Clojure中的Dijkstra&ŧ039；s算法

Posted 2021-02-26

; kototamo at gmail dot com
 
(use 'clojure.contrib.def)
 
(declare dijkstra build-path add-rdist update-rdists take-minnode)
 
 
(defn shortest-path 
  ([net root nodedst children distance]
     " return [path dist]"
     " net is the graph "
     " root the source node "
     " nodedst the destination "
     " children a function returning the children for a node " 
     " distance a function returning the distance between two nodes "
     (let [preds (dijkstra net root nodedst children distance)
	   path (build-path preds root nodedst)]
       (if (nil? path)
	 nil
	 [path (second (preds nodedst))])))
 
  ([net root nodedst children]
     (shortest-path net root nodedst children (constantly 1))))
 
(defn- dijkstra [net root nodedst children distance]
  (loop [rdists (sorted-map 0 {root root})
	 minnode root
	 preds {root [root 0]}
	 dist 0]
    ; (printf "minnode = %s preds = %s rdists = %s


" minnode preds rdists)
    (if (empty? rdists)
      preds
      (let [[nminnode ndist nrdists npreds] (take-minnode rdists preds)
	    [nnrdists nnpreds] (update-rdists nrdists 
					      npreds 
					      net 
					      nminnode 
					      ndist 
					      children distance)]
	(recur nnrdists nminnode nnpreds ndist)))))
 
(defn- build-path [preds root nodedst]
  "reverse walk on preds to reconstruct the shortest path"
  (loop [[pred dist] (preds nodedst) path (list nodedst)]
      (if (nil? pred)
	nil
        (if (= pred root)
          (cons root path)
          (recur (preds pred) (cons pred path))))))
 
(defn- add-rdist 
  ([rdists node pred dist]
  "add a known rdist (rdist = distance to the root)"
  (if-let [nodes (rdists dist)]
    (assoc rdists dist (assoc nodes node pred))
    (assoc rdists dist {node pred})))
 
  ([rdists node pred dist prevdist]
     (let [nrdists (add-rdist rdists node pred dist)
	   minnodes (rdists prevdist)
	   nminnodes (dissoc minnodes node)]
       (if (empty? nminnodes)
	 (dissoc nrdists prevdist)
	 (assoc nrdists prevdist nminnodes)))))
 
(defn- update-rdists [rdists preds net node dist children distance]
  "return [rdists preds] updated"
  (reduce (fn [acc x]
            (let [curdist (+ dist (distance net node x))
                  prevdist (second (preds x))
                  nrdists (first acc)
                  npreds (second acc)]
              (if (nil? prevdist)
                [(add-rdist nrdists x node curdist) (assoc npreds x [node curdist])]
                (if (< curdist prevdist)
                  [(add-rdist nrdists x node curdist prevdist) 
                   (assoc npreds x [node curdist])]
                  [nrdists npreds]))))
          [rdists preds]
          (children net node)))
 
(defn- take-minnode [rdists preds]
  "return a vector [minnode dist rdists preds]"
  (let [ [dist minnodes] (first rdists)
         [minnode pred] (first minnodes)
         others (rest minnodes)]
    [minnode
     dist
     (if (empty? others)
        (dissoc rdists dist)
        (assoc rdists dist others))
     (assoc preds minnode [pred dist]) ]))
 
 
(comment
 
;;
;; Example (based on the french wikipedia)
;; http://fr.wikipedia.org/wiki/Algorithme_de_Dijkstra
;;
 
(def net {:A {:B 85, :C 217, :E 173}, 
	  :B {:F 80},
	  :C {:G 186 :H 103},
	  :D {},
	  :E {:J 502},
	  :F {:I 250}
	  :G {},
	  :H {:D 183 :J 167}
	  :I {:J 84},
	  :J {}
	  })
 
 
(defn children [net node]
  (keys (net node)))
 
(defn distance [net nodesrc nodedst]
  ((net nodesrc) nodedst))
 
;(defn nodes [net]
;  (apply hash-set (keys net)))
 
(let [pathinfo (shortest-path net :A :J children distance)]
  (printf "path = %s
" pathinfo)) ;; [(:A :C :H :J) 487]
 
;; with all distances = 1
(let [pathinfo (shortest-path net :A :J children)]
  (printf "path = %s
" pathinfo)) ;; [(:A :E :J) 2]
 
)