Data Structures Their Algorithms

Using only practically useful techniques, this book teaches methods for organizing, reorganizing, exploring, and retrieving data in digital computers, and the mathematical analysis of those techniques. The authors present analyses that are relatively brief and non-technical but illuminate the important performance characteristics of the algorithms. Data Structures and Their Algorithms covers algorithms, not the expression of algorithms in the syntax of particular programming languages. The authors have adopted a pseudocode notation that is readily understandable to programmers but has a simple syntax.

Data structures and algorithms are presented at the college level in a highly accessible format that presents material with one-page displays in a way that will appeal to both teachers and students. The thirteen chapters cover: Models of Computation, Lists, Induction and Recursion, Trees, Algorithm Design, Hashing, Heaps, Balanced Trees, Sets Over a Small Universe, Graphs, Strings, Discrete Fourier Transform, Parallel Computation. Key features: Complicated concepts are expressed clearly in a single page with minimal notation and without the "clutter" of the syntax of a particular programming language; algorithms are presented with self-explanatory "pseudo-code." * Chapters 1-4 focus on elementary concepts, the exposition unfolding at a slower pace. Sample exercises with solutions are provided. Sections that may be skipped for an introductory course are starred. Requires only some basic mathematics background and some computer programming experience. * Chapters 5-13 progress at a faster pace. The material is suitable for undergraduates or first-year graduates who need only review Chapters 1 -4. * This book may be used for a one-semester introductory course (based on Chapters 1-4 and portions of the chapters on algorithm design, hashing, and graph algorithms) and for a one-semester advanced course that starts at Chapter 5. A year-long course may be based on the entire book. * Sorting, often perceived as rather technical, is not treated as a separate chapter, but is used in many examples (including bubble sort, merge sort, tree sort, heap sort, quick sort, and several parallel algorithms). Also, lower bounds on sorting by comparisons are included with the presentation of heaps in the context of lower bounds for comparison-based structures. * Chapter 13 on parallel models of computation is something of a mini-book itself, and a good way to end a course. Although it is not clear what parallel

Massive modern datasets make traditional data structures and algorithms grind to a halt. This fun and practical guide introduces cutting-edge techniques that can reliably handle even the largest distributed datasets. In Algorithms and Data Structures for Massive Datasets you will learn: Probabilistic sketching data structures for practical problems Choosing the right database engine for your application Evaluating and designing efficient on-disk data structures and algorithms Understanding the algorithmic trade-offs involved in massive-scale systems Deriving basic statistics from streaming data Correctly sampling streaming data Computing percentiles with limited space resources Algorithms and Data Structures for Massive Datasets reveals a toolbox of new methods that are perfect for handling modern big data applications. You’ll explore the novel data structures and algorithms that underpin Google, Facebook, and other enterprise applications that work with truly massive amounts of data. These effective techniques can be applied to any discipline, from finance to text analysis. Graphics, illustrations, and hands-on industry examples make complex ideas practical to implement in your projects—and there’s no mathematical proofs to puzzle over. Work through this one-of-a-kind guide, and you’ll find the sweet spot of saving space without sacrificing your data’s accuracy. About the technology Standard algorithms and data structures may become slow—or fail altogether—when applied to large distributed datasets. Choosing algorithms designed for big data saves time, increases accuracy, and reduces processing cost. This unique book distills cutting-edge research papers into practical techniques for sketching, streaming, and organizing massive datasets on-disk and in the cloud. About the book Algorithms and Data Structures for Massive Datasets introduces processing and analytics techniques for large distributed data. Packed with industry stories and entertaining illustrations, this friendly guide makes even complex concepts easy to understand. You’ll explore real-world examples as you learn to map powerful algorithms like Bloom filters, Count-min sketch, HyperLogLog, and LSM-trees to your own use cases. What's inside Probabilistic sketching data structures Choosing the right database engine Designing efficient on-disk data structures and algorithms Algorithmic tradeoffs in massive-scale systems Computing percentiles with limited space resources About the reader Examples in Python, R, and pseudocode. About the author Dzejla Medjedovic earned her PhD in the Applied Algorithms Lab at Stony Brook University, New York. Emin Tahirovic earned his PhD in biostatistics from University of Pennsylvania. Illustrator Ines Dedovic earned her PhD at the Institute for Imaging and Computer Vision at RWTH Aachen University, Germany. Table of Contents 1 Introduction PART 1 HASH-BASED SKETCHES 2 Review of hash tables and modern hashing 3 Approximate membership: Bloom and quotient filters 4 Frequency estimation and count-min sketch 5 Cardinality estimation and HyperLogLog PART 2 REAL-TIME ANALYTICS 6 Streaming data: Bringing everything together 7 Sampling from data streams 8 Approximate quantiles on data streams PART 3 DATA STRUCTURES FOR DATABASES AND EXTERNAL MEMORY ALGORITHMS 9 Introducing the external memory model 10 Data structures for databases: B-trees, Bε-trees, and LSM-trees 11 External memory sorting

