euler-5

5.clj

(defn max-merge [first second]
  (reduce
    (fn [factors-so-far current-key]
      (let [higher-value (max (get first current-key 0) (get second current-key 0))]
        (assoc factors-so-far current-key higher-value)))
    {}
    (clojure.set/union (set (keys first)) (set (keys second)))))

(def naturals (iterate inc 1))

(defn divides? [bottom top]
  (zero? (mod top bottom)))

(defn assoc-if
  [m key val should-assoc]
  (if should-assoc (assoc m key val) m))

(defn power-for-divisor [base top]
  (let [too-much-power (remove #(divides? (Math/pow base %) top) naturals)
        first-too-high-exponent (first too-much-power)]
    (dec first-too-high-exponent)))

(defn factor [n]
  (loop [remaining n factors {} divisor 2]
    (if (= remaining 1)
      factors
      (let [power-for-divisor (power-for-divisor divisor remaining)
            amount-to-cut-out (Math/pow divisor power-for-divisor)]
        (recur
          (int (/ remaining amount-to-cut-out))
          (assoc-if factors divisor power-for-divisor (> power-for-divisor 0))
          (inc divisor))))))

(defn unfactor [factorization]
  (reduce
    (fn [current-total [k v]]
      (* current-total (Math/pow k v)))
    1
    factorization))

(defn get-answer []
  (unfactor (reduce max-merge (map factor (range 2 21)))))