Priority queue ordering of elements

Question

How come the elements of priority queue are ordered according to natural order by default as it doesn't implement comparable interface.

From the docs, it says elements are ordered based on natural ordering but I can't find anywhere it talks about equals method nor comparable. Hows it happening internally?

All Implemented Interfaces: Serializable, Iterable, Collection, Queue.

If it implements comparable then why doesn't it say in the above line

Example:

    public static void main(String[] args) {
        PriorityQueue<String> pq = new PriorityQueue<String>();
        pq.add("2");
        pq.add("4");
        System.out.println(pq); //prints [2, 4]
        pq.offer("1");
        System.out.println(pq); // prints [1, 4, 2]
        pq.add("3");
        System.out.println(pq); // prints [1, 3, 2, 4]
    }
}

Also third print statement prints [1, 3, 2, 4] instead of prints [1, 2, 3, 4]. Why? It should be natural ordering right?

Answer 1

Actually internal data structure of PriorityQueue is not ordered, it is a heap.

PriorityQueue doesn't need to be ordered, instead, it focuses on head of data. Insertion is in O(log n) time. Sorting wastes time and useless for a queue.

Moreover, either the element is-a Comparable, or a Comparator is provided. Unfortunately, non-comparable checking is at runtime, rather than compile time. Once second element is added, ClassCastException occurs.

PLUS: My answer to why [1, 3, 2, 4] instead of prints [1, 2, 3, 4]?

As I mentioned before, it's not ordered, instead it focuses on head q[0] is minimum, that's it. You could see the [1, 3, 2, 4] as a tree which is NOT linear:

1
| \
3  2
|
4

Answer 2

You are seeing that order because:

1. Internally System.out.println() will be invoking the toString() method which in turn uses the iterator to iterate through the elements of the queue. But the iterator does not guarantee any specific order to traverse the elements. Refer this

http://docs.oracle.com/javase/6/docs/api/java/util/PriorityQueue.html

2. Priority queue is based on priority heap. When an element is inserted without any comparator then priority queue uses siftUpComparable() method internally. siftUpComparable() compares the current element with the element at it's parent position in the heap. If the order is not correct then current element and parent element are swapped. This is done until the current element and parent element are in correct order. Ordering is based on natural order of the element.

3. Since priority queue is based on priority heap its main focus will be on element in front of the queue. So the elements are ordered when an element is dequeued from the queue using poll(). This is done to increase the performance of Priority queue. Priority queue only orders the elements when it requires.
If you want to see the order as [1, 2, 3, 4] then use this

while(pq.size() != 0) { 
    System.out.println(pq.poll());
}