#### 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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# Binary trees

Generally speaking, each node in a basic tree can contain any number of children. However, in the case of binary trees, a node cannot contain more than two children. It means that it can contain zero, one, or two child nodes. Such a requirement has an important impact on the shape of a binary tree, as shown in the following two diagrams presenting binary trees:

Figure 7.4 – Illustration of binary trees

As already mentioned, a node in a binary tree can contain at most two children. For this reason, they are referred to as the left child and the right child. In the case of the binary tree shown on the left-hand side of the preceding diagram, node 21 has two children, namely 68 as the left child and 12 as the right child, while node 100 has only a left child.

## Traversal

Have you thought about how you can iterate through all the nodes in a tree? How can you specify an order of nodes during traversal of a tree? There are three common...