#### Overview of this book

Building your own applications is exciting but challenging, especially when tackling complex problems tied to advanced data structures and algorithms. This endeavor demands profound knowledge of the programming language as well as data structures and algorithms – precisely what this book offers to C# developers. Starting with an introduction to algorithms, this book gradually immerses you in the world of arrays, lists, stacks, queues, dictionaries, and sets. Real-world examples, enriched with code snippets and illustrations, provide a practical understanding of these concepts. You’ll also learn how to sort arrays using various algorithms, setting a solid foundation for your programming expertise. As you progress through the book, you’ll venture into more complex data structures – trees and graphs – and discover algorithms for tasks such as determining the shortest path in a graph before advancing to see various algorithms in action, such as solving Sudoku. By the end of the book, you’ll have learned how to use the C# language to build algorithmic components that are not only easy to understand and debug but also seamlessly applicable in various applications, spanning web and mobile platforms.
Chapter 1: Data Types
Free Chapter
Chapter 2: Introduction to Algorithms
Chapter 3: Arrays and Sorting
Chapter 4: Variants of Lists
Chapter 5: Stacks and Queues
Chapter 6: Dictionaries and Sets
Chapter 7: Variants of Trees
Chapter 8: Exploring Graphs
Chapter 9: See in Action
Chapter 10: Conclusion
Index
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# Hash sets

In many algorithms, it is necessary to perform operations on sets with various data. However, what is a set? A set is a collection of distinct objects without duplicated elements and without a particular order. Therefore, you can only get to know whether a given element is in the set or not. These sets are strictly connected with mathematical models and operations, such as union, intersection, subtraction, and symmetric difference. A set can store various data, such as integer or string values. Of course, you can also create a set with instances of a user-defined class or record, as well as add and remove elements from the set at any time.

Imagine a hash set

If you want to better visualize a hash set, think for a moment about the game of chance, which is popular in many countries and involves selecting a few numbers that are then drawn from among many available ones. Depending on how many numbers you got from those drawn, you receive a prize. Of course, the chance of...