# Data Structures and Algorithm Analysis in Java, 3rd edition

Published by Pearson (November 18, 2011) Â© 2012

**Mark A. Weiss**

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*Data Structures and Algorithm Analysis in Java *is an advanced algorithms book that fits between traditional CS2 and Algorithms Analysis courses. In the old ACM Curriculum Guidelines, this course was known as CS7. It is also suitable for a first-year graduate course in algorithm analysis

As the speed and power of computers increases, so does the need for effective programming and algorithm analysis. By approaching these skills in tandem, Mark Allen Weiss teaches readers to develop well-constructed, maximally efficient programs in Java.

Weiss clearly explains topics from binary heaps to sorting to *NP*-completeness, and dedicates a full chapter to amortized analysis and advanced data structures and their implementation. Figures and examples illustrating successive stages of algorithms contribute to Weissâ€™ careful, rigorous and in-depth analysis of each type of algorithm. A logical organization of topics and full access to source code complement the textâ€™s coverage.

- This text is designed to teach students good programming and algorithm analysis skills simultaneously so that they can develop intricate programs with the maximum amount of efficiency.
- By analyzing an algorithm before it is actually coded, students can decide if a particular solution will be feasible and see how careful implementations can reduce the time constraint for large amounts of data. No algorithm or data structure is presented without an explanation of its running time.
- This book is suitable for either an advanced data structures (CS7) course or a first-year graduate course in algorithm analysis. As introductory sequences expand from two to three courses, this book is ideal at the end of the third course, bridging the way to the Algorithms course.
- Integrated coverage of the Java Collections Library.
- Discussion of algorithm and design techniques covers greedy algorithms, divide and conquer algorithms, dynamic programming, randomized algorithms, and backtracking.
- Covers topics and data structures such as Fibonacci heaps, skew heaps, binomial queue, skip lists and splay trees.
- A full chapter on amortized analysis examines the advanced data structures presented earlier in the book.
- Chapter on advanced data structures and their implementation covers red black trees, top down splay trees, k-d trees, pairing heaps, and more.
- Numerous figures and examples illustrate successive stages of algorithms.
- End-of-chapter exercises, ranked by difficulty, reinforce key chapter concepts.
- End-of-chapter references are either historical, representing the original source of the material, or they represent extensions and improvements to the results given in the text.
- The following Instructor Resources are available on the Instructor Resource Center:
- Source code for example programs
- PowerPoint slides
- Solution Manual

- Chapter 4 includes implementation of the AVL tree deletion algorithmâ€“a topic often requested by readers.
- Chapter 5 has been extensively revised and enlarged and now contains material on two newer algorithms: cuckoo hashing and hopscotch hashing. Additionally, a new section on universal hashing has been added.
- Chapter 7 now contains material on radix sort, and a new section on lower bound proofs has been added.
- Chapter 8 uses the new union/find analysis by Seidel and Sharir, and shows the O( MÎ±(M,N) ) bound instead of the weaker O( Mlogâˆ— N ) bound in prior editions.
- Chapter 12 adds material on suffix trees and suffix arrays, including the linear-time suffix array construction algorithm by Karkkainen and Sanders (with implementation).
- The sections covering deterministic skip lists and AA-trees have been removed.
- Throughout the text, the code has been updated to use the diamond operator from Java 7.

## Table of Contents

- Chapter 1 Introduction
- 1.1 Whatâ€™s the Book About?
- 1.2 Mathematics Review
- 1.2.1 Exponents
- 1.2.2 Logarithms
- 1.2.3 Series
- 1.2.4 Modular Arithmetic
- 1.2.5 The P Word

- 1.3 A Brief Introduction to Recursion
- 1.4 Implementing Generic Components Pre-Java 5
- 1.4.1 Using Object for Genericity
- 1.4.2 Wrappers for Primitive Types
- 1.4.3 Using Interface Types for Genericity
- 1.4.4 Compatibility of Array Types

- 1.5 Implementing Generic Components Using Java 5 Generics
- 1.5.1 Simple Generic Classes and Interfaces
- 1.5.2 Autoboxing/Unboxing
- 1.5.3 The Diamond Operator
- 1.5.4 Wildcards with Bounds
- 1.5.5 Generic Static Methods
- 1.5.6 Type Bounds
- 1.5.7 Type Erasure
- 1.5.8 Restrictions on Generics

- 1.6 Function Objects

- Summary
- Exercises
- References

- Chapter 2 Algorithm Analysis
- 2.1 Mathematical Background
- 2.2 Model
- 2.3 What to Analyze
- 2.4 Running Time Calculations
- 2.4.1 A Simple Example
- 2.4.2 General Rules
- 2.4.3 Solutions for the Maximum Subsequence Sum Problem
- 2.4.4 Logarithms in the Running Time
- 2.4.5 A Grain of Salt

