Stack Overview

A Stack is a linear data structure that follows the LIFO (Last-In, First-Out) principle. Imagine a stack of plates: you can only add a new plate to the top (Push) and can only remove the top plate (Pop). The last element added is the first one to be removed.

Consider the problem of checking if a string of brackets is valid: {[()]}.

To solve this, you need to remember the most recent opening bracket to match it with the correct closing one. A Stack is perfect for this "remembering the most recent" state.

Without a stack, you might try to count open and close brackets. However, ([)] has balanced counts but is invalid. You need to track the order. Repeatedly finding and deleting matching pairs () in the string is an O(N²) operation due to string manipulation.

If you just count, you lose the nested structure information. You need a way to say "Wait, I'm currently inside a {, so I expect a } next, unless I start a new ( group."

By using a stack, we can process elements one by one. If we see a 'start' signal (like (), we push it. If we see an 'end' signal (like )), we pop the top of the stack and check if it matches. This resolves dependencies locally in O(N).