#### 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

## Fibonacci heaps

A Fibonacci heap is an interesting variant of heaps, which in some ways is similar to a binomial heap. First of all, it also consists of many trees, but there are no constraints regarding the shape of each tree, so it is much more flexible than the binomial heap. Moreover, it is allowed to have more than one tree with exactly the same shape in the heap.

An example of a Fibonacci heap is as follows:

One of the important assumptions is that each tree is a min-heap. Thus, the minimum value in the whole Fibonacci heap is certainly a root node in one of the trees. Moreover, the presented data structure supports performing various operations in the lazy way. That means that it does not perform additional complex operations unless it is really necessary. For example, it can add a new node just as a new tree with only one node.