Book Image

Learning Functional Data Structures and Algorithms

By : Raju Kumar Mishra
Book Image

Learning Functional Data Structures and Algorithms

By: Raju Kumar Mishra

Overview of this book

Functional data structures have the power to improve the codebase of an application and improve efficiency. With the advent of functional programming and with powerful functional languages such as Scala, Clojure and Elixir becoming part of important enterprise applications, functional data structures have gained an important place in the developer toolkit. Immutability is a cornerstone of functional programming. Immutable and persistent data structures are thread safe by definition and hence very appealing for writing robust concurrent programs. How do we express traditional algorithms in functional setting? Won’t we end up copying too much? Do we trade performance for versioned data structures? This book attempts to answer these questions by looking at functional implementations of traditional algorithms. It begins with a refresher and consolidation of what functional programming is all about. Next, you’ll get to know about Lists, the work horse data type for most functional languages. We show what structural sharing means and how it helps to make immutable data structures efficient and practical. Scala is the primary implementation languages for most of the examples. At times, we also present Clojure snippets to illustrate the underlying fundamental theme. While writing code, we use ADTs (abstract data types). Stacks, Queues, Trees and Graphs are all familiar ADTs. You will see how these ADTs are implemented in a functional setting. We look at implementation techniques like amortization and lazy evaluation to ensure efficiency. By the end of the book, you will be able to write efficient functional data structures and algorithms for your applications.
Table of Contents (20 chapters)
Learning Functional Data Structures and Algorithms
Credits
About the Authors
About the Reviewer
www.PacktPub.com
Customer Feedback
Preface

Red-Black trees


Given this rotation algorithm, we can now look at the core Red-Black tree.

A Red-Black tree node always has a color, either red or black, with the following invariants:

  • A red node can never have a red child

  • Every path from the root to an empty node contains the same number of black nodes

An empty node is a leaf nil node. This nil node indicates termination and is also known as a sentinel node.

Here is an example of a Red-Black tree. Note that each node is annotated with its black height. The black height is the number of black nodes from the node to the leaf.

Note these important points:

  1. The root is always black.

  2. Every leaf is black.

  3. Both the children of a red node are black (as a red node cannot have a red child).

  4. Every path from a node to a leaf contains the same number of black nodes.

The following diagram shows a Red-Black tree:

Take each of the invariants from earlier and check whether the tree satisfies each one of them.

When we look at rebalancing, we will see how the first invariant...