In a Clojure program, I have a sequence of numbers:
(2 3 4 6 8 1)
I want to find the longest sub-sequence where the items are sequential:
(2 3 4)
I am assuming that it will involve (take-while ...) or (reduce ...).
Any ideas?
Clarification: I need the longest initial list of sequential items. Much easier, I'm sure. Thanks for the solutions to the more difficult problem I initially posed.
If you are only interested in the longest initial sequence, it's a 1-liner:
(defn longest-initial-sequence [[x :as s]]
(take-while identity (map #(#{%1} %2) s (iterate inc x))))
Taking into account the OP's comment on the question -- which completely changes the game! -- this can be written very simply:
(let [doubletons (partition 2 1 [1 2 3 5 6])
increment? (fn increment? [[x y]]
(== (inc x) y))]
(cons (ffirst doubletons)
(map second (take-while increment? doubletons))))
;; returns (1 2 3)
Note that this is actually lazy. I expect it not to hold onto the head of doubletons thanks to locals clearing. Another version:
(cons (first [1 2 3 5 6])
(map second (take-while increment? (partition 2 1 [1 2 3 5 6]))))
The original version of the question is more fun, though! :-) A super-simple solution to that could be built using the above, but of course that would be significantly less performant than using reduce. I'll see if I have anything substantially different from zmila's and dnolen's solutions -- and yet still reasonably performant -- to add to that part of this thread later. (Not very likely, I guess.)
Answer to original:
(defn conj-if-sequential
([] [])
([a] a)
([a b] (let [a (if (vector? a) a [a])]
(if (= (inc (last a)) b)
(conj a b)
a))))
(reduce conj-if-sequential [2 3 4 6 8 1])
A more generic solution for those interested:
(defn sequential-seqs
([] [])
([a] a)
([a b] (let [n (last (last a))]
(if (and n (= (inc n) b))
(update-in a [(dec (count a))] conj b)
(conj a [b])))))
(defn largest
([] nil)
([a] a)
([a b] (if (> (count b) (count a)) b a)))
(reduce largest (reduce sequential-seqs [] [2 3 4 6 8 1 4 5 6 7 8 9 13]))
I think this is much better.
(defn find-max-seq [lst]
(let [[f & r] lst,
longest-seq (fn [a b] (if (> (count a) (count b)) a b)),
[last-seq max-seq] (reduce
(fn [ [[prev-num & _ :as cur-seq] max-seq] cur-num ]
(if (== (inc prev-num) cur-num)
[(conj cur-seq cur-num) max-seq]
[(list cur-num) (longest-seq cur-seq max-seq)]
))
[(list f) ()]
r)]
(reverse (longest-seq last-seq max-seq))))
(find-max-seq '(2 3 4 6 8 1)) ; ==> (2 3 4)
(find-max-seq '(3 2 3 4 6 8 9 10 11)) ; ==> (8 9 10 11)
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 need a function that maps a function only on every other element, e.g.
(f inc '(1 2 3 4))
=> '(2 2 4 4)
I came up with:
(defn flipflop [f l]
(loop [k l, b true, r '()]
(if (empty? k)
(reverse r)
(recur (rest k)
(not b)
(conj r (if b
(f (first k))
(first k)))))))
Is there a prettier way to achieve this ?
(map #(% %2)
(cycle [f identity])
coll)
It's a good idea to look at Clojure's higher level functions before using loop and recur.
user=> (defn flipflop
[f coll]
(mapcat #(apply (fn ([a b] [(f a) b])
([a] [(f a)]))
%)
(partition-all 2 coll)))
#'user/flipflop
user=> (flipflop inc [1 2 3 4])
(2 2 4 4)
user=> (flipflop inc [1 2 3 4 5])
(2 2 4 4 6)
user=> (take 11 (flipflop inc (range))) ; demonstrating laziness
(1 1 3 3 5 5 7 7 9 9 11)
this flipflop doesn't need to reverse the output, it is lazy, and I find it much easier to read.
The function uses partition-all to split the list into pairs of two items, and mapcat to join a series of two element sequences from the calls back into a single sequence.
