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00 Formatted prime factorization.md

Formatted prime factorization

Prime factorization means representing an integer as a product of primes. A function that factorizes a number will return a vector of primes, like so: [2 2 3 5]. Your job is to take such a vector and create a nice string that shows the mathematical notation of the product.

Examples

(format-product [2 2 3 5]) ;=> "2^2 x 3 x 5"
(format-product [2 3 3 3 11 11]) ;=> "2 x 3^2 x 11^2"
(format-product [7]) ;=> "7"

Use x to indicate multiplication and ^ to indicate exponentiation.

Thanks to this site for the problem idea, where it is rated Hard in Ruby. The problem has been modified.

Please submit your solutions as comments on this gist.

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(defn format-product [xs]
  (->> (frequencies xs)
       (sort-by first)
       (reduce (fn [res [n cnt]]
                 (str
                  res
                  (if (empty? res) "" " x ")
                  (if (= cnt 1) n (str n "^" cnt))))
               "")))

(defn ffact [[fk fv]] (if (= fv 1) (str fk) (str fk "^" fv)))

(defn format-product [pf]
  (apply str (interpose " x " (map ffact (frequencies pf)))))

(defn format-product [nums]
  (->> (into (sorted-map) (frequencies nums))
       (map (fn [[x n]] (if (= n 1) x (str x \^ n))))
       (clojure.string/join " x ")))

The into call can be skipped if we don't care about order.

(defn string-builder
  ([] (StringBuilder.))
  ([sb] (str sb))
  ([sb x] (.append ^StringBuilder sb (str x))))

(defn format-product [factors]
  (transduce (comp (map (fn [[f cnt]] (if (= cnt 1) f (str f "^" cnt))))
                   (interpose " x "))
             string-builder
             (sort (frequencies factors))))