Implementing stacks and understanding their LIFO (Last-In, First-Out) behavior.
A stack is an abstract data type that serves as a collection of elements, with two principal operations: `push`, which adds an element to the collection, and `pop`, which removes the most recently added element that was not yet removed. This behavior is known as Last-In, First-Out (LIFO). A third important operation is `peek` or `top`, which allows you to view the top element without removing it. A stack can be implemented easily using either an array/vector or a linked list. When using an array, we can simply maintain a `top` index. Pushing an element involves placing it at the `top` index and incrementing `top`. Popping involves decrementing `top`. We must handle overflow (pushing to a full stack) and underflow (popping from an empty stack) conditions. An implementation using a linked list avoids the fixed-size limitation of an array. Here, `push` corresponds to adding a new node at the head of the list, and `pop` corresponds to removing the head node. Both operations are O(1). Stacks are fundamental in computer science, famously used for managing the call stack for function execution, undo mechanisms in text editors, and for parsing and evaluating mathematical expressions.