Random product subset

rand-product-subset.clj

(defn rand-approx-product-subset
  "Generates a randomized subset of a coll of integers whose product has a chance of
  approximating `goal`."
  [goal coll]
  (let [midrange      (-> (apply max coll) (- (apply min coll)) (/ 2.0))
        tipping-point (/ goal (Math/sqrt midrange))]
    (loop [product 1N coll' (shuffle coll) subset []]
      (if (> product tipping-point) subset
        (let [x (first coll')]
          (recur (*' product x) (rest coll') (conj subset x)))))))

(defn best-rand-approx-product-subset
  "Repeatedly generates randomized subsets of a coll of integers, takes the first
  `sample-size` subsets whose product is `goal` ± `precision`%, and returns the subset 
  among those that is closest to `goal`."
  [goal coll sample-size precision]
  (->> (repeatedly #(rand-approx-product-subset2 goal coll))
       (keep #(let [ratio (/ (reduce *' 1.0 %) goal)]
                (when (<= (- 1 precision) ratio (+ 1 precision))
                  {:error (abs (- 1 ratio)) :subset %})))
       (take sample-size)
       (apply min-key :error)
       :subset))