Implement Stack using Queue(s) Problem

Leetcode Lesson: Implement Stack using Queues

1. Problem Statement

Implement a last-in-first-out (LIFO) stack using only two queues. The implemented stack should support all the functions of a normal stack (push, pop, top, empty).

Implement the MyStack class:

  • push(x) Pushes element x to the top of the stack.
  • pop() Removes the element on the top of the stack and returns it.
  • top() Returns the element on the top of the stack.
  • empty() Returns true if the stack is empty, false otherwise.

Notes:

  • You must use only standard queue operations, which means only push to back, peek/pop from front, size, and is empty are valid.
  • Depending on your language, the queue may not be supported natively. You may simulate a queue using a list or deque (double-ended queue), as long as you use only a queue's standard operations.

2. Conceptual Understanding

This problem challenges us to implement a stack (LIFO - Last In, First Out) data structure using only queue (FIFO - First In, First Out) operations. It's like trying to create a stack of plates (where you add and remove from the top) using only queues (where you add to the back and remove from the front).

The key is to find a way to reverse the order of elements when needed, as stacks and queues have opposite ordering principles.

3. Approach Brainstorming

We can consider two main approaches:

  1. Make push operation costly: Keep the elements in the correct stack order, but make pushing a new element expensive.
  2. Make pop operation costly: Allow pushing to be simple, but make popping an element more complex.

We'll focus on making the push operation costly, as it provides a more straightforward implementation for the other operations.

4. Optimal Solution Walkthrough

Here's how we can implement the stack using two queues:

  1. Use two queues: q1 and q2.
  2. For push operation:
    • Add the new element to q2.
    • Move all elements from q1 to q2.
    • Swap q1 and q2.
  3. For pop, top, and empty operations:
    • Perform these operations directly on q1.

This approach ensures that q1 always has the elements in the correct stack order (newest on top).

5. Python Implementation

from queue import Queue

class MyStack:
    def __init__(self):
        self.q1 = Queue()
        self.q2 = Queue()

    def push(self, x: int) -> None:
        self.q2.put(x)
        while not self.q1.empty():
            self.q2.put(self.q1.get())
        self.q1, self.q2 = self.q2, self.q1

    def pop(self) -> int:
        return self.q1.get()

    def top(self) -> int:
        return self.q1.queue[0]

    def empty(self) -> bool:
        return self.q1.empty()
  • We use Python's Queue class for our queues.
  • push adds the new element to q2, moves all elements from q1 to q2, then swaps q1 and q2.
  • pop and top operate directly on q1.
  • empty checks if q1 is empty.

6. Time and Space Complexity Analysis

Time Complexity:

  • push: O(n), where n is the number of elements in the stack
  • pop: O(1)
  • top: O(1)
  • empty: O(1)

Space Complexity: O(n), where n is the number of elements in the stack

The push operation is costly in terms of time, but this allows other operations to be very efficient.

7. Edge Cases and Testing

Consider these test cases:

  • Push multiple elements, then pop all
  • Push, pop, push again
  • Check top after multiple pushes
  • Check empty on a new stack and after operations
  • Push, pop, check empty, push again

8. Common Pitfalls and Mistakes

  • Forgetting to swap queues after push operation
  • Implementing pop or top incorrectly when the stack is empty
  • Using list methods instead of queue methods

9. Optimization Opportunities

  • We could use a single queue instead of two, rotating the queue after each push operation.
  • If many consecutive push operations are expected, we could optimize by delaying the reordering until a pop or top operation is called.
  • "Implement Queue using Stacks" (reverse problem)
  • Understanding of stack and queue data structures
  • Adapter design pattern (adapting one interface to another)

11. Reflection Questions

  1. How would the implementation change if we made the pop operation costly instead of push?
  2. Can you think of a real-world scenario where you might need to implement a stack interface using queue-like operations?
  3. How does this implementation compare to a native stack implementation in terms of efficiency?

12. Additional Resources