I recently found out by doing Hackerrank’s Breadth First Search: Shortest Reach that Java’s Priority Queue does not maintain the heap property if you modify the priority of one of the elements in the queue. The only moment where the heap property is maintained is when the queue is being populated, i.e: when elements are added to the queue.

This is better shown with a small example.

Here’s a simple PriorityQueue used as a min priority queue, of Vertex, which represents a vertex (node) of a Graph and its members are its index and its distance to the source vertex.

The relevant parts of the implementation are:

class Vertex {
    private int distance;
    private int index;
    
    public int getDistance() {
        return distance;
    }

    public void setDistance(int d) {
        distance = d;
    }
.
.
.

import java.util.PriorityQueue;

class Example {
    public static void main(String[] args) {
        PriorityQueue<Vertex> queue = new PriorityQueue<Vertex>(n, new Comparator<Vertex>() {
            @Override
            public int compare(Vertex o1, Vertex o2) {
                if (o1.getDistance() < o2.getDistance()) {
                    return -1;
                } else if (o1.getDistance() > o2.getDistance()) {
                    return 1;
                }
                return 0;
            }
        });
        
        Vertex[] vertices = new Vertex[10];
        
        // initialize the vertices and add them to the queue
        for (int i = 0; i < 10; i++) {
            vertices[i] = new Vertex(i);
            vertices[i].setDistance(i + 1);
            queue.add(v);
        }
    }
    
.
.
.
}

The constructor that takes a Comparator is necessary to establish the priority of the elements and the structure of the heap in the backend. In our case, the priority is given by the distance of the Vertex.

The problem surges in that if we later do:

    v[i].setDistance(0);

The position in the queue will not change, i.e the heap in the backend remains in the same state as it was before the distance for v[i] was changed. The only moment where the priority queue actually runs the comparator is when is when the queue is being acted upon i.e: either when using add or remove methods.

    \\ initial state
    v[i].setDistance(0);
    \\ same state as 'initial state'!

The only way to achieve the expected result is to do this:

    // initial state i.e: v[i] is in position P
    v[i].setDistance(0);
    // same state as initial state i.e: v[i] is in position P
    queue.remove(v[i]);
    queue.add(v[i]);
    // different state i.e: v[i] is in position Q, in a different from the position it was in `initial state`

It’s crazy to think I spent the better part of two hours thinking and looking into the code just to start doubting everything I know and then realize that the issue is in that the implementation doesn’t work as one might expect.

I don’t suppose everyone thinks the same way I do, but it would have been nice if the class contained some method that could reheapify the priority queue or something in that regard.

Oh well, I’ve learned my lesson now, Java Class Library. Never make any assumption about your behaviour