• ArrayList vs LinkedList
  • What are LinkedLists even for?
  • Built-in optimizations

ArrayList vs LinkedList

This module shows some short experiments to show various changes and how List selection effects performance. Nothing here will be really new, so you can proceed to the next module and consider this reading optional. However, I feel it’s worth pointing out a few examples of additional changes and how they could affect performance.

Building from the example in the last module, lets consider the performance impact if we consider a LinkedList for PointListPath. I will note that, in general, LinkedLists are bad. To show off just how bad LinkedList can be, I wanted to illustrate by making one change to the constructor in PointListPath

    public PointListPath(int initialCapacity) {
        points = new LinkedList<>();
    }

Let’s compare the runtimes of the old PointListPath with an ArrayList vs. the new one with a LinkedList. Note that by its nature, LinkedList cannot “pre-allocate” space. So yes, it’s not a completely fair comparison to not use the “capacity” argument, but that is a limitation of the LinkedList. It’s also bad style that the constructor’s initialCapacity argument is ignored, but fixing it would involve changing the interface, which would change other code, and I wanted to keep this benchmark simple.

Looking only at the distance with PointListPath

All the N/As are because, after running for 30 minutes on 1 million inputs, I stopped the process and never bothered trying larger sizes. Why is LinkedList so bad? Well, the main reason is that my code simply not implemented to iterate through a LinkedList correctly.

    public double totalDistance() {
        double totalDistance = 0.0;
        //Iterate through all but the last point, getting distance to next point
        for (int i = 0; i < size()-1; i++) {
            Point firstPoint = points.get(i);
            Point secondPoint = points.get(i + 1);
            totalDistance += firstPoint.distanceTo(secondPoint);
        }
        return totalDistance;
    }

The problem is the two calls to get. This is fine for an ArrayList, as get is a constant-time operation. But in a LinkedList, get is linear. That is, the number of steps you need to take is proportional to the index. The problem is that I’m doing this in a loop that executes once for each element of the list (well, technially size() - 1, but you get the idea). This means that for a LinkedList my code isn’t O(n), it’s O(n^2)! This means using a LinkedList in this way is actually wrong, and will have a serious enough impact on performance that it simply cannot be ignored.

In general, if you have a LinkedList that you need to iterate through, you should always use an Iterator, so that getting each next node in the list is a constant time operation. However, adjusting my code to account for this makes it more complicated

    public double totalDistance() {
        double totalDistance = 0.0;
        Iterator<Point> iterator = points.listIterator();
        Point currentPoint = iterator.next();
        while (iterator.hasNext()) {
            Point nextPoint = iterator.next();
            double distance = currentPoint.distanceTo(nextPoint);
            totalDistance += distance;
            currentPoint = nextPoint;
        }
        return totalDistance;
    }

I’m not saying this code is too complex, but it’s one of those instances where an iterator can feel awkward to use, since I need both the Point I’m currently visiting and the next Point. I need to use next() both to get the nextPoint for a distance calculation and to update my currentPoint variable, which forces me to do some manual reference manipulation. It’s not bad, but it makes the code more difficult to understand. But, if I insisted on using a LinkedList (I wouldn’t as we’ll see it a bit), this is more or less how I have to use it in order to not end up with O(n^2) running time.

For the note, the iterator approach also would work with ArrayList, but since using get is constant time with ArrayList, I would simply stick with my previous code. In theory, this could give a very very very slightly worse performance, since we are introducing another object. In practice, ArrayList if there was a difference in performance, I couldn’t demonstrate it. I got effectively the same runtimes using either get or iterator with ArrayList, and didn’t see a consistent difference even at 100 million input size.

So, let’s see how this change helps, again only looking at distance

* - the 1ms at 10 input size is an aberration, and I am assuming either my computer hitched on some other process or I just happened to reach the “start time” point just before a millisecond ticked over. I only include to let you know that benchmarking can produce misleading results with small input sizes.

It’s still way slower than an ArrayList, and I still was unable to run my 100 Million input benchmark. This is because, as I mentioned earlier, references are slower than data. Each node of the LinkedList is not a point. It’s a Node object which has separate references to the Point and the next Node. This means instead of our old approach, where we had to travel 2 references (from PointListPath -> ArrayList -> Point), we now have to travel 3 references. PointListPath -> Iterator -> Node -> Point).

