How to implement a queue using two stacks?

Keep 2 stacks, let’s call them inbox and outbox.

Enqueue:

• Push the new element onto inbox

Dequeue:

• If outbox is empty, refill it by popping each element from inbox and pushing it onto outbox

• Pop and return the top element from outbox

Using this method, each element will be in each stack exactly once – meaning each element will be pushed twice and popped twice, giving amortized constant time operations.

Here’s an implementation in Java:

public class Queue<E>
{

    private Stack<E> inbox = new Stack<E>();
    private Stack<E> outbox = new Stack<E>();

    public void queue(E item) {
        inbox.push(item);
    }

    public E dequeue() {
        if (outbox.isEmpty()) {
            while (!inbox.isEmpty()) {
               outbox.push(inbox.pop());
            }
        }
        return outbox.pop();
    }

}