jneira-4clojure-solution67.clj

;; jneira's solution to http://4clojure.com/problem/67
(defn primes [n]
  (let
      [next-prime
       (fn [prs]
         (letfn
             [(aux [[f & r :as c] nxt]
                   (cond
                    (empty? c) (conj prs nxt)
                    (zero? (mod nxt f)) (recur prs (inc nxt))
                    :else (recur (take-while #(< % (quot nxt f)) r)
                                 nxt)))]
           (aux prs (inc (last prs)))))]
    (->> (iterate next-prime [2])
         (take n)
         (last))))

four-clojure> (doseq [i (take 10 (iterate #(* 2 %) 2))]
                     (time (dorun (primes3 i))))
"Elapsed time: 3.657657 msecs"
"Elapsed time: 0.235296 msecs"
"Elapsed time: 0.608317 msecs"
"Elapsed time: 2.046 msecs"
"Elapsed time: 71.857247 msecs"
"Elapsed time: 22.308631 msecs"
"Elapsed time: 21.346638 msecs"
"Elapsed time: 34.725852 msecs"
"Elapsed time: 102.604032 msecs"
"Elapsed time: 341.840932 msecs"
nil

;; comparation with filter solution

(defn primes4 [n]
  (let  [prime?
         (fn [x] (every? #(not= 0 (mod x %)) (range 2 x)))] 
    (take n (filter prime?
                    (drop 2 (range))))))

four-clojure> (doseq [i (take 10 (iterate #(* 2 %) 2))]
                     (time (dorun (primes4 i))))
"Elapsed time: 1.733042 msecs"
"Elapsed time: 0.7084 msecs"
"Elapsed time: 0.704 msecs"
"Elapsed time: 2.185822 msecs"
"Elapsed time: 92.96859 msecs"
"Elapsed time: 18.939349 msecs"
"Elapsed time: 65.61225 msecs"
"Elapsed time: 266.519977 msecs"
"Elapsed time: 1159.456579 msecs"
"Elapsed time: 5412.307849 msecs"
nil