#### Overview of this book

Data structures allow organizing data efficiently. They are critical to various problems and their suitable implementation can provide a complete solution that acts like reusable code. In this book, you will learn how to use various data structures while developing in the C# language as well as how to implement some of the most common algorithms used with such data structures. At the beginning, you will get to know arrays, lists, dictionaries, and sets together with real-world examples of your application. Then, you will learn how to create and use stacks and queues. In the following part of the book, the more complex data structures will be introduced, namely trees and graphs, together with some algorithms for searching the shortest path in a graph. We will also discuss how to organize the code in a manageable, consistent, and extendable way. By the end of the book,you will learn how to build components that are easy to understand, debug, and use in different applications.
Title Page
Packt Upsell
Contributors
Preface
Free Chapter
Getting Started
Arrays and Lists
Stacks and Queues
Dictionaries and Sets
Variants of Trees
Exploring Graphs
Summary
Other Books You May Enjoy
Index

## Binomial heaps

Another kind of heap is a binomial heap. This data structure consists of a set of binomial trees with different orders. The binomial tree with order 0 is just a single node. You can construct the tree with order n using two binomial trees with order n-1. One of them should be attached as the left-most child of the parent of the first tree. It does sound a bit complicated, but the following diagram should remove any confusion:

As already mentioned, the binomial tree with order 0 is only a single node, as shown on the left. The tree with order 1 consists of two trees with order 0 (marked with the dashed border) connected to each other. In the case of the tree with order 2, two trees with order 1 are used. The second is attached as the left-most child of the parent of the first tree. In the same way, you can configure the binomial trees with the following orders.

However, how can you know how many binomial trees should be located in the binomial heap, as well as how many nodes...