Stack Data Structure Quiz

What does LIFO stand for in relation to stacks and how does it affect the operations?

Provide an example of a real-world object that illustrates the concept of a stack.

Explain the purpose of the Size() operation in a stack.

What does the IsEmpty() operation return when the stack contains elements?

In the context of parenthesis counting, how is a left parenthesis handled during the expression scan?

What happens if a right parenthesis is encountered and the stack is empty?

What does a valid arithmetic expression with parentheses require regarding the Parenthesis Count at the end?

How can you determine if an arithmetic expression with parentheses is invalid during the evaluation process?

Describe the stack actions taken when scanning the expression '(()' from left to right.

Why is it important to implement a stack for solving the parenthesis count problem?

Stack Data Structure

A stack is an ordered collection of items where items are inserted and removed from one end only, called the top.
It follows the LIFO (Last-In, First-Out) principle.
Common examples include stacks of trays, books, or plates.

Stack Operations

Push: Adds a new item to the top of the stack.
Pop: Removes and returns the item from the top of the stack.
Size: Returns the number of items in the stack.
IsEmpty: Returns True if the stack is empty, False otherwise.

Stack Applications

Parentheses Balancing: Counting parentheses in an arithmetic expression.
- Each opening parenthesis (() pushes onto the stack.
- Each closing parenthesis ()) pops from the stack.
- A valid expression has a final empty stack.

Valid Arithmetic Expressions

Parentheses count must be non-negative at any point in the expression.
Parentheses count must be zero at the end of the expression.

Stack Implementation for Parentheses Count

Scan the expression from left to right.
Open parentheses (() push onto the stack.
Closing parentheses ()) pop from the stack.
If the stack is empty at the end, the expression is valid.
If the stack is not empty, or an error occurs (pop from empty stack), the expression is invalid.

Algorithm

Create an empty stack.
Scan the expression from left to right:
- If a ( is encountered, push it onto the stack.
- If a ) is encountered, pop from the stack.
- If popping from an empty stack results in an error, then the parentheses aren't balanced.
If the stack is empty after processing the entire expression, it's valid; otherwise, it's invalid.

Different Forms of Arithmetic Expressions

Infix: Operator between operands (e.g., a + b).
Prefix: Operator precedes operands (e.g., + a b).
Postfix: Operator follows operands (e.g., a b +).

Test your knowledge of stack data structures, including their operations and applications. Learn about the LIFO principle and how stacks are utilized in validating arithmetic expressions. This quiz will cover essential concepts such as push, pop, and maintaining balance with parentheses.