What is the time complexity of queue operations using stacks?

The amortized time complexity for both enqueue and dequeue is O(1).

How Do You Implement a Queue Using Stacks? | FullStackPrep.Dev

Q: How do you implement a queue using stacks?

A queue can be implemented using two stacks by pushing elements into one and popping them in reverse from another to simulate FIFO behavior.

💡 Concept Name

Queue Using Stacks – A clever approach to mimic queue behavior (FIFO) by utilizing two Last-In-First-Out (LIFO) stacks.

📘 Quick Intro

You can implement a queue by pushing new elements onto one stack and popping elements from the other stack, which reverses the order to provide FIFO behavior.

🧠 Analogy / Short Story

Think of one stack as an inbox holding new messages, and the other as an outbox you flip messages into when ready to read, reversing their order to mimic a queue.

🔧 Technical Explanation

📥 Maintain two stacks: stackIn for enqueue operations and stackOut for dequeue operations.
➕ Enqueue(x): Push element onto stackIn.
➖ Dequeue(): If stackOut is empty, transfer all items from stackIn to stackOut (reversing order), then pop from stackOut.
⏱ Amortized time complexity is O(1) per operation due to efficient transfers.

🎯 Purpose & Use Case

✅ Common interview challenge to test understanding of stacks and queues.
✅ Useful when only stack operations are allowed but queue behavior is needed.
✅ Helps illustrate amortized analysis in algorithm efficiency.

💻 Real Code Example

public class QueueUsingStacks
{
    private Stack<int> stackIn = new();
    private Stack<int> stackOut = new();

    public void Enqueue(int x)
    {
        stackIn.Push(x);
    }

    public int Dequeue()
    {
        if (stackOut.Count == 0)
        {
            while (stackIn.Count > 0)
            {
                stackOut.Push(stackIn.Pop());
            }
        }
        if (stackOut.Count == 0)
            throw new InvalidOperationException("Queue is empty");
        return stackOut.Pop();
    }
}

// Usage example:
var q = new QueueUsingStacks();
q.Enqueue(1);
q.Enqueue(2);
q.Enqueue(3);
Console.WriteLine(q.Dequeue()); // Output: 1

❓ Interview Q&A

Q1: How can a queue be implemented using stacks?
A: By using two stacks where one stack is used for enqueue operations and the other for dequeue operations.

Q2: What is the role of the first stack in queue using stacks?
A: It stores elements during enqueue operations.

Q3: What does the second stack do in this implementation?
A: It holds elements in reverse order for dequeue operations.

Q4: How do you dequeue an element in queue using stacks?
A: By popping from the second stack; if it’s empty, transfer all elements from the first stack to the second.

Q5: What is the time complexity of enqueue operation?
A: O(1).

Q6: What is the amortized time complexity of dequeue operation?
A: O(1) amortized, though worst case can be O(n) when transferring elements.

Q7: Why use two stacks instead of one?
A: To reverse the order of elements to achieve FIFO behavior.

Q8: Can this method handle empty queue situations?
A: Yes, by checking if both stacks are empty before dequeue.

Q9: Is the queue implemented using stacks efficient?
A: It is efficient with amortized O(1) operations.

Q10: Can this approach be used to implement other data structures?
A: Yes, it demonstrates how stacks can simulate queues.

📝 MCQs

Q1. How many stacks are used to implement a queue?

One
Two
Three
Four

Q2. What does the first stack do?

Dequeues elements
Stores elements for enqueue
Reverses elements
Deletes elements

Q3. What does the second stack do?

Stores elements for enqueue
Stores elements for dequeue
Stores duplicates
Sorts elements

Q4. How do you dequeue when the second stack is empty?

Return null
Transfer elements from first to second stack
Throw error
Insert new elements

Q5. What is the time complexity of enqueue?

O(1)
O(n)
O(log n)
O(n log n)

Q6. What is the amortized time complexity of dequeue?

O(1)
O(n)
O(log n)
O(n log n)

Q7. Why use two stacks in this implementation?

To speed up
To reverse order for FIFO
To save memory
To sort elements

Q8. How to check if queue is empty?

Check first stack only
Check second stack only
Check both stacks empty
No check needed

Q9. Is this queue efficient?

No
Yes, amortized O(1)
Depends on data
Rarely

Q10. What does this implementation demonstrate?

Queue simulating stack
Stack simulating queue
List simulating stack
Array simulating queue

💡 Bonus Insight

This method is ideal when enqueue operations dominate. For dequeue-heavy use cases, alternative implementations can be considered.

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How Do You Implement a Queue Using Stacks?