VTU Notes | 18CS32 - DATA STRUCTURES AND APPLICATIONS

Stacks

Module-2

4.9
2018 Scheme | CSE Department

Created by VtuNotes.in
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5 Modules

18CS32 - DATA STRUCTURES AND APPLICATIONS | Module-2 VTU Notes

VTU | 18CS2 | Module - 2

Stacks, Stack Applications, and Recursion in Data Structures

This summary outlines the core concepts of stacks, their operations, applications, and recursion as covered in the "Data Structures and Applications" course.

Stacks: Definition and Operations:

A stack is a linear data structure that follows the Last-In-First-Out (LIFO) principle. Elements are added and removed from the top only. Key stack operations include:

- Push: Adding an element onto the top of the stack.

- Pop: Removing and returning the top element.

- Peek (Top): Viewing the top element without removing it.

- IsEmpty: Checking if the stack is empty.

- IsFull: Checking if the stack is full.

Array Representation of Stacks:

Stacks can be implemented using arrays. Proper tracking of the top element's index is essential for efficient stack operations.

Stacks using Dynamic Arrays:

Dynamic arrays allow the stack to resize when full, ensuring space availability for new elements.

Stack Applications:

- Polish Notation (Prefix): Mathematical expressions without parentheses; operators precede operands.

- Infix to Postfix Conversion: Transforming mathematical expressions to postfix form for easier evaluation.

- Postfix Expression Evaluation: Calculating the result of postfix expressions using stacks.

Recursion:

Recursion is a technique where a function calls itself to solve a smaller instance of a problem. Recursion is applied to various problems:

- Factorial: Computing the factorial of a number using recursion.

- GCD (Greatest Common Divisor): Finding the largest number that divides two given numbers.

- Fibonacci Sequence: Generating Fibonacci numbers using recursive methods.

- Tower of Hanoi: Solving the classic puzzle using recursion.

- Ackermann's Function: A function to explore recursion's theoretical limits.

Conclusion:

Stacks serve as an important tool for managing data in a Last-In-First-Out manner. Understanding their operations, representation, and applications like expression evaluation enhances problem-solving skills. Recursion is a powerful technique for solving problems by breaking them down into smaller instances. Through the study of stacks and recursion, students develop a solid foundation in fundamental data structures and algorithmic techniques, setting the stage for more advanced topics in the field.

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