Praise for Design Patterns in Ruby "Design Patterns in Ruby documents smart ways to resolve many problems that Ruby developers commonly encounter. Russ Olsen has done a great job of selecting classic patterns and augmenting these with newer patterns that have special relevance for Ruby. He clearly explains each idea, making a wealth of experience available to Ruby developers for their own daily work." —Steve Metsker, Managing Consultant with Dominion Digital, Inc. "This book provides a great demonstration of the key 'Gang of Four' design patterns without resorting to overly technical explanations. Written in a precise, yet almost informal style, this book covers enough ground that even those without prior exposure to design patterns will soon feel confident applying them using Ruby. Olsen has done a great job to make a book about a classically 'dry' subject into such an engaging and even occasionally humorous read." —Peter Cooper "This book renewed my interest in understanding patterns after a decade of good intentions. Russ picked the most useful patterns for Ruby and introduced them in a straightforward and logical manner, going beyond the GoF's patterns. This book has improved my use of Ruby, and encouraged me to blow off the dust covering the GoF book." —Mike Stok "Design Patterns in Ruby is a great way for programmers from statically typed objectoriented languages to learn how design patterns appear in a more dynamic, flexible language like Ruby." —Rob Sanheim, Ruby Ninja, Relevance Most design pattern books are based on C++ and Java. But Ruby is different—and the language's unique qualities make design patterns easier to implement and use. In this book, Russ Olsen demonstrates how to combine Ruby's power and elegance with patterns, and write more sophisticated, effective software with far fewer lines of code. After reviewing the history, concepts, and goals of design patterns, Olsen offers a quick tour of the Ruby language—enough to allow any experienced software developer to immediately utilize patterns with Ruby. The book especially calls attention to Ruby features that simplify the use of patterns, including dynamic typing, code closures, and "mixins" for easier code reuse. Fourteen of the classic "Gang of Four" patterns are considered from the Ruby point of view, explaining what problems each pattern solves, discussing whether traditional implementations make sense in the Ruby environment, and introducing Ruby-specific improvements. You'll discover opportunities to implement patterns in just one or two lines of code, instead of the endlessly repeated boilerplate that conventional languages often require. Design Patterns in Ruby also identifies innovative new patterns that have emerged from the Ruby community. These include ways to create custom objects with metaprogramming, as well as the ambitious Rails-based "Convention Over Configuration" pattern, designed to help integrate entire applications and frameworks. Engaging, practical, and accessible, Design Patterns in Ruby will help you build better software while making your Ruby programming experience more rewarding.

Algorithms and data structures are much more than abstract concepts. Mastering them enables you to write code that runs faster and more efficiently, which is particularly important for today’s web and mobile apps. Take a practical approach to data structures and algorithms, with techniques and real-world scenarios that you can use in your daily production code, with examples in JavaScript, Python, and Ruby. This new and revised second edition features new chapters on recursion, dynamic programming, and using Big O in your daily work. Use Big O notation to measure and articulate the efficiency of your code, and modify your algorithm to make it faster. Find out how your choice of arrays, linked lists, and hash tables can dramatically affect the code you write. Use recursion to solve tricky problems and create algorithms that run exponentially faster than the alternatives. Dig into advanced data structures such as binary trees and graphs to help scale specialized applications such as social networks and mapping software. You’ll even encounter a single keyword that can give your code a turbo boost. Practice your new skills with exercises in every chapter, along with detailed solutions. Use these techniques today to make your code faster and more scalable.

