I would like to write a clojure function that has the following behaviour :
(take 4 (floyd))
=> '((1) (2 3) (4 5 6) (7 8 9 10))
(take 3 (floyd))
=> '((1) (2 3) (4 5 6))
(take 1 (floyd))
=> '((1)))
I tried using partition and partition-all to validate these tests however i couldn't get the right solution. If you have any idea of how to do it, i would really appreciate a little help. I started using clojure a few weeks ago and still have some issues.
Thanks
Here's another option:
(defn floyd []
(map (fn [lo n] (range lo (+ lo n 1)))
(reductions + 1 (iterate inc 1))
(range)))
(take 5 (floyd))
;=> ((1) (2 3) (4 5 6) (7 8 9 10) (11 12 13 14 15))
This was arrived at based on the observation that you want a series of increasing ranges (the (range) argument to map is used to produce a sequence of increasingly longer ranges), each one starting from almost the triangular number sequence:
(take 5 (reductions + 0 (iterate inc 1)))
;=> (0 1 3 6 10)
If we start that sequence from 1 instead, we get the starting numbers in your desired sequence:
(take 5 (reductions + 1 (iterate inc 1)))
;=> (1 2 4 7 11)
If the + 1 inside the mapped function bothers you, you could do this instead:
(defn floyd []
(map (fn [lo n] (range lo (+ lo n)))
(reductions + 1 (iterate inc 1))
(iterate inc 1)))
it is not possible to solve it with partition / partition-all, since they split your sequence into predefined size chunks.
What you can do, is to employ recursive lazy function for that:
user> (defn floyd []
(letfn [(f [n rng]
(cons (take n rng)
(lazy-seq (f (inc n) (drop n rng)))))]
(f 1 (iterate inc 1))))
#'user/floyd
user> (take 1 (floyd))
;;=> ((1))
user> (take 2 (floyd))
;;=> ((1) (2 3))
user> (take 3 (floyd))
;;=> ((1) (2 3) (4 5 6))
user> (take 4 (floyd))
;;=> ((1) (2 3) (4 5 6) (7 8 9 10))
another variant can use similar approach, but only track chunk-start/chunk-size:
user> (defn floyd []
(letfn [(f [n start]
(cons (range start (+ start n))
(lazy-seq (f (inc n) (+ start n)))))]
(f 1 1)))
another approach is to use clojure's collection operating functions:
user> (defn floyd-2 []
(->> [1 1]
(iterate (fn [[start n]]
[(+ n start) (inc n)]))
(map (fn [[start n]] (range start (+ start n))))))
#'user/floyd-2
user> (take 4 (floyd-2))
;;=> ((1) (2 3) (4 5 6) (7 8 9 10))
user> (take 5 (floyd-2))
;;=> ((1) (2 3) (4 5 6) (7 8 9 10) (11 12 13 14 15))
user> (take 1 (floyd-2))
;;=> ((1))
How about this:
(defn floyd []
(map (fn[n]
(let [start (/ (* n (inc n)) 2)]
(range (inc start) (+ start n 2))))
(iterate inc 0)))
(take 4 (floyd))
Related
Hi I am a clojure newbie,
I am trying to create a function that splits a collection into chunks of increasing size something along the lines of
(apply #(#(take %) (range 1 n)) col)
where n is the number of chunks
example of expected output:
with n = 4 and col = (range 1 4)
(1) (2 3) (4)
with n = 7 and col = (range 1 7)
(1) (2 3) (4 5 6) (7)
You can use something like this:
(defn partition-inc
"Partition xs at increasing steps of n"
[n xs]
(lazy-seq
(when (seq xs)
(cons (take n xs)
(partition-inc (inc n) (drop n xs))))))
; (println (take 5 (partition-inc 1 (range))))
; → ((0) (1 2) (3 4 5) (6 7 8 9) (10 11 12 13 14))
Or if you want to have more influence, you could alternatively provide
a sequence for the sizes (behaves the same as above, if passed (iterate inc 1) for sizes:
(defn partition-sizes
"Partition xs into chunks given by sizes"
[sizes xs]
(lazy-seq
(when (and (seq sizes) (seq xs))
(let [n (first sizes)]
(cons (take n xs) (partition-sizes (rest sizes) (drop n xs)))))))
; (println (take 5 (partition-sizes (range 1 10 2) (range))))
; → ((0) (1 2 3) (4 5 6 7 8) (9 10 11 12 13 14 15) (16 17 18 19 20 21 22 23 24))
An eager solution would look like
(defn partition-inc [coll]
(loop [rt [], c (seq coll), n 1]
(if (seq c)
(recur (conj rt (take n c)) (drop n c) (inc n))
rt)))
another way would be to employ some clojure sequences functions:
(->> (reductions (fn [[_ x] n] (split-at n x))
[[] (range 1 8)]
(iterate inc 1))
(map first)
rest
(take-while seq))
;;=> ((1) (2 3) (4 5 6) (7))
Yet another approach...
