Question

我对Clojure中的递归关系的一般函数有一个想法：

(defn recurrence [f inits]
  (let [answer (lazy-seq (recurrence f inits))
        windows (partition (count inits) 1 answer)]
    (concat inits (lazy-seq (map f windows)))))

然后，例如，我们可以将Fibonacci序列定义为

(def fibs (recurrence (partial apply +) [0 1N]))

这适用于小数字：

(take 10 fibs)
;(0 1N 1N 2N 3N 5N 8N 13N 21N 34N)

但是如果被要求实现一个很长的序列，那它就会打击堆栈：

(first (drop 10000 fibs))
;StackOverflowError ...

有没有办法克服这个问题？

Answer 1

这里的问题是你在每次迭代时都会建立对concat的调用，并且concat调用会在你最终要求一个值时产生大量未评估的thunk。通过使用cons并仅传递所需的值计数（和concat，但不是递归堆栈concat），我们得到了更好的懒惰序列：

user> 
(defn recurrence
  [f seed]
  (let [step (apply f seed)
        new-state (concat (rest seed) (list step))]
    (lazy-seq (cons step (recurrence f new-state)))))
#'user/recurrence
user> (def fibs (recurrence +' [0 1]))
#'user/fibs
user> (take 10 fibs)
(1 2 3 5 8 13 21 34 55 89)
user> (first (drop 1000 fibs))
113796925398360272257523782552224175572745930353730513145086634176691092536145985470146129334641866902783673042322088625863396052888690096969577173696370562180400527049497109023054114771394568040040412172632376N

Answer 2

从the accepted answer开始。

我们希望使用seed开始序列。
正如作者所说，我们使用队列来提高效率。我们不需要deque：clojure＆＃39; s PersistentQueue就是我们所需要的。

改编后的recurrence可能如下所示：

(defn recurrence
  [f seed]
  (let [init-window (into (clojure.lang.PersistentQueue/EMPTY) seed)
        unroll (fn unroll [w] (lazy-seq (cons
                                          (peek w)
                                          (unroll (-> w
                                                      pop
                                                      (conj (apply f w)))))))]
    (unroll init-window)))

......和以前一样......

(def fibs (recurrence +' [0 1]))

然后

(take 12 fibs)
;(0 1 1 2 3 5 8 13 21 34 55 89)

和

(first (drop 10002 fibs))
;88083137989997064605355872998857923445691333015376030932812485815888664307789011385238647061572694566755888008658862476758094375234981509702215595106015601812940878487465890539696395631360292400123725490667987980947195761919733084221263262792135552511961663188744083262743015393903228035182529922900769207624088879893951554938584166812233127685528968882435827903110743620870056104022290494963321073406865860606579792362403866826411642270661211435590340090149458419810817251120025713501918959350654895682804718752319215892119222907223279849851227166387954139546662644064653804466345416102543306712688251378793506564112970620367672131344559199027717813404940431009754143637417645359401155245658646088296578097547699141284451819782703782878668237441026255023475279003880007450550868002409533068098127495095667313120369142331519140185017719214501847645741030739351025342932514280625453085775191996236343792432215700850773568257988920265539647922172315902209901079830195949058505943508013044450503826167880993094540503572266189964694973263576375908606977788395730196227274629745722872833622300472769312273603346624292690875697438264265712313123637644491367875538847442013130532147345613099333195400845560466085176375175045485046787815133225349388996334014329318304865656815129208586686515835880811316065788759195646547703631454040090435955879604123186007481842117640574158367996845627012099571008761776991075470991386301988104753915798231741447012236434261594666985397841758348337030914623617101746431922708522824868155612811426016775968762121429282582582088871795463467796927317452368633552346819405423359738696980252707545944266042764236577381721803749442538053900196250284054406347238606575093877669323501452512412179883698552204038865069179867773579705703841178650618818357366165649529547898801198617541432893443650952033983923542592952070864044249738338089778163986683069566736505126466886304227253105034231716761535350441178724210841830855527586882822093246545813120624113290391593897765219320931179697869997243770533719319530526369830529543842405655495229382251039116426750156771132964376N

另一种方式，基于一个被盗的想法 - 我认为 - 来自 Clojure的喜悦，是......

(defn recurrence
  [f seed]
  (let [init-window (into (clojure.lang.PersistentQueue/EMPTY) seed)
        windows (iterate
                  (fn [w] (-> w, pop, (conj (apply f w))))
                  init-window)]
    (map peek windows)))

如何在Clojure中定义一般递归函数

2 个答案: