Time complexity of unshift() vs. push() in Javascript

Question

I know what is the difference between unshift() and push() methods in JavaScript, but I\'m wondering what is the difference in time complexity?

Answer 1

push() is faster.

js>function foo() {a=[]; start = new Date; for (var i=0;i<100000;i++) a.unshift(1); return((new Date)-start)}
js>foo()
2190
js>function bar() {a=[]; start = new Date; for (var i=0;i<100000;i++) a.push(1); return((new Date)-start)}
js>bar()
10

function foo() {a=[]; start = new Date; for (var i=0;i<100000;i++) a.unshift(1); return((new Date)-start)}
console.log(foo())

function bar() {a=[]; start = new Date; for (var i=0;i<100000;i++) a.push(1); return((new Date)-start)}
console.log(bar());

---

Update

The above does not take into consideration the order of the arrays. If you want to compare them properly, you must reverse the pushed array. However, push then reverse is still faster by ~10ms for me on chrome with this snippet:

var a=[]; 
var start = new Date; 
for (var i=0;i<100000;i++) {
  a.unshift(1);
}
var end = (new Date)-start;
console.log(`Unshift time: ${end}`);

var a=[];
var start = new Date;
for (var i=0;i<100000;i++) {
  a.push(1);
}

a.reverse();
var end = (new Date)-start;
console.log(`Push and reverse time: ${end}`);

Answer 2

For people curious about the v8 implementation here is the source. Because unshift takes an arbitrary number of arguments, the array will shift itself to accommodate all arguments.

UnshiftImpl ends up calling AddArguments with a start_position of AT_START which kicks it to this else statement

  // If the backing store has enough capacity and we add elements to the
  // start we have to shift the existing objects.
  Isolate* isolate = receiver->GetIsolate();
  Subclass::MoveElements(isolate, receiver, backing_store, add_size, 0,
                         length, 0, 0);

and takes it to the MoveElements.

  static void MoveElements(Isolate* isolate, Handle<JSArray> receiver,
                           Handle<FixedArrayBase> backing_store, int dst_index,
                           int src_index, int len, int hole_start,
                           int hole_end) {
    Heap* heap = isolate->heap();
    Handle<BackingStore> dst_elms = Handle<BackingStore>::cast(backing_store);
    if (len > JSArray::kMaxCopyElements && dst_index == 0 &&
        heap->CanMoveObjectStart(*dst_elms)) {
      // Update all the copies of this backing_store handle.
      *dst_elms.location() =
          BackingStore::cast(heap->LeftTrimFixedArray(*dst_elms, src_index))
              ->ptr();
      receiver->set_elements(*dst_elms);
      // Adjust the hole offset as the array has been shrunk.
      hole_end -= src_index;
      DCHECK_LE(hole_start, backing_store->length());
      DCHECK_LE(hole_end, backing_store->length());
    } else if (len != 0) {
      WriteBarrierMode mode = GetWriteBarrierMode(KindTraits::Kind);
      dst_elms->MoveElements(heap, dst_index, src_index, len, mode);
    }
    if (hole_start != hole_end) {
      dst_elms->FillWithHoles(hole_start, hole_end);
    }
  }

I also want to call out that v8 has a concept of different element kinds depending what the array contains. This also can affect the performance.

It's hard to actually say what the performance is because truthfully it depends on what types of elements are passed, how many holes are in the array, etc. If I dig through this more, maybe I can give a definitive answer but in general I assume since unshift needs to allocate more space in the array, in general you can kinda assume it's O(N) (will scale linerally depending on the number of elements) but someone please correct me if I'm wrong.

Answer 3

The JavaScript language spec does not mandate the time complexity of these functions, as far as I know.

It is certainly possible to implement an array-like data structure (O(1) random access) with O(1) push and unshift operations. The C++ std::deque is an example. A Javascript implementation that used C++ deques to represent Javascript arrays internally would therefore have O(1) push and unshift operations.

But if you need to guarantee such time bounds, you will have to roll your own, like this:

http://code.stephenmorley.org/javascript/queues/

Answer 4

imho it depends on the javascript-engine... if it will use a linked list, unshift should be quite cheap...

Answer 5

One way of implementing Arrays with both fast unshift and push is to simply put your data into the middle of your C-level array. That's how perl does it, IIRC.

Another way to do it is have two separate C-level arrays, so that push appends to one of them, and unshift appends to the other. There's no real benefit to this approach over the previous one, that I know of.

Regardless of how it's implemented, a push or and unshift will take O(1) time when the internal C-level array has enough spare memory, otherwise, when reallocation must be done, at least O(N) time to copy the old data to the new block of memory.