June 2018 Update

Task/Permutations-by-swapping/Clojure/permutations-by-swapping-1.clj

@@ -1,5 +1,37 @@
-(defn permutations [a-set]
-  (cond (empty? a-set) '(())
-        (empty? (rest a-set)) (list (apply list a-set))
-        :else (for [x a-set y (permutations (remove #{x} a-set))]
-                (cons x y))))
+(defn permutation-swaps
+  "List of swap indexes to generate all permutations of n elements"
+  [n]
+  (if (= n 2) `((0 1))
+    (let [old-swaps (permutation-swaps (dec n))
+          swaps-> (partition 2 1 (range n))
+          swaps<- (reverse swaps->)]
+      (mapcat (fn [old-swap side]
+                (case side
+                  :first swaps<-
+                  :right (conj swaps<- old-swap)
+                  :left (conj swaps-> (map inc old-swap))))
+              (conj old-swaps nil)
+              (cons :first (cycle '(:left :right)))))))
+
+
+(defn swap [v [i j]]
+  (-> v
+      (assoc i (nth v j))
+      (assoc j (nth v i))))
+
+
+(defn permutations [n]
+  (let [permutations (reduce
+                       (fn [all-perms new-swap]
+                         (conj all-perms (swap (last all-perms)
+                                               new-swap)))
+                       (vector (vec (range n)))
+                       (permutation-swaps n))
+        output (map vector
+                    permutations
+                    (cycle '(1 -1)))]
+    output))
+
+
+(doseq [n [2 3 4]]
+  (dorun (map println (permutations n))))