Problem 41 is yet another variation on the theme of pandigitality and primality. If nothing else, it is teaching me how to reuse my own code…

;; from euler-32
(defn all-unique? [digits]
  (let [unique (distinct digits)]
    (= (count unique) (count digits))))

(defn n-pandigital? [n digits]
  (and (nil? (some zero? digits))
       (nil? (some #(< n %) digits))
       (= n (count digits))
       (all-unique? digits)))

;; as-digits is from euler-30
(defn pandigital-prime? [pr]
  (let [d (as-digits pr)]
    (n-pandigital? (count d) d)))

(defn euler-41 []
  (last (filter pandigital-prime?
                (take-while #(< % 1000000)
                            (drop-while #(< % 100000) primes)))))
                                                             
(time (euler-41)) ;;  "Elapsed time: 9591.044968 msecs"

Hmm, performance isn’t bad, especially when the primes are already cached into memory; the speed improves by about 3x. However, we also could try an algorithm that tests for primality instead of pandigitality:

(use '[clojure.contrib.combinatorics :only (permutations)])

;; Use prime? and as-int from problem euler-37
(defn euler-41-alt
  ([] (euler-41-alt "987654321"))
  ([s] (first (filter #(prime? (as-int %))
                      (lazy-cat (permutations s)
                                [(euler-41-alt (rest s))])))))

(time (euler-41-alt)) ;; "Elapsed time: 1866.518849 msecs"

I guess it’s cheaper to check generate pandigital permutations and check primality than to generate primes and check pandigitality.