(defn growing-chunks [src]
(->> (range)
(reductions #(drop %2 %1) src)
(take-while seq)
(map-indexed take)
rest))
(growing-chunks [:a :b :c :d :e :f :g :h :i])
;; => ((:a) (:b :c) (:d :e :f) (:g :h :i))
I have a function that takes n random items from a collection such that the same item is never picked twice. I could accomplish this quite easily:
(defn take-rand [n coll]
(take n (shuffle coll)))
But I have a pesky requirement that I need to return the same random subset when the same seed is provided, i.e.
(defn take-rand [n coll & [seed]] )
(take-rand 5 (range 10) 42L) ;=> (2 5 8 6 7)
(take-rand 5 (range 10) 42L) ;=> (2 5 8 6 7)
(take-rand 5 (range 10) 27L) ;=> (7 6 9 1 3)
(take-rand 5 (range 10)) ;=> (9 7 8 5 0)
I have a solution for this, but it feels a bit clunky and not very idiomatic. Can any Clojure veterans out there propose improvements (or a completely different approach)?
Here's what I did:
(defn take-rand
"Returns n randomly selected items from coll, or all items if there are fewer than n.
No item will be picked more than once."
[n coll & [seed]]
(let [n (min n (count coll))
rng (if seed (java.util.Random. seed) (java.util.Random.))]
(loop [out [], in coll, n n]
(if (or (empty? in) (= n 0))
out
(let [i (.nextInt rng n)]
(recur (conj out (nth in i))
(concat (take i in) (nthrest in (inc i)))
(dec n)))))))
Well, I'm no clojure veteran, but how about:
(defn shuffle-with-seed
"Return a random permutation of coll with a seed"
[coll seed]
(let [al (java.util.ArrayList. coll)
rnd (java.util.Random. seed)]
(java.util.Collections/shuffle al rnd)
(clojure.lang.RT/vector (.toArray al))))
(defn take-rand [n coll & [seed]]
(take n (if seed
(shuffle-with-seed coll seed)
(shuffle coll))))
shuffle-with-seed is similiar to clojure's shuffle, it just passes an instance of Random to Java's java.util.Collections.shuffle().
