How to implement a queue using two stacks?

Question

Suppose we have two stacks and no other temporary variable.

Is to possible to "construct" a queue data structure using only the two stacks?

Answer 1

here is my solution in java using linkedlist.

class queue<T>{
static class Node<T>{
    private T data;
    private Node<T> next;
    Node(T data){
        this.data = data;
        next = null;
    }
}
Node firstTop;
Node secondTop;

void push(T data){
    Node temp = new Node(data);
    temp.next = firstTop;
    firstTop = temp;
}

void pop(){
    if(firstTop == null){
        return;
    }
    Node temp = firstTop;
    while(temp != null){
        Node temp1 = new Node(temp.data);
        temp1.next = secondTop;
        secondTop = temp1;
        temp = temp.next;
    }
    secondTop = secondTop.next;
    firstTop = null;
    while(secondTop != null){
        Node temp3 = new Node(secondTop.data);
        temp3.next = firstTop;
        firstTop = temp3;
        secondTop = secondTop.next;
    }
}

}

Note : In this case, pop operation is very time consuming. So i won't suggest to create a queue using two stack.

Answer 2

With O(1) dequeue(), which is same as pythonquick's answer:

// time: O(n), space: O(n)
enqueue(x):
    if stack.isEmpty():
        stack.push(x)
        return
    temp = stack.pop()
    enqueue(x)
    stack.push(temp)

// time: O(1)
x dequeue():
    return stack.pop()

With O(1) enqueue() (this is not mentioned in this post so this answer), which also uses backtracking to bubble up and return the bottommost item.

// O(1)
enqueue(x):
    stack.push(x)

// time: O(n), space: O(n)
x dequeue():
    temp = stack.pop()
    if stack.isEmpty():
        x = temp
    else:
        x = dequeue()
        stack.push(temp)
    return x

Obviously, it's a good coding exercise as it inefficient but elegant nevertheless.

Answer 3

Queue implementation using two java.util.Stack objects:

public final class QueueUsingStacks<E> {

        private final Stack<E> iStack = new Stack<>();
        private final Stack<E> oStack = new Stack<>();

        public void enqueue(E e) {
            iStack.push(e);
        }

        public E dequeue() {
            if (oStack.isEmpty()) {
                if (iStack.isEmpty()) {
                    throw new NoSuchElementException("No elements present in Queue");
                }
                while (!iStack.isEmpty()) {
                    oStack.push(iStack.pop());
                }
            }
            return oStack.pop();
        }

        public boolean isEmpty() {
            if (oStack.isEmpty() && iStack.isEmpty()) {
                return true;
            }
            return false;
        }

        public int size() {
            return iStack.size() + oStack.size();
        }

}

Answer 4

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();
    }

}

Answer 5

A solution in c#

 public class Queue<T> where T : class
    {
        private Stack<T> input = new Stack<T>();
        private Stack<T> output = new Stack<T>();
        public void Enqueue(T t)
        {
            input.Push(t);
        }

        public T Dequeue()
        {
            if (output.Count == 0)
            {
                while (input.Count != 0)
                {
                    output.Push(input.Pop());
                }
            }
            return output.Pop();
        }
}

Answer 6

Two stacks in the queue are defined as stack1 and stack2.

Enqueue: The euqueued elements are always pushed into stack1

Dequeue: The top of stack2 can be popped out since it is the first element inserted into queue when stack2 is not empty. When stack2 is empty, we pop all elements from stack1 and push them into stack2 one by one. The first element in a queue is pushed into the bottom of stack1. It can be popped out directly after popping and pushing operations since it is on the top of stack2.

The following is same C++ sample code:

template <typename T> class CQueue
{
public:
    CQueue(void);
    ~CQueue(void);

    void appendTail(const T& node); 
    T deleteHead();                 

private:
    stack<T> stack1;
    stack<T> stack2;
};

template<typename T> void CQueue<T>::appendTail(const T& element) {
    stack1.push(element);
} 

template<typename T> T CQueue<T>::deleteHead() {
    if(stack2.size()<= 0) {
        while(stack1.size()>0) {
            T& data = stack1.top();
            stack1.pop();
            stack2.push(data);
        }
    }


    if(stack2.size() == 0)
        throw new exception("queue is empty");


    T head = stack2.top();
    stack2.pop();


    return head;
}

This solution is borrowed from my blog. More detailed analysis with step-by-step operation simulations is available in my blog webpage.