There has been an explosive growth in the field of combinatorial algorithms. These algorithms depend not only on results in combinatorics and especially in graph theory, but also on the development of new data structures and new techniques for analyzing algorithms. Four classical problems in network optimization are covered in detail, including a development of the data structures they use and an analysis of their running time. Data Structures and Network Algorithms attempts to provide the reader with both a practical understanding of the algorithms, described to facilitate their easy implementation, and an appreciation of the depth and beauty of the field of graph algorithms.

Algorithms are at the heart of every nontrivial computer application, and algorithmics is a modern and active area of computer science. Every computer scientist and every professional programmer should know about the basic algorithmic toolbox: structures that allow efficient organization and retrieval of data, frequently used algorithms, and basic techniques for modeling, understanding and solving algorithmic problems. This book is a concise introduction addressed to students and professionals familiar with programming and basic mathematical language. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, and optimization. The algorithms are presented in a modern way, with explicitly formulated invariants, and comment on recent trends such as algorithm engineering, memory hierarchies, algorithm libraries and certifying algorithms. The authors use pictures, words and high-level pseudocode to explain the algorithms, and then they present more detail on efficient implementations using real programming languages like C++ and Java. The authors have extensive experience teaching these subjects to undergraduates and graduates, and they offer a clear presentation, with examples, pictures, informal explanations, exercises, and some linkage to the real world. Most chapters have the same basic structure: a motivation for the problem, comments on the most important applications, and then simple solutions presented as informally as possible and as formally as necessary. For the more advanced issues, this approach leads to a more mathematical treatment, including some theorems and proofs. Finally, each chapter concludes with a section on further findings, providing views on the state of research, generalizations and advanced solutions.

Advanced Algorithms and Data Structures introduces a collection of algorithms for complex programming challenges in data analysis, machine learning, and graph computing. Summary As a software engineer, you’ll encounter countless programming challenges that initially seem confusing, difficult, or even impossible. Don’t despair! Many of these “new” problems already have well-established solutions. Advanced Algorithms and Data Structures teaches you powerful approaches to a wide range of tricky coding challenges that you can adapt and apply to your own applications. Providing a balanced blend of classic, advanced, and new algorithms, this practical guide upgrades your programming toolbox with new perspectives and hands-on techniques. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Can you improve the speed and efficiency of your applications without investing in new hardware? Well, yes, you can: Innovations in algorithms and data structures have led to huge advances in application performance. Pick up this book to discover a collection of advanced algorithms that will make you a more effective developer. About the book Advanced Algorithms and Data Structures introduces a collection of algorithms for complex programming challenges in data analysis, machine learning, and graph computing. You’ll discover cutting-edge approaches to a variety of tricky scenarios. You’ll even learn to design your own data structures for projects that require a custom solution. What's inside Build on basic data structures you already know Profile your algorithms to speed up application Store and query strings efficiently Distribute clustering algorithms with MapReduce Solve logistics problems using graphs and optimization algorithms About the reader For intermediate programmers. About the author Marcello La Rocca is a research scientist and a full-stack engineer. His focus is on optimization algorithms, genetic algorithms, machine learning, and quantum computing. Table of Contents 1 Introducing data structures PART 1 IMPROVING OVER BASIC DATA STRUCTURES 2 Improving priority queues: d-way heaps 3 Treaps: Using randomization to balance binary search trees 4 Bloom filters: Reducing the memory for tracking content 5 Disjoint sets: Sub-linear time processing 6 Trie, radix trie: Efficient string search 7 Use case: LRU cache PART 2 MULTIDEMENSIONAL QUERIES 8 Nearest neighbors search 9 K-d trees: Multidimensional data indexing 10 Similarity Search Trees: Approximate nearest neighbors search for image retrieval 11 Applications of nearest neighbor search 12 Clustering 13 Parallel clustering: MapReduce and canopy clustering PART 3 PLANAR GRAPHS AND MINIMUM CROSSING NUMBER 14 An introduction to graphs: Finding paths of minimum distance 15 Graph embeddings and planarity: Drawing graphs with minimal edge intersections 16 Gradient descent: Optimization problems (not just) on graphs 17 Simulated annealing: Optimization beyond local minima 18 Genetic algorithms: Biologically inspired, fast-converging optimization

