Project Euler Problem 24

pep024+.clj

(require '[clojure.test :refer (is)])

(defn pms
  "Permutations lexicographic by index."
  [[a & [b & [c & _]] :as ls]]
  (cond
    (nil? a) '()
    (nil? b) `(~a)
    (nil? c) `((~a ~b) (~b ~a))
    :else (mapcat (fn [h] (map (fn [r] (cons h r))
                               (lazy-seq (pms (remove #(= % h) ls)))))
                  ls)))

(is (= (pms '(a b c))
       '((a b c) (a c b) (b a c) (b c a) (c a b) (c b a))))

(defn pep024+
  ([] (pep024+ "0123456789" 1000000))
  ([digits n] (apply str (nth (pms digits) (dec n)))))

(is (= (pep024+ "012" 5) "201"))

(time (pep024+)) ; "Elapsed time: 14099.017 msecs" in my environment

pep024.clj

(require '[clojure.test :refer (is)])

;; dependent on [org.clojure/math.combinatorics "0.0.3"]
(require '[clojure.math.combinatorics :refer (permutations)])

(defn pep024
  ([] (pep024 "0123456789" 1000000))
  ([digits n] (apply str (nth (permutations digits) (dec n)))))

(is (= (pep024 "012" 5) "201"))

(time (pep024)) ; "Elapsed time: 983.816 msecs" in my environment

「可視化すると何かが見える」

なるほど.
確かに樹形図を実際に書いてみると「こっから下は書かなくても大きさが分かればいいじゃない？」ってなりそうですね.
見習います.