#### Overview of this book

Java 9 Data Structures and Algorithms covers classical, functional, and reactive data structures, giving you the ability to understand computational complexity, solve problems, and write efficient code. This book is based on the Zero Bug Bounce milestone of Java 9. We start off with the basics of algorithms and data structures, helping you understand the fundamentals and measure complexity. From here, we introduce you to concepts such as arrays, linked lists, as well as abstract data types such as stacks and queues. Next, we’ll take you through the basics of functional programming while making sure you get used to thinking recursively. We provide plenty of examples along the way to help you understand each concept. You will also get a clear picture of reactive programming, binary searches, sorting, search trees, undirected graphs, and a whole lot more!
Java 9 Data Structures and Algorithms
Credits
www.PacktPub.com
Customer Feedback
Preface
Free Chapter
Why Bother? – Basic
Cogs and Pulleys – Building Blocks
Protocols – Abstract Data Types
Detour – Functional Programming
Efficient Searching – Binary Search and Sorting
Efficient Sorting – quicksort and mergesort
Concepts of Tree
More About Search – Search Trees and Hash Tables
Concepts of Graph
Reactive Programming
Index

## Binomial forest

A binomial forest is a very interesting data structure. But, to discuss it, we need to first start with a binomial tree. A binomial tree is a tree in which a combination of two smaller binomial trees of the same size are combined in a particular way:

Binomial tree

The preceding figure shows how binomial trees combine to create larger binomial trees. In the first row, two binomial trees of height 1 combine to create a new binomial tree of height 2. In the second row, two binomial trees of height 2 combine to create a new binomial tree of height 3. In the final example, two binomial trees of height 3 combine to create a binomial tree of height 4, and it continues. The two trees that are combined together are not treated symmetrically. Instead, the root of one becomes the parent of the other. The next figure shows one more step in the sequence and then shows a different way to look at a binomial tree. In the last row, I have highlighted the subtrees differently. Notice how:

Figure...