How to Implement stack using priority queue?

Pseudocode:

// stack of Key
class Stack {
    class Element { int prio, Key elem; };
    MaxPriorityQueue<Element> q;
    int top_priority = 0;

    void push(Key x) { q.push(Element(top_priority++, x)); }
    Key pop() { top_priority--; return q.pop().elem; }
};

LIFO behavior follows from the fact that every new element is pushed with a priority higher than all the current elements, so it will be popped before any of them.

There are two ways to respond to this interview question. One is to explain in detail the structure above. The second is to briefly mention it, mumble something about O(lg n) and say you'd never implement a stack this way.

If you don't know what a priority queue is, ask. If you don't know what a stack is, ask. If you don't understand the question, ask. By now you should hopefully be able to work out that an adaptor like the following is required.

Stack :
    private:
      q : MaxPriorityQueue
      counter : 0

    public:
      push(x) : q.add(x, counter++)
      pop() : q.remove()

Here is the java implementation for this question.

public class StackPriorityQueue {

PriorityQueue<StackElement> queue = new PriorityQueue<>(10, new Comparator<StackElement>() {
    @Override
    public int compare(StackElement o1, StackElement o2) {
        return o2.key - o1.key;
    }
});

int order = 1;

public void push(int val){
    StackElement element = new StackElement(order++,val);
    queue.add(element);
}

public Integer pop(){
    if(queue.isEmpty()){
        System.out.println("Stack Underflow");
        return null;
    }
    return queue.poll().value;
}

public static void main(String... args){
    StackPriorityQueue q = new StackPriorityQueue();
    q.push(5);
    q.push(10);
    q.push(1);
    q.push(3);
    q.push(50);
    q.push(500);
    q.push(60);
    q.push(30);
    q.push(40);
    q.push(23);
    q.push(34);

    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());
    System.out.println(q.pop());

   }

}

class StackElement {
  int key;
  int value;

  public StackElement(int key, int value) {
    this.key = key;
    this.value = value;
  }

}