So, I read that the count operation is O(1) for a Clojure vectors, lists and maps.
(count [1 2 3]) ;=> 3
But is it also O(1) for a Clojure set? I imagine it probably is, but I'm not really sure how to find out. I had a quick read of http://clojure.org/data_structures#Data%20Structures-Sets, but couldn't see the info there.
It is O(1)
You can verify this by observing that clojure.lang.PersistentSet maintains a _count field in the Java source code:
https://github.com/clojure/clojure/blob/master/src/jvm/clojure/lang/PersistentList.java
Related
I know that clojure's clojure.lang.IPersistentVector implements assoc, as in (assoc [0 1 2 3] 0 -1) ; => [-1 1 2 3]. I have also heard (as in this answer) that clojure's vector doesn't implement dissoc, as in (dissoc [0 1 2 3] 0) ; => [1 2 3]. If this functionality is so easily reproducible using subvec, is there any real reason why it shouldn't be implemented in clojure.lang, clojure.core, or even contrib? If not, is there any reasoning behind that?
Dissoc doesn't make much sense for vectors for two reasons:
The meaning of dissoc is "remove a key". You can't remove a key from a vector without causing other side effects (e.g. moving all future values)
dissoc would perform relatively badly on vectors if it had to move all subsequent keys - roughly O(n) with quite a lot of GC. Clojure core generally avoids implementing operations that aren't efficient / don't make sense for a particular data structure.
Basically, if you find yourself wanting to do dissoc on a vector, you are probably using the wrong data structure. A persistent hashmap or set is probably a better choice.
If you want a data structure which works as a vector but supports cutting out and inserting elements or subsequences efficiently, then it is worth checking out RRB trees: https://github.com/clojure/core.rrb-vector
Every collection in clojure is said to be "sequable" but only list and cons are actually seqs:
user> (seq? {:a 1 :b 2})
false
user> (seq? [1 2 3])
false
All other seq functions first convert a collection to a sequence and only then operate on it.
user> (class (rest {:a 1 :b 2}))
clojure.lang.PersistentArrayMap$Seq
I cannot do things like:
user> (:b (rest {:a 1 :b 2}))
nil
user> (:b (filter #(-> % val (= 1)) {:a 1 :b 1 :c 2}))
nil
and have to coerce back to concrete data type. This looks like bad design to me, but most likely I just don't get it as yet.
So, why clojure collections don't implement ISeq interface directly and all seq functions don't return an object of the same class as the input object?
This has been discussed on the Clojure google group; see for example the thread map semantics from February of this year. I'll take the liberty of reusing some of the points I made in my message to that thread below while adding several new ones.
Before I go on to explain why I think the "separate seq" design is the correct one, I would like to point out that a natural solution for the situations where you'd really want to have an output similar to the input without being explicit about it exists in the form of the function fmap from the contrib library algo.generic. (I don't think it's a good idea to use it by default, however, for the same reasons for which the core library design is a good one.)
Overview
The key observation, I believe, is that the sequence operations like map, filter etc. conceptually divide into three separate concerns:
some way of iterating over their input;
applying a function to each element of the input;
producing an output.
Clearly 2. is unproblematic if we can deal with 1. and 3. So let's have a look at those.
Iteration
For 1., consider that the simplest and most performant way to iterate over a collection typically does not involve allocating intermediate results of the same abstract type as the collection. Mapping a function over a chunked seq over a vector is likely to be much more performant than mapping a function over a seq producing "view vectors" (using subvec) for each call to next; the latter, however, is the best we can do performance-wise for next on Clojure-style vectors (even in the presence of RRB trees, which are great when we need a proper subvector / vector slice operation to implement an interesting algorithm, but make traversals terrifying slow if we used them to implement next).
In Clojure, specialized seq types maintain traversal state and extra functionality such as (1) a node stack for sorted maps and sets (apart from better performance, this has better big-O complexity than traversals using dissoc / disj!), (2) current index + logic for wrapping leaf arrays in chunks for vectors, (3) a traversal "continuation" for hash maps. Traversing a collection through an object like this is simply faster than any attempt at traversing through subvec / dissoc / disj could be.
Suppose, however, that we're willing to accept the performance hit when mapping a function over a vector. Well, let's try filtering now:
(->> some-vector (map f) (filter p?))
There's a problem here -- there's no good way to remove elements from a vector. (Again, RRB trees could help in theory, but in practice all the RRB slicing and concatenating involved in producing "real vector" for filtering operations would absolutely destroy performance.)
Here's a similar problem. Consider this pipeline:
(->> some-sorted-set (filter p?) (map f) (take n))
Here we benefit from laziness (or rather, from the ability to stop filtering and mapping early; there's a point involving reducers to be made here, see below). Clearly take could be reordered with map, but not with filter.
The point is that if it's ok for filter to convert to seq implicitly, then it is also ok for map; and similar arguments can be made for other sequence functions. Once we've made the argument for all -- or nearly all -- of them, it becomes clear that it also makes sense for seq to return specialized seq objects.
