As an exercise for myself (I'm learning clojure). I wanted to implement the Depth-first search algorithm.

How I did it

Using recursion

(def graph 
  {:s {:a 3 :d 4}
   :a {:s 3 :d 5 :b 4}
   :b {:a 4 :e 5 :c 4} 
   :c {:b 4} 
   :d {:s 4 :a 5 :e 2} 
   :e {:d 2 :b 5 :f 4} 
   :f {:e 4 :g 1}})

(def stack [[:s]])

(def goal :g)

(defn cost [Graph start goal]
  (goal (start Graph)))

(defn hasloop? [path]
  (not (= (count path) (count (set path)))))

(defn atgoal? [path]
  (= goal (last path)))

(defn solved? [stack]
  (some true? (map atgoal? stack)))

(defn addtopath [path node]
    (conj path node))

(defn pop* [stack]
    (last stack))

(defn findpath [stack]
    (if (not (solved? stack))
        (let [first* (pop* stack) l (last first*) ] 
                (findpath (drop-last 
                    (remove hasloop?  (lazy-cat
                                            (map #(addtopath first* %) 
                                            (keys (l graph))) stack)))))
        [(first stack)]))

How to use

(findpath stack)


I'm really really interested in how this code can be improved. Both in readability, efficiency and performance.


1 Answer 1


I wrote the modified version of your findpath function using recursion:

(defn- dfs
  [graph goal]
  (fn search
    [path visited]
    (let [current (peek path)]
      (if (= goal current)
        (->> current graph keys
             (remove visited)
             (mapcat #(search (conj path %) (conj visited %))))))))

(defn findpath
  "Returns a lazy sequence of all directed paths from start to goal
  within graph."
  [graph start goal]
  ((dfs graph goal) [start] #{start}))

Instead of using your hasloop? function, my search function keeps track of visited nodes in order to avoid visiting the same node twice. It seems to work for your settings:

user> (def graph 
  {:s {:a 3 :d 4}
   :a {:s 3 :d 5 :b 4}
   :b {:a 4 :e 5 :c 4} 
   :c {:b 4} 
   :d {:s 4 :a 5 :e 2} 
   :e {:d 2 :b 5 :f 4} 
   :f {:e 4 :g 1}})
user> (findpath graph :s :g)
([:s :a :b :e :f :g] [:s :a :d :e :f :g] [:s :d :a :b :e :f :g] [:s :d :e :f :g])

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