Скачать или смотреть LeetCode 232 | Queue Using Stacks Explained | From Brute Force to Amortized O(1)

LeetCode 232 – Implement Queue using Stacks is one of those problems that looks simple… until you realize you’re trying to make a queue behave using only stacks.

In this video, I’ll take you through:

🔹 The Problem Statement

We need to design a queue using only two stacks, supporting these operations:

push(x) → add element to the end
pop() → remove element from the front
peek() → return the front element
empty() → check if the queue is empty

Sounds easy? The catch: stacks only allow LIFO (last-in, first-out), while queues need FIFO (first-in, first-out).

🔹 Brute Force Approach

The first idea is straightforward:

For push(), push into the main stack.
For pop() or peek(), transfer elements back and forth between two stacks until you get to the “front” element.

✅ It works.
❌ But every pop/peek takes O(n) time, which is very inefficient.

It’s like moving an entire bookshelf just to grab the book at the bottom. 📚

🔹 Optimized Approach (Two Stacks, Amortized O(1))

Here’s the clever trick:

We use two stacks:

Input Stack (inStack) → where new elements are pushed.
Output Stack (outStack) → used only when we need to pop/peek.

How it works:

On push(x): just push into inStack. ✅ O(1)

On pop() or peek():
If outStack is empty, transfer all elements from inStack to outStack.
Then pop/peek from outStack.

Why is this efficient?

Each element is moved at most once from inStack → outStack.
So across many operations, the average (amortized) cost of pop/peek becomes O(1).

This means while some operations take O(n), overall performance balances out to O(1) per operation.

🔹 System Design Insight

This problem is a classic example of batching work to reduce cost — something used everywhere in real-world systems:

Databases batch writes for efficiency.
Caches delay updates until needed.
Message queues reorder operations for speed.

By learning this trick, you’re not just solving a coding interview question — you’re training your brain to think like a systems engineer.

✅ By the end of this video, you’ll clearly understand:

Why brute force solutions are slow
How amortized analysis works
How to apply the two-stack trick for queues

And how this thinking applies to real-world software engineering

💡 If you’re preparing for coding interviews, or just want to strengthen your data structures foundation, this is a must-learn problem.

👉 Don’t forget to Like 👍, Subscribe 🔔, and Share this video with your fellow developers — it might be the queue solution they’ve been searching for! 🚀