#### 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
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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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# Fractal generation

The recursion can be applied to many various algorithms, also related to computer graphics. For this reason, let’s take a look at another example – fractal generation creating interesting patterns, such as the following:

Figure 9.4 – An exemplary fractal generated using the recursive function

It’s really beautiful, isn’t it? Can you see some tree patterns in this image? If not, let’s follow the bold line in the middle of the image (the tree trunk) and note that it is divided into two lines (branches), each rotated by a given degree. Then, follow one of these lines and see that it is divided according to the same rule. This process is applied further and further until the specified number of levels is reached.

The description of this recursive algorithm in the natural language is quite easy, so let’s take a look at code to calculate the coordinates of the start and end points of the...