Even worse, while Java could leverage the cache with the ArrayList as an automatic optimization, it cannot do so with the LinkedList because the data is not sequential. In fact, a Node may reference a Point that is stored nowhere near it in memory, and the reference to the next Node may also be nowhere nearby. In short, you can’t expect Java to do any cache optimization and it shows.

The reason LinkedList failed at 100 Million inputs is that a LinkedList also comes up with a significant memory overhead, because in addition to storing Points, we now have to also store Nodes, which contain two references. So, we are creating twice as many objects, they are non-sequential, and we can’t leverage the cache.

What are LinkedLists even for?

The key takeaway is that just because two operations are linear time, or O(n), doesn’t mean they are equally fast. It just means they grow at the same rate. Because of their construction, any O(n) operation on a LinkedList will be slower than an ArrayList.

In fact, the only time LinkedLists are even theoretically better than ArrayLists is adding/removing from the front of the structure (which we need to do when implementing a Queue). That’s because adding at the front of a LinkedList is constant time , or O(1), while for an ArrayList it’s linear time, or O(n), because you have to shift all the values right to make room.

So, I ran a benchmark to compare calling add(0, value) (add to the front) and remove(0) remove from the front on both a LinkedList and an ArrayList with different sized inputs. Here are those results:

In the table above, “LL” means LinkedList and “AL” means ArrayList, “add” refers to the .add(0, value) operation, “rem” to the .remove(0) operation, and tot to the total time for both operations combined. So, for example at size = 100, for the both lists, I call use add 100 times, then remove(100) times. So I’m looking at both operations separately and combined. To be clear, this is only for adding/removing at the front.

Ignoring the 153-second elephant in the room for a second, it’s worth noticing that adding on a LinkedList is slower than removing, despite bother operations seemingly working with the same number of references. The reason for the difference is memory allocation. Allocating memory takes significant more time than dereferencing memory. Be aware, however, that this time does not account for Java’s garbage collection to actually free the memory.

And, yeah, this is the one case where ArrayList is waaaaay worse, and it’s because adding/removing n elements at the front of an ArrayList becomes an O(n^2) problem, whereas it’s simply O(n) for the Linked List. However, you’ll notice that I don’t get a spike until 100 thousand, and while slower, it’s still really quick at 10 thousand. I think the reason for the spike is two-fold: 1) It’s quadratic, and quadratic grows more rapidly
2) At 10000 and below, while we still have to shift values, the ArrayList is small enough that we can do everything in the cache, and Java has a lot of optimizations built for this. Once we exceed the cache limit, those optimizations can no longer be used.

That said, this is the only time when LinkedList is better. Anytime you expect to need random access (i.e., using get) or adding anywhere but the front, ArrayList are going to be as good or better.

For example, when add-ing or remove-ing from the end of the List, ArrayLists are proportionally much better, though the concrete difference is small. The following graph shows adding then removing only from the end of the list.

Here, we can see that both operations are very fast, but ArrayList is definitely faster. So in general, unless you absolutely know you want a LinkedList, default to an ArrayList for List implementations in Java. But, you should know when a LinkedList is better.

Built-in optimizations

A common need in lists is sorting, which can be done with the List.sort() method to use natural order, or the Collections.sort() method to define your own sorting Comparator. In general, Java uses a variant of a merge sort for List objects. But with a merge sort, we definitely need random-access, which sounds like bad news for a LinkedList. That means LinkedList sort times must be horrible, right? Well, let’s test:

Wait, how is LinkedList not slow if sorting using random access?

Well, because you never actually sort a LinkedList. The way Java Collections sort is by first dumping the contents of the List into an array, and then sorting the array. After the array is sorted, it simply sets the value of each element into the List to the value that matches its index in the sorted array (using an iterator to ensure a linear-time copy). You can think of this as the LinkedList being turned into an array, sorted, then turned back into a LinkedList. This means the actual sorting step for both LinkedList and ArrayList is identical, so the only difference is the time to iterate through the List twice (once to copy to the array, once to copy the array to the List). Because iterating through a LinkedList is slower, that accounts for the time difference. But both are still O(n * log(n)).