99-clojure-exercises/arithmetic.clj at master · tmeits/99-clojure-exercises · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
(comment
  "Solutions to Ninety-Nine Clojure Problems. Arithmetic.")
(ns c99.arithmetic
  (:use clojure.contrib.math)
  (:use clojure.contrib.profile)
  (:use clojure.test))

;; Являются ли два целых числа взаимно простыми?
(defn coprime?
  "Determine whether two positive integer numbers are coprime."
  [a b]
  ;; Целые числа называются взаимно простыми,
  ;; если они не имеют никаких общих делителей, кроме ±1.
  (= 1 (clojure.contrib.math/gcd a b)))

;;Примеры: 14 и 25 взаимно просты, а 15 и 25 не взаимно просты (у них имеется общий делитель 5).

(coprime? 14 25) ; true
(coprime? 15 25) ; false


(deftest goldbach-conjecture-test
  (do
    (is (= '(5 37) (goldbach-conjecture-pair 42)))
    (is (= '(3 5) (goldbach-conjecture-pair 8)))
    (is (= '(3 17) (goldbach-conjecture-pair 20)))
    (is (= '(5 23) (goldbach-conjecture-pair 28)))))

(defn prime? [n]
    "Determines whether or not N is prime."
    (cond
     (not (number? n)) (throw (IllegalArgumentException. "prime? requires a number"))
     (< n 2)  false
     :else
     (empty? (filter #(= 0 %) (map #(rem n %) (range 2 n))))))


(defn goldbach-conjecture "Goldbach's conjecture. Write a predicate to find the two prime
    numbers that sum up to a given even integer." [n]
    (map #(sort (rest %))
	 (filter #(= (first %) true)
		 (for [x (range 0 (inc n)) y (range 0 n)]
		   (list (and (= (+ x y) n) (prime? x) (prime? y)) x y)))))

(defn goldbach-conjecture-pair [n]
  "Choose the pair where the difference (- b a) is maximized."
  (let [gc (goldbach-conjecture n)]
    (when-not (empty? gc)
     ;;(println "For" n "Goldbach's conjecture is wrong.")
     (next (first (sort-by first > (map #(let [f (first %) s (second %)]
					   (list (- s f) f s)) gc)))))))


(defn goldbach-list [lower upper & limit]
  "A list of Goldbach compositions."
  (count
   (let [limit (if (empty? limit) 0 (first limit))]
     (map #(let [gcp (goldbach-conjecture-pair %)]
             (when (and (> (count gcp) 1) (> (first gcp) limit))
               (println % "=" (first gcp) "+" (first (rest gcp)))))
          (filter even? (range lower (inc upper)))))))

;; http://jondotcomdotorg.net/tag/clojure/
;; http://www.google.com/webfonts/family?family=Inconsolata&subset=latin
;; http://rubykoans.com/

(comment

c99.arithmetic> (goldbach-list 2 3000 50)
992 = 73 + 919
1382 = 61 + 1321
1856 = 67 + 1789
1928 = 61 + 1867
2078 = 61 + 2017
2438 = 61 + 2377
2512 = 53 + 2459
2530 = 53 + 2477
2618 = 61 + 2557
2642 = 103 + 2539
2999
p99.arithmetic>

  )


;; http://unityenvironment.blogspot.com/
;; http://bigdingus.com/category/clojure/
;; http://code.google.com/p/jngmisc/source/browse/clojure/primes/primes.clj
;; http://githowto.com