck)
d :  (draft dregs drift droll drunk dryly)
e :  (equal equator)
f :  (frail freak friar frock fruit)
g :  (graft grenade grill groan gruff)
h :  ()
i :  (illegal)
j :  ()
k :  (knack knead knife knifing knock knuckle)
l :  (lying lymph lynch lyric)
m :  ()
n :  (nylon nymph)
o :  (ozone)
p :  (pneumatic)
q :  (quack quell quick quonset)
r :  ()
s :  (squeamish squeeze squeezing squelch)
t :  (twain tweed twice twofold)
u :  (ulcer ultra)
v :  (vulture)
w :  (whack wheat which whoop)
y :  (yield)
z :  ()
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