The function uses apply, plus multiple arities, in order to handle the case where the final element of the partitioned collection is a singleton (the input was odd in length).
also, since you want to apply the function to some specific indiced items in the collection (even indices in this case) you could use map-indexed, like this:
(defn flipflop [f coll]
(map-indexed #(if (even? %1) (f %2) %2) coll))
Whereas amalloy's solution is the one, you could simplify your loop - recur solution a bit:
(defn flipflop [f l]
(loop [k l, b true, r []]
(if (empty? k)
r
(recur (rest k)
(not b)
(conj r ((if b f identity) (first k)))))))
This uses couple of common tricks:
If an accumulated list comes out in the wrong order, use a vector
instead.
Where possible, factor out common elements in a conditional.
I would like to "chunk" a seq into subseqs the same as partition-by, except that the function is not applied to each individual element, but to a range of elements.
So, for example:
(gather (fn [a b] (> (- b a) 2))
[1 4 5 8 9 10 15 20 21])
would result in:
[[1] [4 5] [8 9 10] [15] [20 21]]
Likewise:
(defn f [a b] (> (- b a) 2))
(gather f [1 2 3 4]) ;; => [[1 2 3] [4]]
(gather f [1 2 3 4 5 6 7 8 9]) ;; => [[1 2 3] [4 5 6] [7 8 9]]
The idea is that I apply the start of the list and the next element to the function, and if the function returns true we partition the current head of the list up to that point into a new partition.
I've written this:
(defn gather
[pred? lst]
(loop [acc [] cur [] l lst]
(let [a (first cur)
b (first l)
nxt (conj cur b)
rst (rest l)]
(cond
(empty? l) (conj acc cur)
(empty? cur) (recur acc nxt rst)
((complement pred?) a b) (recur acc nxt rst)
:else (recur (conj acc cur) [b] rst)))))
and it works, but I know there's a simpler way. My question is:
Is there a built in function to do this where this function would be unnecessary? If not, is there a more idiomatic (or simpler) solution that I have overlooked? Something combining reduce and take-while?
Thanks.
Original interpretation of question
We (all) seemed to have misinterpreted your question as wanting to start a new partition whenever the predicate held for consecutive elements.
Yet another, lazy, built on partition-by
(defn partition-between [pred? coll]
(let [switch (reductions not= true (map pred? coll (rest coll)))]
(map (partial map first) (partition-by second (map list coll switch)))))
(partition-between (fn [a b] (> (- b a) 2)) [1 4 5 8 9 10 15 20 21])
;=> ((1) (4 5) (8 9 10) (15) (20 21))
Actual Question
The actual question asks us to start a new partition whenever pred? holds for the beginning of the current partition and the current element. For this we can just rip off partition-by with a few tweaks to its source.
(defn gather [pred? coll]
(lazy-seq
(when-let [s (seq coll)]
(let [fst (first s)
run (cons fst (take-while #((complement pred?) fst %) (next s)))]
(cons run (gather pred? (seq (drop (count run) s))))))))
(gather (fn [a b] (> (- b a) 2)) [1 4 5 8 9 10 15 20 21])
;=> ((1) (4 5) (8 9 10) (15) (20 21))
(gather (fn [a b] (> (- b a) 2)) [1 2 3 4])
;=> ((1 2 3) (4))
(gather (fn [a b] (> (- b a) 2)) [1 2 3 4 5 6 7 8 9])
;=> ((1 2 3) (4 5 6) (7 8 9))
Since you need to have the information from previous or next elements than the one you are currently deciding on, a partition of pairs with a reduce could do the trick in this case.
This is what I came up with after some iterations:
(defn gather [pred s]
(->> (partition 2 1 (repeat nil) s) ; partition the sequence and if necessary
; fill the last partition with nils
(reduce (fn [acc [x :as s]]
(let [n (dec (count acc))
acc (update-in acc [n] conj x)]
(if (apply pred s)
(conj acc [])
acc)))
[[]])))
(gather (fn [a b] (when (and a b) (> (- b a) 2)))
[1 4 5 8 9 10 15 20 21])
;= [[1] [4 5] [8 9 10] [15] [20 21]]
The basic idea is to make partitions of the number of elements the predicate function takes, filling the last partition with nils if necessary. The function then reduces each partition by determining if the predicate is met, if so then the first element in the partition is added to the current group and a new group is created. Since the last partition could have been filled with nulls, the predicate has to be modified.
