#### 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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# Basic trees

Let’s start with introducing trees. What are they? Do you have any ideas about how such a data structure should look? If not, let’s take a look at the following diagram, which depicts a tree with captions regarding its particular elements:

Figure 7.1 – Illustration of a tree

A tree consists of multiple nodes, including one root (100 in the diagram). The root does not contain a parent node, while all other nodes do. For example, the parent element of node 1 is 100, while node 96 has node 30 as the parent.

Moreover, each node can have any number of child nodes, such as three children (that is, 50, 1, and 150) in the case of the root. The child nodes of the same node can be named siblings, as in the case of nodes 70 and 61. A node without children is named a leaf, such as 45 and 6 in the diagram.

Let’s take a look at the rectangle with three nodes (that is, 30, 96, and 9). Such a part of the tree can be called...