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

Leftist trees


Think about the problem we'd face if we try to adapt this array-based algorithm to a persistent version. The swap will result in expensive copying, so an insert/pop would have complexity amounting to O(n).

A leftist tree is a data structure that we can use to implement the priority queue ADT. Before you look at the core data structure, look at the rank of the tree.

We first make the tree a full binary tree. If we put explicit leaves in such a tree, every node (other than the leaves) will have two children.

For more information, visit:

http://stackoverflow.com/questions/12359660/difference-between-complete-binary-tree-strict-binary-tree-full-binary-tre

Let's have a look at the figure now:

We define the rank of a binary tree as per the length of its right spine. The rank of the leaf is 0. In the preceding figure, the rank of the tree at root 9 is 2 as we need to cross over the right node with value 27. The right spine for every node is drawn with a dashed line.

A leftist tree is...