Stack Data Structure Overview

Stack Data Structure

• A stack is a linear data structure that follows a specific order, Last-In, First-Out (LIFO).
• Elements are added (pushed) and removed (popped) from the same end, the top.
• The last element added is the first one removed.
• Addition and deletion of elements occur at the same end.

Stack Operations

• push(): Adds an element to the top of the stack. Overflow occurs if the stack is full.
• pop(): Removes the top element from the stack. Underflow occurs if the stack is empty.
• top() / peek(): Returns the top element of the stack without removing it. Returns an error message if the stack is empty.
• isEmpty(): Returns true if the stack is empty, false otherwise.
• isFull(): Returns true if the stack is full, false otherwise (typically for fixed-size stacks).

Stack Types

• Fixed-size stack: Has a predefined maximum capacity. Overflow errors occur when adding to a full stack, underflow errors occur when removing from an empty stack.
• Dynamic-size stack: Automatically adjusts its size as needed, typically using a linked list. Overflow errors are less common (but might still occur depending on the linked list implementation).

Stack Advantages

• Simplicity: Easy to understand and implement.
• Efficiency: Push and pop operations are typically constant-time (O(1)).
• LIFO: Useful in scenarios where the last item processed needs to be handled first (e.g., function calls, expression evaluation).
• Memory Efficiency: Stacks only store the elements currently present, potentially saving memory compared to other data structures.

Stack Disadvantages

• Limited Access: Elements in the middle of the stack are not readily accessible without popping elements first.
• Overflow Potential: Fixed-size stacks can lead to overflow errors if there are more items than their capacity. More complex implementations still have the potential for this error if memory allocation fails.
• Not Suitable for Random Access: Data access is sequential using push and pop, so random accessing is difficult.
• Limited Capacity: Fixed-size stacks may have limitations if the amount of data is unpredictable.

Stack Applications

• Infix to Postfix/Prefix Conversion: Used for evaluating mathematical expressions in a way that respects operator precedence.
• Redo/Undo Features: In software applications like text editors and image editors, a stack can handle redo and undo operations.
• Forward/Backward Navigation: In web browsers, a stack can maintain a history of visited web pages for forward or backward navigation.
• Memory Management: Modern computer systems use stacks for managing memory allocations for running programs. Each program has its own stack.
• Function Calls: In programming languages, function calls use stacks to track which one was called most recently, ensuring its return when finished.

Infix to Postfix (Conversion)

• Algorithm (high-level): The process of converting an infix expression to postfix involves moving operands directly into the output and using a stack (often a temporary storage) for operators. Operators of higher precedence need to be popped from the stack and processed in the output before operators of lower precedence. Operators associated with the opening and closing parenthesis need special care.
• Example: Infix: 8 / 2 + 7 - 4 * 2. Postfix: 8 2 / 7 + 4 2 * -

This quiz covers the fundamentals of stack data structures, including key operations like push, pop, and peek. It explains the Last-In, First-Out (LIFO) principle and discusses types of stacks, such as fixed-size stacks. Test your knowledge of how stacks operate and their various functionalities.