The stack data structure is a fundamental concept in computer science and plays a crucial role in many algorithms and programming languages. It is a last-in, first-out (LIFO) data structure, meaning that the most recently added element is the first one to be removed. In this article, we will explore the working of the stack data structure and its various operations.

## Stack Operations

A stack supports two main operations:

**Push:**This operation adds an element to the top of the stack.**Pop:**This operation removes and returns the topmost element from the stack.

Additionally, we have two more operations that allow us to access information about the stack without modifying it:

**Peek (or Top):**This operation returns the topmost element without removing it.**isEmpty:**This operation checks whether the stack is empty or not.

## The Stack’s Internal Structure

A stack can be implemented using arrays or linked lists. Let’s consider an array-based implementation for simplicity.

We maintain a variable called ‘top’ that keeps track of the index of the topmost element in the array. Initially, when the stack is empty, ‘top’ is set to -1.

As elements are pushed onto the stack, ‘top’ gets incremented by 1. Similarly, as elements are popped from the stack, ‘top’ gets decremented by 1.

This way, we can always access and modify the topmost element in constant time O(1).

## The Working of Push Operation

The push operation involves adding an element to the top of the stack. Here are the steps involved:

__Check for Overflow:__If the stack is full (i.e., ‘top’ is equal to the maximum capacity of the array minus 1), then we cannot add any more elements, and an overflow condition occurs.__Increment ‘top’:__If there is no overflow, we increment the value of ‘top’ by 1.__Add Element:__We then add the new element at the index specified by ‘top’ in the array.

## The Working of Pop Operation

The pop operation involves removing and returning the topmost element from the stack. Here are the steps involved:

__Check for Underflow:__If the stack is empty (i., ‘top’ is equal to -1), then there are no elements to remove, and an underflow condition occurs.__Retrieve Element:__If there is no underflow, we retrieve the element at the index specified by ‘top’ in the array.__Decrement ‘top’:__After retrieving the element, we decrement the value of ‘top’ by 1.

## An Example Scenario

To better understand how a stack works, let’s walk through an example scenario using a stack with a capacity of 5. Initially, our stack is empty (represented by -1).

- We push elements A, B, C onto the stack. The stack now contains A at index 0 (top), B at index 1, C at index 2 (bottom).
- We perform a pop operation, which removes and returns element C. The stack now contains A at index 0 (top), B at index 1.
- We push element D onto the stack. The stack now contains A at index 0 (top), B at index 1, D at index 2 (bottom).

## Conclusion

The stack data structure follows the LIFO principle and is widely used in various applications ranging from expression evaluation to backtracking algorithms. Understanding its working and operations is crucial for any programmer or computer science enthusiast. With proper usage of push, pop, peek, and isEmpty operations, you can effectively utilize the power of stacks in your programs.