Introduction -- Array-based lists -- Linked lists -- Skiplists -- Hash tables -- Binary trees -- Random binary search trees -- Scapegoat trees -- Red-black trees -- Heaps -- Sorting algorithms -- Graphs -- Data structures for integers -- External memory searching.

Learn Data Structures and Algorithms! This book is a collection of lectures notes on Data Structures and Algorithms. The content found in this book supplements the free video lecture series, of the same name, "Advanced Data Structures", by the author, Dr. Daniel Page. This video lecture series is available at http://www.pagewizardgames.com/datastructures. This book: -Contains Computer Science topics and materials comparable to those found among university courses at a similar level (second-year) at top Canadian universities. -Provides an accessible written companion and supplemental notes for those that wish to learn the subject of Data Structures and Algorithms from the video lecture series, but have difficulties taking notes, or would prefer having a written alternative to follow along. This book is ideal for those with already an introductory programming background, know a little bit about computing, and wish to learn more about Data Structures and Algorithms and begin a more formal study of Computer Science. The materials here are a great place to start for supplemental/additional learning materials on the subject for self-study, university students, or those that want to learn more about Computer Science. Dr. Daniel Page places great emphasis on the introductory mathematical aspects of Computer Science, a natural transition from a basic programming background to thinking a bit more like a computer scientist about Computer Science. This book is not a textbook. The author assumes the reader is familiar with algebra, functions, common finite and infinite series such as arithmetic series and geometric series, and basic control structures in programming or logic. All the algorithms in this book are described in English, or using Java-like pseudocode. Chapters -Chapter 1 - Introduction: Data Structures, Problems, Input Size, Algorithms, The Search Problem. -Chapter 2 - Intro to Analysis of Algorithms I: Complexity Analysis, Comparing Algorithms, Growth Rate of Functions (Asymptotics), Showing f is O(g), Showing f is not O(g). -Chapter 3 - Intro to Analysis of Algorithms II: Some Properties of O, An Iterative Example, Back to our "Easy" Search Problem. -Chapter 4 - Dictionaries: The Dictionary Problem, Simple Implementations of a Dictionary. -Chapter 5 - Hashing: Hash Function, Hash Code, Separate Chaining, Open Addressing, Revisiting the Load Factor. -Chapter 6 - Trees: Tree ADT, Linked Tree Representation, Tree Property, Computing Height of a Tree, Tree Traversals -Chapter 7 - Priority Queues & Heaps: Priority Queues, Heaps, Array-Based Implementation, Building a Heap, Application: Sorting, Introduction to Amortized Analysis -Chapter 8 - Binary Search Trees: Ordered Dictionary ADT, BST Implementations, Inorder Traversal, Smallest, Get, Put, Remove, Successor. -Chapter 9 - AVL Trees: Height, AVL Trees, Re-Balancing AVL Trees, putAVL, removeAVL, AVL Tree Performance. -Chapter 10 - Graphs: Degrees and the Handshaking Lemma, Complete Graphs, Paths and Cycles, Trees, Forests, Subgraphs, and Connectivity, Graph Representations. -Chapter 11 - Graph Traversals: Depth-First Search (DFS), Path-Finding, Cycle Detection, Counting Vertices, DFS Tree, Breadth-First Search (BFS), Summary. -Chapter 12 - Minimum Spanning Trees: Weighted Graphs, Minimum Spanning Trees & Algorithms, Prim's Algorithm, Heap-Based Implementation of Prim's Algorithm and More! -Chapter 13 - Shortest Paths: Single-Source Shortest Path Problem, Dijkstra's Algorithm. -Chapter 14 - Multiway Search Trees: Beyond Binary Search Trees, Get, Put, Successor and Remove, (2,4)-Trees, B-Trees.