Replace the shuffle function in your first solution with the reproducible one. I will show you my solution below:
(defn- shuffle'
[seed coll]
(let [rng (java.util.Random. seed)
rnd #(do % (.nextInt rng))]
(sort-by rnd coll)))
(defn take-rand'
([n coll]
(->> coll shuffle (take n)))
([n coll seed]
(->> coll (shuffle' seed) (take n))))
I hope this solution make results you expected:
user> (take-rand' 5 (range 10))
(5 4 7 2 6)
user> (take-rand' 5 (range 10))
(1 9 0 8 5)
user> (take-rand' 5 (range 10))
(5 2 3 1 8)
user> (take-rand' 5 (range 10) 42)
(2 6 4 8 1)
user> (take-rand' 5 (range 10) 42)
(2 6 4 8 1)
user> (take-rand' 5 (range 10) 42)
(2 6 4 8 1)
If I use the reductions function like so:
(reductions + [1 2 3 4 5])
Then I get
(1 3 6 10 15)
Which is great - but I'd like to apply a binary function in the same way without the state being carried forward - something like
(magic-hof + [1 2 3 4 5])
leads to
(1 3 5 7 9)
ie it returns the operation applied to the first pair, then steps 1 to the next pair.
Can someone tell me the higher-order function I'm looking for? (Something like reductions)
This is my (non-working) go at it:
(defn thisfunc [a b] [(+ a b) b])
(reduce thisfunc [1 2 3 4 5])
You can do it with map:
(map f coll (rest coll))
And if you want a function:
(defn map-pairwise [f coll]
(map f coll (rest coll)))
And if you really need the first element to remain untouched (thanx to juan.facorro's comment):
(defn magic-hof [f [x & xs :as s]]
(cons x (map f s xs)))
partition will group your seq:
user> (->> [1 2 3 4 5] (partition 2 1) (map #(apply + %)) (cons 1))
(1 3 5 7 9)
So, you want to apply a function to subsequent pairs of elements?
(defn pairwise-apply
[f sq]
(when (seq sq)
(->> (map f sq (next sq))
(cons (first sq)))))
Let's try it:
(pairwise-apply + (range 1 6))
;; => (1 3 5 7 9)
This is sufficient:
(#(map + (cons 0 %) %) [1 2 3 4 5])
;; => (1 3 5 7 9)
I'm trying to implement a Overhand Shuffle in Clojure as a bit of a learning exercise
So I've got this code...
(defn overhand [cards]
(let [ card_count (count cards)
_new_cards '()
_rand_ceiling (if (> card_count 4) (int (* 0.2 card_count)) 1)]
(take card_count
(reduce into (mapcat
(fn [c]
(-> (inc (rand-int _rand_ceiling))
(take cards)
(cons _new_cards)))
cards)))))
It is very close to doing what I want, but it is repeatedly taking the first (random) N number of cards off the front, but I want it to progress through the list...
calling as
(overhand [1 2 3 4 5 6 7 8 9])
instead of ending up with
(1 2 3 1 2 1 2 3 4)
I want to end up with
(7 8 9 5 6 1 2 3 4)
Also, as a side note this feels like a really ugly way to indent/organize this function, is there a more obvious way?
this function is creating a list of lists, transforming each of them, and cating them back together. the problem it that it is pulling from the same thing every time and appending to a fixed value. essentially it is running the same operation every time and so it is repeating the output over with out progressing thgough the list. If you break the problem down differently and split the creation of random sized chunks from the stringing them together it gets a bit easier to see how to make it work correctly.
some ways to split the sequence:
(defn random-partitions [cards]
(let [card_count (count cards)
rand_ceiling (if (> card_count 4) (inc (int (* 0.2 card_count))) 1)]
(partition-by (ƒ [_](= 0 (rand-int rand_ceiling))) cards)))
to keep the partitions less than length four
(defn random-partitions [cards]
(let [[h t] (split-at (inc (rand-int 4)) cards)]
(when (not-empty h) (lazy-seq (cons h (random-partition t))))))
or to keep the partitions at the sizes in your original question
(defn random-partitions [cards]
(let [card_count (count cards)
rand_ceiling (if (> card_count 4) (inc (int (* 0.2 card_count))) 1)
[h t] (split-at (inc (rand-int rand_ceiling)) cards)]
(when (not-empty h) (lazy-seq (cons h (random-partition t))))))
(random-partitions [1 2 3 4 5 6 7 8 9 10])
((1 2 3 4) (5) (6 7 8 9) (10))
this can also be written without directly using lazy-seq:
(defn random-partitions [cards]
(->> [[] cards]
(iterate
(ƒ [[h t]]
(split-at (inc (rand-int 4)) t)))
rest ;iterate returns its input as the first argument, drop it.
