Introduction to the Lesson

Today, we embark on a journey through the functioning of stacks and their practical applications in solving algorithmic problems. Like a pile of plates in a cafeteria, stacks allow us to add and remove data in a last-in, first-out manner. This lesson revolves around leveraging stacks to tackle two common algorithmic challenges.

Problem 1: Validate Parentheses

Our first challenge involves ensuring that parentheses, braces, and brackets within a string are correctly matched — crucial for verifying syntax in programming languages and mathematical formulas.

Imagine devising a tool within a code editor that flags syntax errors by checking for mismatched brackets — a much-needed feature for developers to catch common errors early in the coding process.

Problem 1: Naive Approach

In a naive approach, one might consider scanning the string and manually checking for matching closing brackets for each opening one. While this might initially seem straightforward, it fails to handle nested structures efficiently, leading to repeat scanning and potential (O(n^2)) performance in the worst-case scenario.

Problem 1: Efficient Approach Explanation

A stack, however, is ideally suited for this task. It acts as a memory model, helping track the last opened bracket and ensuring its closure before moving on to the prior ones.

Problem 1: Solution Building

Our JavaScript implementation lays out the process in a structured, step-by-step manner:

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