#### 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.
Table of Contents (13 chapters)
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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# Binary search trees

A binary tree is an interesting data structure that allows the creation of a hierarchy of elements, with the restriction that each node can contain at most two children, but without any rules about relationships between the nodes. For this reason, if you want to check whether a binary tree contains a given value, you need to check each node, traversing the tree using one of three available modes: pre-order, in-order, or post-order. This means that the lookup time is linear, namely O(n).

What about a situation where there are some precise rules regarding relations between nodes in a tree? Let’s imagine a scenario where you know that the left subtree contains nodes with values smaller than the root’s value, while the right subtree contains nodes with values greater than the root’s value. Then, you can compare the searched value with the current node and decide whether you should continue searching in the left or right subtree. Such an approach...