#### 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

## Recursive algorithms

As I have already pointed out, recursive algorithms are a different way of thinking about solving a problem. For example, say our problem is to write a program that, given a positive integer `n`, returns the sum of numbers from zero to `n`. The known imperative way of writing it is simple:

```public int sum_upto(int n){
int sum=0;
for(int i=0;i<=n;i++){
sum+=i;
}
return sum;
}```

The following would be the functional version of the problem:

```public int sum_upto_functional(int n){
return n==0?0:n+sum_upto_functional(n-1);
}```

That's it–just a one-liner! This is probably nothing new to Java programmers, as they do understand recursive functions. However, an imperative programmer would use recursion only when nothing else worked. But this is a different way of thinking. How do we justify that it is equivalent to solving the problem for a smaller input and then composing it with something else? Well, we are certainly first computing the same function for an input that is...