Stirling numbers

stirling-dynamic.clj

(defn- stirling-loop-internal
  [^long n ^long k compfunc]
  { :pre [(<= k n)] }
  (let [workitems (for [n' (range 1 (inc n)) k' (range 0 (inc (- n k))) 
    :when (and (>= (- n' k') 0) (>= k (- n' k')))] [n' (- n' k')])]
    (loop [current (first workitems) items (rest workitems) results {}]
      (cond
        (= current [n k]) ((compfunc current results) current)
        (= (current 0) (current 1)) 
          (recur (first items) (rest items) 
            (assoc results current 1))
        (= (current 1) 0)
          (recur (first items) (rest items) 
            (assoc results current 0))
        :else
          (recur (first items) (rest items) 
            (compfunc current results))))))

(defn stirling-1
  "Returns the Stirling number of the first kind s(n, k)"
  [^long n ^long k]
  { :pre [(<= k n) (>= k 0) (pos? n)] }
  (stirling-loop-internal n k 
    (fn [[n' k'] resultmap]
      (assoc resultmap [n' k']
        (- (resultmap [(dec n') (dec k')]) 
          (*' (dec n') (resultmap [(dec n') k'])))))))

(defn stirling-2
  "Returns the Stirling number of the second kind s(n, k)"
  [^long n ^long k]
  { :pre [(<= k n) (>= k 0) (pos? n)] }
  (stirling-loop-internal n k 
    (fn [[n' k'] resultmap]
      (assoc resultmap [n' k']
        (- (resultmap [(dec n') (dec k')]) 
          (*' k' (resultmap [(dec n') k'])))))))

stirling-recursive.clj

(defn stirling-1-recursive 
  "Returns the Stirling number of the first kind s(n, k) (recursively)."
  [n k]
  { :pre [(<= k n) (>= k 0) (pos? n)] }
  (cond 
    (= k n) 1
    (= k 0) 0
    :else (- (stirling-1-recursive (dec n) (dec k)) 
      (*' (dec n) (stirling-1-recursive (dec n) k)))))


(defn stirling-2-recursive
  "Returns the Stirling number of the second kind s(n, k) (recursively)."
  [n k]
  { :pre [(<= k n) (>= k 0) (pos? n)] }
  (cond 
    (= k n) 1
    (= k 0) 0
    :else (- (stirling-2-recursive (dec n) (dec k)) 
      (*' k (stirling-2-recursive (dec n) k)))))