#### 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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# Self-balancing trees

In this section, you will get to know two variants of a self-balancing tree, which keeps the tree balanced all the time while adding and removing nodes. However, why is it so important? As already mentioned, the lookup performance depends on the shape of the tree. In the case of improper organization of nodes, forming a list, the process of searching for a given value can be an O(n) operation. With a correctly arranged tree, the performance can be significantly improved with O(log n).

Do you know that a BST can very easily become an unbalanced tree? Let’s make a simple test of adding the following nine numbers to the tree, from 1 to 9. Then, you will receive a tree with the shape shown in the following diagram on the left. However, the same values can be arranged in another way, as a balanced tree, with a significantly better breadth-depth ratio, which is shown on the right:

Figure 7.19 – Difference between an unbalanced...