I recently ran into an interesting problem to solve for my side project: how can I efficiently select the top k elements from a very large list in Java / Groovy? There are many recommendations about how to do that, but I didn’t find a comparison of the suggested implementations. This is a crucial problem for my application so I tried out a number of them and here are the results. I chose Groovy for it’s syntactical sugar with collections and closures, but you can do the same in plain Java. The code is on github, you can run it with a simple mvn compile groovy:execute if you want to play around yourself.

Task: select the top 5 elements from a list of 10 million

Plain sort: 6,500ms

Sorting the whole list and picking the top elements is okay for small lists, but it doesn’t scale for larger lists as the time for sorting a list grows with O(nlogn). For a list with 10 million numbers, it’s completely out of the competition.

    topElements = unorderedList.sort()[numberCount-1..numberCount-k]

(QuickSelect: 2,500ms)

Also called Hoares Selection Algorithm, was mentioned in a few articles, so wanted to give it a try. However I only found implementations for educational purposes like this one. It’s probably not fair to compare this demo implementation with the highly optimized other ones that follow, so I put the result in brackets as I don’t want to discredit the algorithm. [source too long to quote here, see article on brilliantsheep.com]

(Heap Select: 2,200ms)

Again, this is just a demonstration on how to implement a heap select based on Steve Hanov’s great article. I’ve ported his Python implementation to Groovy, which was easy enough. I’m sure there is a more efficient way to do a Heap Select - the old rule holds true: don’t try and implement it yourself if someone else brighter has done it already for you. Anyway, this was my naive attempt:

    def heapSelect(List list, k) {
        def heap = new PriorityQueue(k)
        list.each{ item ->
            if (heap.size() < k || item > heap.peek()) {
                if (heap.size() == k)
        return heap as List

PriorityQueue: 300ms

Ships with the JRE, so there’s no need for external libraries. It let’s you add a list of elements to a priority heap and then poll the top element from the heap one by one. Simple and fast!

    heap = new PriorityQueue(unorderedList.size())
    topElements = (1..k).collect{heap.poll()}

Guava Ordering: 170ms

Google Guava (formerly Google Collections) comes with an Ordering class that works even faster than the PriorityQueue for our task. Under the hood it seems to use QuickSort to sort only parts of a collection, however I haven’t dug too deep in their implementation. An obstacle on using this could be that your data has to be in a structure that implements Iterable, e.g. an ArrayList. If you have a plain int[] and need to convert it first, you might be better off to go for a PriorityQueue in the first place. On the other hand, maybe an ArrayIterator can do this very efficiently.. haven’t tried it out though.

    .greatestOf(arrayList, k)

By the way...

I often saw the suggestion to add the elements into a TreeMap which orders them for you. While this works fine it will never be the most efficient solution because it sorts all data in the map, whereas we’re only interested in the highest k items.

Please bear in mind that I put all this together at home on my own, so if you find any mistakes please leave a comment or drop me a mail and I’m happy to update this entry - and give you all the credit, of course ;) Again: the code is on github - all it takes is mvn compile groovy:execute to run it on your machine.

Comment from Sebastiano Vigna on 23/05/2015

Just as a reference, on my hardware extracting 5 top elements out of 10M distinct integer objects…

  • Takes 586ms using a Java PriorityQueue and addAll.
  • Takes 400ms using a Java PriorityQueue, but creating it using the constructor based on a collection. Making a vector into a heap is O(n), whereas adding n elements is O(n log n), so by using addAll() you’re wasting a log n factor. The constructor based on collections is there for that purpose. The time is then O(n + k log n), similarly to Guavas’s solution.
  • Takes 360ms using fastutil’s ObjectHeapPriorityQueue, which is a better implementation of a heap than java.util’s (using the constructor based on collections).
  • Takes 200ms using Guava.
  • Takes 71ms using fastutil’s IntHeapPriorityQueue, which doesn’t use objects.

In general, I think that primitive collections are unbeatable. But in any case you can gain a lot by using the O(n) heap construction. I guess that Guava’s strategy implemented with primitive types would be faster than anything else. I hope this is useful information!

Ciao, seba

PS: If instead of 10M distinct integers I use random integers from a smaller range times decrease considerably, which I think is the reason for the difference in timings with your results.