(map first)
(take-while not-empty)))
which can then be reduced back into a single sequence:
(reduce into (random-partitions [1 2 3 4 5 6 7 8 9 10]))
(10 9 8 7 6 5 4 3 1 2)
if you reverse the arguments to into it looks like a much better shuffle
(reduce #(into %2 %1) (random-partitions [1 2 3 4 5 6 7 8 9 10]))
(8 7 1 2 3 4 5 6 9 10)
Answering your indentation question, you could refactor your function. For instance, pull out the lambda expression from mapcat, defn it, then use its name in the call to mapcat. You'll not only help with the indentation, but your mapcat will be clearer.
For instance, here's your original program, refactored. Please note that issues with your program have not been corrected, I'm just showing an example of refactoring to improve the layout:
(defn overhand [cards]
(let [ card_count (count cards)
_new_cards '()
_rand_ceiling (if (> card_count 4) (int (* 0.2 card_count)) 1)]
(defn f [c]
(-> (inc (rand-int _rand_ceiling))
(take cards)
(cons _new_cards)))
(take card_count (reduce into (mapcat f cards)))))
You can apply these principles to your fixed code.
A great deal of indentation issues can be resolved by simply factoring out complex expressions. It also helps readability in general.
A better way to organise the function is to separate the shuffling action from the random selection of splitting points that drive it. Then we can test the shuffler with predictable splitters.
The shuffling action can be expressed as
(defn shuffle [deck splitter]
(if (empty? deck)
()
(let [[taken left] (split-at (splitter (count deck)) deck)]
(concat (shuffle left splitter) taken))))
where
deck is the sequence to be shuffled
splitter is a function that chooses where to split deck, given its
size.
We can test shuffle for some simple splitters:
=> (shuffle (range 10) (constantly 3))
(9 6 7 8 3 4 5 0 1 2)
=> (shuffle (range 10) (constantly 2))
(8 9 6 7 4 5 2 3 0 1)
=> (shuffle (range 10) (constantly 1))
(9 8 7 6 5 4 3 2 1 0)
It works.
Now let's look at the way you choose your splitting point. We can illustrate your choice of _rand_ceiling thus:
=> (map
(fn [card_count] (if (> card_count 4) (int (* 0.2 card_count)) 1))
(range 20))
(1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3)
This implies that you will take just one or two cards from any deck of less than ten. By the way, a simpler way to express the function is
(fn [card_count] (max (quot card_count 5) 1))
So we can express your splitter function as
(fn [card_count] (inc (rand-int (max (quot card_count 5) 1))))
So the shuffler we want is
(defn overhand [deck]
(let [splitter (fn [card_count] (inc (rand-int (max (quot card_count 5) 1))))]
(shuffle deck splitter)))
In Clojure, what would be the nicest way to have a sliding window over a (finite, not too large) seq? Should I just use drop and take and keep track of the current index or is there a nicer way I'm missing?
I think that partition with step 1 does it:
user=> (partition 3 1 [3 1 4 1 5 9])
((3 1 4) (1 4 1) (4 1 5) (1 5 9))
If you want to operate on the windows, it can also be convenient to do this with map:
user=> (def a [3 1 4 1 5 9])
user=> (map (partial apply +) (partition 3 1 a))
(8 6 10 15)
user=> (map + a (next a) (nnext a))
(8 6 10 15)
I didn't know partition could do this so I implemented it this way
(defn sliding-window [seq length]
(loop [result ()
remaining seq]
(let [chunk (take length remaining)]
(if (< (count chunk) length)
(reverse result)
(recur (cons chunk result) (rest remaining))))))