project euler 69

pe_69.clj

;; Problem 69  : 2011/12/6

;; This needs too long time.
;; "Elapsed time: 980693.545995 msecs"

(defn get-n-slash-phi-n [n]
  (/ 1 (reduce * (map #(- 1 (/ 1 %)) (distinct (factors n))))))

(defn pe-69 [end-val]
  (reduce #(if (> (first %1) (first %2)) %1 %2)
	  (pmap #(vector (get-n-slash-phi-n %) %) (range 2 (inc end-val)))))


;; Another implementation.
;; "Elapsed time: 0.225784 msecs"

(defn product-list
  ([col] (product-list (rest col) (first col)))
  ([col p]
     (if (empty? col)
       (list p)
       (lazy-seq 
	(cons p
	      (product-list (next col) (* p (first col))))))))

(defn pe-69 [n]
  (let [max-prime-product (last
			   (take-while #(< % n)
				       (product-list (get-prime-list))))]
    (take-while #(< % n)
		(map #(* max-prime-product %) (iterate inc 1)))))


;; 2013/1/11
;; finaly found that product-list do exactly same as (reductions *)
;; this is my final (really?) answer contains only 1 function.
;; "Elapsed time: 0.654412 msecs" includes prime sequence generation time.

(defn pe-69 [n]
  (let [max-prime-product
        (last
         (take-while #(< % n)
                     (reductions * (create-primes (make-is-prime?)))))]
    (last
     (take-while #(< % n)
		(map #(* max-prime-product %) (iterate inc 1))))))

アクセスがあったので、ちらっと見てみたら、prodect-list が (reductions * ) と同じ処理であることに気づいたので、作りなおした。
必要な素数列作成コスト込みで1msec以下。