euler_fizz_buzz.clj

(ns euler-fizz-buzz)

;; Inspired by http://philcrissman.net/posts/eulers-fizzbuzz/

(defn mod-pow [b e m] (long (.modPow (biginteger b) (biginteger e) (biginteger m))))
(defn fizz-buzz [] (map #({6 "Fizz" 10 "Buzz" 0 "FizzBuzz"} (mod-pow % 4 15) %) (range 1 100)))


;;https://en.wikipedia.org/wiki/Euler%27s_totient_function
;;https://oeis.org/A000010
(defn totient[n]
  (get [1 1 2 2 4 2 6 4 6 4 10 4 12 6 8 8 16 6 18 8 12 10 22 8 20 12 18 12 28 8 30 16 20 16 24 12 36 18 24 16 40 12 42 20 24 22 46 16 42 20 32 24 52 18 40 24 36 28 58 16 60 30 36 32 48 20 66 32 44] (dec n)))

;; https://rosettacode.org/wiki/Least_common_multiple#Clojure
;; available in clojure.math.numeric-tower
(defn gcd [a b]
      (if (zero? b)
      a
      (recur b, (mod a b))))

(defn lcm [a b]
      (/ (* a b) (gcd a b)))

(defn foo-bar [m]
  (assert (= 2 (count m)) "map should contain 2 entries")
  (let  [[keys vals] ((juxt keys vals) m)
         div (reduce * keys)
         lcm (->> keys (map totient) (reduce lcm))
         m (-> #(mod-pow % lcm div)
               (map keys)
               (zipmap vals)
               (assoc 0 (reduce str vals)))]
    (->> (range 1 100)
         (map #(m (mod-pow % lcm div) %)))))

(comment
  (fizz-buzz)
  (foo-bar {7 "foo" 11 "bar"})
  )