Priority queue ADT

A priority queue is like a queue in that you can enqueue and dequeue elements. However, the element that gets dequeued is the one with the minimum value of a feature, called its priority. We will use a comparator to compare elements and learn which one has the lowest priority. We will use the following interface for the priority queue:

public interface PriorityQueue<E> {
    E checkMinimum();
    E dequeueMinimum();
    void enqueue(E value);
}

We require the following set of behaviors from the methods:

• checkMinimum: This method must return the next value to be dequeued without dequeuing it. If the queue is empty, it must return null.

• dequeueMinimum: This must dequeue the element with the minimum priority and return it. It should return null when the queue is empty.

• enqueue: This should insert a new element in the priority queue.

We would also like to do these operations as efficiently as possible. We will see two different ways to implement it.