Tow possible improvements to this function would be to let the user:
Define the value to fill the last partition, so the reducing function could check if any of the elements in the partition is this value.
Specify the arity of the predicate, thus allowing to determine the grouping taking into account the current and the next n elements.
I wrote this some time ago in useful:
(defn partition-between [split? coll]
(lazy-seq
(when-let [[x & more] (seq coll)]
(lazy-loop [items [x], coll more]
(if-let [[x & more] (seq coll)]
(if (split? [(peek items) x])
(cons items (lazy-recur [x] more))
(lazy-recur (conj items x) more))
[items])))))
It uses lazy-loop, which is just a way to write lazy-seq expressions that look like loop/recur, but I hope it's fairly clear.
I linked to a historical version of the function, because later I realized there's a more general function that you can use to implement partition-between, or partition-by, or indeed lots of other sequential functions. These days the implementation is much shorter, but it's less obvious what's going on if you're not familiar with the more general function I called glue:
(defn partition-between [split? coll]
(glue conj []
(fn [v x]
(not (split? [(peek v) x])))
(constantly false)
coll))
Note that both of these solutions are lazy, which at the time I'm writing this is not true of any of the other solutions in this thread.
Here is one way, with steps split up. It can be narrowed down to fewer statements.
(def l [1 4 5 8 9 10 15 20 21])
(defn reduce_fn [f x y]
(cond
(f (last (last x)) y) (conj x [y])
:else (conj (vec (butlast x)) (conj (last x) y)) )
)
(def reduce_fn1 (partial reduce_fn #(> (- %2 %1) 2)))
(reduce reduce_fn1 [[(first l)]] (rest l))
keep-indexed is a wonderful function. Given a function f and a vector lst,
(keep-indexed (fn [idx it] (if (apply f it) idx))
(partition 2 1 lst)))
(0 2 5 6)
this returns the indices after which you want to split. Let's increment them and tack a 0 at the front:
(cons 0 (map inc (.....)))
(0 1 3 6 7)
Partition these to get ranges:
(partition 2 1 nil (....))
((0 1) (1 3) (3 6) (6 7) (7))
Now use these to generate subvecs:
(map (partial apply subvec lst) ....)
([1] [4 5] [8 9 10] [15] [20 21])
Putting it all together:
(defn gather
[f lst]
(let [indices (cons 0 (map inc
(keep-indexed (fn [idx it]
(if (apply f it) idx))
(partition 2 1 lst))))]
(map (partial apply subvec (vec lst))
(partition 2 1 nil indices))))
(gather #(> (- %2 %) 2) '(1 4 5 8 9 10 15 20 21))
([1] [4 5] [8 9 10] [15] [20 21])
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)
What would be a more idiomatic way to partition a seq based on a seq of integers instead of just one integer?
Here's my implementation:
(defn partition-by-seq
"Return a lazy sequence of lists with a variable number of items each
determined by the n in ncoll. Extra values in coll are dropped."
[ncoll coll]
(let [partition-coll (mapcat #(repeat % %) ncoll)]
(->> coll
(map vector partition-coll)
(partition-by first)
(map (partial map last)))))
Then (partition-by-seq [2 3 6] (range)) yields ((0 1) (2 3 4) (5 6 7 8 9 10)).
Your implementation looks fine, but there could be a more simple solution which uses simple recursion wrapped in lazy-seq(and turns out to be more efficient) than using map and existing partition-by as in your case.
(defn partition-by-seq [ncoll coll]
(if (empty? ncoll)
'()
(let [n (first ncoll)]
(cons (take n coll)
(lazy-seq (partition-by-seq (rest ncoll) (drop n coll)))))))
A variation on Ankur's answer, with a minor addition of laziness and when-let instead of an explicit test for empty?.
(defn partition-by-seq [parts coll]
(lazy-seq
(when-let [s (seq parts)]
(cons
(take (first s) coll)
(partition-by-seq (rest s) (nthrest coll (first s)))))))
(first (reduce (fn [[r l] n]
[(conj r (take n l)) (drop n l)])
[[] (range)]
[2 3 6]))
=> [(0 1) (2 3 4) (5 6 7 8 9 10)]