Incidentally, filtering or mapping a function over a collection without producing a similar collection as a result is very useful. For example, often we care only about the result of reducing the sequence produced by a pipeline of transformations to some value or about calling a function for side effect at each element. For these scenarios, there is nothing whatsoever to be gained by maintaining the input type and quite a lot to be lost in performance.
Producing an output
As noted above, we do not always want to produce an output of the same type as the input. When we do, however, often the best way to do so is to do the equivalent of pouring a seq over the input into an empty output collection.
In fact, there is absolutely no way to do better for maps and sets. The fundamental reason is that for sets of cardinality greater than 1 there is no way to predict the cardinality of the output of mapping a function over a set, since the function can "glue together" (produce the same outputs for) arbitrary inputs.
Additionally, for sorted maps and sets there is no guarantee that the input set's comparator will be able to deal with outputs from an arbitrary function.
So, if in many cases there is no way to, say, map significantly better than by doing a seq and an into separately, and considering how both seq and into make useful primitives in their own right, Clojure makes the choice of exposing the useful primitives and letting users compose them. This lets us map and into to produce a set from a set, while leaving us the freedom to not go on to the into stage when there is no value to be gained by producing a set (or another collection type, as the case may be).
Not all is seq; or, consider reducers
Some of the problems with using the collection types themselves when mapping, filtering etc. don't apply when using reducers.
The key difference between reducers and seqs is that the intermediate objects produced by clojure.core.reducers/map and friends only produce "descriptor" objects that maintain information on what computations need to be performed in the event that the reducer is actually reduced. Thus, individual stages of the computation can be merged.
This allows us to do things like
(require '[clojure.core.reducers :as r])
(->> some-set (r/map f) (r/filter p?) (into #{}))
Of course we still need to be explicit about our (into #{}), but this is just a way of saying "the reducers pipeline ends here; please produce the result in the form of a set". We could also ask for a different collection type (a vector of results perhaps; note that mapping f over a set may well produce duplicate results and we may in some situations wish to preserve them) or a scalar value ((reduce + 0)).
Summary
The main points are these:
the fastest way to iterate over a collection typically doesn't involve produce intermediate results similar to the input;
seq uses the fastest way to iterate;
the best approach to transforming a set by mapping or filtering involves using a seq-style operation, because we want to iterate very fast while accumulating an output;
thus seq makes a great primitive;
map and filter, in their choice to deal with seqs, depending on the scenario, may avoid performance penalties without upsides, benefit from laziness etc., yet can still be used to produce a collection result with into;
thus they too make great primitives.
Some of these points may not apply to a statically typed language, but of course Clojure is dynamic. Additionally, when we do want to a return that matches input type, we're simply forced to be explicit about it and that, in itself, may be viewed as a good thing.
Sequences are a logical list abstraction. They provide access to a (stable) ordered sequence of values. They are implemented as views over collections (except for lists where the concrete interface matches the logical interface). The sequence (view) is a separate data structure that refers into the collection to provide the logical abstraction.
Sequence functions (map, filter, etc) take a "seqable" thing (something which can produce a sequence), call seq on it to produce the sequence, and then operate on that sequence, returning a new sequence. It is up to you whether you need to or how to re-collect that sequence back into a concrete collection. While vectors and lists are ordered, sets and maps are not and thus sequences over these data structures must compute and retain the order outside the collection.
Specialized functions like mapv, filterv, reduce-kv allow you to stay "in the collection" when you know you want the operation to return a collection at the end instead of sequence.
Seqs are ordered structures, whereas maps and sets are unordered. Two maps that are equal in value may have a different internal ordering. For example:
user=> (seq (array-map :a 1 :b 2))
([:a 1] [:b 2])
user=> (seq (array-map :b 2 :a 1))
([:b 2] [:a 1])
It makes no sense to ask for the rest of a map, because it's not a sequential structure. The same goes for a set.
So what about vectors? They're sequentially ordered, so we could potentially map across a vector, and indeed there is such a function: mapv.
You may well ask: why is this not implicit? If I pass a vector to map, why doesn't it return a vector?
Well, first that would mean making an exception for ordered structures like vectors, and Clojure isn't big on making exceptions.
But more importantly you'd lose one of the most useful properties of seqs: laziness. Chaining together seq functions, such as map and filter is a very common operation, and without laziness this would be much less performant and far more memory-intensive.
The collection classes follow a factory pattern i.e instead of implementing ISeq they implement Sequable i.e you can create a ISeq from the collection but the collection itself is not an ISeq.
Now even if these collections implemented ISeq directly I am not sure how that would solve your problem of having general purpose sequence functions that would return the original object, as that would not make sense at all as these general purpose functions are supposed to work on ISeq, they have no idea about which object gave them this ISeq
Example in java:
interface ISeq {
....
