#### 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
Other Books You May Enjoy

# The Fibonacci series

As the first example, let’s take a look at calculating a given number from the Fibonacci series, using the following recursive function:

Figure 9.1 – A formula for calculating a number from the Fibonacci series

Its interpretation is very simple:

• F(0) is equal to 0
• F(1) is equal to 1
• F(n) is a sum of F(n-1) and F(n-2), which means that this number is a sum of the two preceding ones

As an example, F(2) is equal to the sum of F(0) and F(1). Thus, it is equal to 1, while F(3) is equal to 2. It is worth mentioning that there are two base cases, namely for n equal to 0 and 1. For both of them, there is a specific value defined, namely 0 and 1.

The recursive implementation in the C# language is shown as follows:

```long Fibonacci(int n)
{
if (n == 0) { return 0; }
if (n == 1) { return 1; }
return Fibonacci(n - 1) + Fibonacci(n ...```