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

Complexity


What is the runtime complexity of node insertion? A Red-Black tree of n internal nodes has height at 2*log(n+1).

This means that operations, such as searching for a node, have logarithmic time. The insertion operation we just saw is also proportional to the height of the tree.

When we insert a new node and violate the second invariant, we fix it and always color the subtree's root red. This could create further invariant violation upward in the tree.

However, as the height is at most 2*log(n+1), the insertion operation has a runtime complexity of O(logn). So, for example, for a tree with 4294967296 nodes, which is 232, we have to perform up to 32 invariant fixes. This is a very good number, making Red-Black trees one of the most popular variants of Binary Search Trees.

Linux's completely fair scheduler uses Red-Black trees. See http://www.ibm.com/developerworks/library/l-completely-fair-scheduler/ for more information.

Java 8's TreeMap is implemented using Red-Black trees. See https...