A stack is a simple data structure that follows the Last-In, First-Out (LIFO) principle. It’s akin to a stack of books, where the most recent addition is at the top and easily accessible.

Core Characteristics

• Data Representation: Stacks can hold homogeneous or heterogeneous data.
• Access Restrictions: Restricted access primarily to the top of the stack, making it more efficient for certain algorithms.

Stack Operations

1. Push: Adds an element to the top of the stack.
2. Pop: Removes and returns the top element.
3. Peek: Returns the top element without removing it.
4. isEmpty: Checks if the stack is empty.
5. isFull (for array-based stacks): Checks if the stack is full.

All the above operations typically have a time complexity of $O(1)$, making stack operations highly efficient.

Visual Representation

Practical Applications

1. Function Calls: The call stack keeps track of program flow and memory allocation during method invocations.

2. Text Editors: The undo/redo functionality often uses a stack.

3. Web Browsers: The Back button’s behavior can be implemented with a stack.

4. Parsing: Stacks can be used in language processing for functions like balanced parentheses, and binary expression evaluation.

5. Memory Management: Stacks play a role in managing dynamic memory in computer systems.

6. Infix to Postfix Conversion: It’s a crucial step for evaluating mathematical expressions such as 2 + 3 * 5 - 4 in the correct precedence order. Stack-based conversion simplifies parsing and involves operators such as push and pop until the correct order is achieved.

7. Graph Algorithms: Graph traversal algorithms such as Depth First Search (DFS) deploy stacks as a key mechanism to remember vertices and explore connected components.

Code Example: Basic Stack

Here is the Python code:

class Stack:
    def __init__(self):
        self.stack = []

    def push(self, item):
        self.stack.append(item)

    def pop(self):
        if not self.is_empty():
            return self.stack.pop()

    def peek(self):
        if not self.is_empty():
            return self.stack[-1]

    def is_empty(self):
        return len(self.stack) == 0

    def size(self):
        return len(self.stack)