}
class A implements ISeq {
}
class B implements ISeq {
}
static class Helpers {
/*
Filter can only work with ISeq, that's what makes it general purpose.
There is no way it could return A or B objects.
*/
public static ISeq filter(ISeq coll, ...) { }
...
}
If I do
user => (next [1 2 3])
I get
(2 3)
It seems that an implicit conversion between vector and list is being operated.
Conceptually, applying next on a vector does not make a lot of sense because a vector is not a sequence. Indeed Clojure does not implement next for a vector. When I apply next on a vector, Clojure kindly suggests that "You wanted to say (next seq), right?".
Isn't it more straight forward to say that a vector does not have next method? What can be reasons why this implicit conversion is more advantageous and/or necessary?
If you look at the docs, next says:
Returns a seq of the items after the first. Calls seq on its argument.
If there are no more items, returns nil.
meaning that this method calls seq on the collection you give it (in your case, its a vector), and it returns a seq containing the rest.
In clojure, lots of things are "colls", such as sequences, vectors, sets and even maps, so for example, this would also work:
(next {:a 1 :b 2}) ; returns ([:b 2])
so the behavior is consistent - transform any collection of items into a seq. This is very common in clojure, map and partition for example do the same thing:
(map inc [1 2 3]) ; returns (2 3 4)
(partition 2 [1 2 3 4]) ; returns ((1 2)(3 4))
this is useful for two main reasons (more are welcome!):
it allows these core functions to operate on any data type you throw at them, as long as it is a "collection"
it allows for lazy computation, eg. even if try to map a large vector but you only asked for the first few items, map wont have to actually pre-compute all items.
Clojure has the concept of a sequence (which just happens to display the same as a list.
next is a function that makes sense on any collection that is a sequence (or can reasonably be coerced into one).
(type '(1 2 3))
=> clojure.lang.PersistentList
(type (rest [1 2 3]))
=>clojure.lang.PersistentVector$ChunkedSeq
There are tradeoffs in the design of any language or library. Allowing the same operation to work on different collection types makes it easier to write many programs. You often don't have to worry about differences between lists and vectors if you don't want to worry about them. If you decide you want to use one sequence type rather than another, you might be able to leave all of the rest of the code as it was. This is all implicit in Shlomi's answer, which also points out an advantage involving laziness.
There are disadvantages to Clojure's strategy, too. Clojure's flexible operations on collections mean that Clojure might not tell you that you have mistakenly used a collection type that you didn't intend. Other languages lack Clojure's flexibility, but might help you catch certain kinds of bugs more quickly. Some statically typed languages, such as Standard ML, for example, take this to an extreme--which is a good thing for certain purposes, but bad for others.
Clojure lets you control performance / abstractions operating a choice between list and vector.
List
is fast on operations at the beginning of the sequence like cons / conj
is fast on iteration with first / rest
Vector
is fast on operations at the end of the sequence like pop / peek
participates in associative abstraction with indexes as keys
is fast on subvec
Both participate in sequence abstraction. Clojure functions and conversions they operate, are made to ease idiomatic code writing.
In clojure lists grow from the left and vectors grow from the right, so:
user> (conj '(1 2 3) 4)
(4 1 2 3)
user> (conj [1 2 3] 4)
[1 2 3 4]
What's the most efficient method of inserting values both into the front and the back of a sequence?
You need a different data structure to support fast inserting at both start and end. See https://github.com/clojure/data.finger-tree
As I understand it, a sequence is just a generic data structure so it depends on the specific implementation you are working with.
For a data structure that supports random access (e.g. a vector), it should take constant time, O(1).
For a list, I would expect inserting at the front of the list with a cons operation to take constant time, but inserting to the back of the list will take O(n) since you have to traverse the entire structure to get to the end.
There is, of course, a lot of other data structures that can theoretically be a sequence (e.g. trees) that will have their own O(n) characteristics.
I was reading in Practical Clojure (Chapter 5) that the rseq function operation executes in constant time. It seems to me that it should be a linear time operation. Can anyone shed some light on this for me?
Try this:
(class [1 2 3 4])
You'll see:
clojure.lang.PersistentVector
Now try this:
(class (rseq [1 2 3 4]))
And the sequence implementation is different:
clojure.lang.APersistentVector$RSeq
As Roman said, it is a changed interface to a sequence. All the elements are where they were you are just accessing them in a reverse order.
You can see RSeq class to see how it's implemented here: https://github.com/clojure/clojure/blob/b578c69d7480f621841ebcafdfa98e33fcb765f6/src/jvm/clojure/lang/APersistentVector.java
I don't know how it's implemented, but I would think it just returns some object that implements sequence interface and knows how to traverse the structure (vector or sorted map) in reverse order. The result sequence is lazy, so it doesn't have to traverse the whole structure immediately.
It returns the new interface in constant time like Goran Jovic said but printing it out is linear. So displaying it in the REPL is linear, but putting it in a def is constant.