- Summary
- Exercises
- References

- Chapter 3 Lists, Stacks, and Queues
- 3.1 Abstract Data Types (ADTs)
- 3.2 The List ADT
- 3.2.1 Simple Array Implementation of Lists
- 3.2.2 Simple Linked Lists

- 3.3 Lists in the Java Collections API
- 3.3.1 Collection Interface
- 3.3.2 Iterators
- 3.3.3 The List Interface, ArrayList, and LinkedList
- 3.3.4 Example: Using remove on a LinkedList
- 3.3.5 ListIterators

- 3.4 Implementation of ArrayList
- 3.4.1 The Basic Class
- 3.4.2 The Iterator and Java Nested and Inner Classes

- 3.5 Implementation of LinkedList
- 3.6 The Stack ADT
- 3.6.1 Stack Model
- 3.6.2 Implementation of Stacks
- 3.6.3 Applications

- 3.7 The Queue ADT
- 3.7.1 Queue Model
- 3.7.2 Array Implementation of Queues
- 3.7.3 Applications of Queues

- Summary
- Exercises

- Chapter 4 Trees
- 4.1 Preliminaries
- 4.1.1 Implementation of Trees
- 4.1.2 Tree Traversals with an Application

- 4.2 Binary Trees
- 4.2.1 Implementation
- 4.2.2 An Example: Expression Trees

- 4.3 The Search Tree ADTâ€“Binary Search Trees
- 4.3.1 contains
- 4.3.2 findMin and findMax
- 4.3.3 insert
- 4.3.4 remove
- 4.3.5 Average-Case Analysis

- 4.4 AVL Trees
- 4.4.1 Single Rotation
- 4.4.2 Double Rotation

- 4.5 Splay Trees
- 4.5.1 A Simple Idea (That Does Not Work)
- 4.5.2 Splaying

- 4.6 Tree Traversals (Revisited)
- 4.7 B-Trees
- 4.8 Sets and Maps in the Standard Library
- 4.8.1 Sets
- 4.8.2 Maps
- 4.8.3 Implementation of TreeSet and TreeMap
- 4.8.4 An Example That Uses Several Maps

- Summary
- Exercises
- References

- 4.1 Preliminaries
- Chapter 5 Hashing
- 5.1 General Idea
- 5.2 Hash Function
- 5.3 Separate Chaining
- 5.4 Hash Tables Without Linked Lists
- 5.4.1 Linear Probing
- 5.4.2 Quadratic Probing
- 5.4.3 Double Hashing

- 5.5 Rehashing
- 5.6 Hash Tables in the Standard Library
- 5.7 Hash Tables with Worst-Case O(1) Access
- 5.7.1 Perfect Hashing
- 5.7.2 Cuckoo Hashing
- 5.7.3 Hopscotch Hashing

- 5.8 Universal Hashing
- 5.9 Extendible Hashing

- Summary
- Exercises
- References

- Chapter 6 Priority Queues (Heaps)
- 6.1 Model
- 6.2 Simple Implementations
- 6.3 Binary Heap
- 6.3.1 Structure Property
- 6.3.2 Heap-Order Property
- 6.3.3 Basic Heap Operations
- 6.3.4 Other Heap Operations

- 6.4 Applications of Priority Queues
- 6.4.1 The Selection Problem
- 6.4.2 Event Simulation

- 6.5 d-Heaps
- 6.6 Leftist Heaps
- 6.6.1 Leftist Heap Property
- 6.6.2 Leftist Heap Operations

- 6.7 Skew Heaps
- 6.8 Binomial Queues
- 6.8.1 Binomial Queue Structure
- 6.8.2 Binomial Queue Operations
- 6.8.3 Implementation of Binomial Queues

- 6.9 Priority Queues in the Standard Library

- Summary
- Exercises
- References

- Chapter 7 Sorting
- 7.1 Preliminaries
- 7.2 Insertion Sort
- 7.2.1 The Algorithm
- 7.2.2 Analysis of Insertion Sort

- 7.3 A Lower Bound for Simple Sorting Algorithms
- 7.4 Shellsort
- 7.4.1 Worst-Case Analysis of Shellsort

- 7.5 Heapsort
- 7.5.1 Analysis of Heapsort

- 7.6 Mergesort
- 7.6.1 Analysis of Mergesort

- 7.7 Quicksort
- 7.7.1 Picking the Pivot
- 7.7.2 Partitioning Strategy
- 7.7.3 Small Arrays
- 7.7.4 Actual Quicksort Routines
- 7.7.5 Analysis of Quicksort
- 7.7.6 A Linear-Expected-Time Algorithm for Selection

- 7.8 A General Lower Bound for Sorting
- 7.8.1 Decision Trees

- 7.9 Decision-Tree Lower Bounds for Selection Problems
- 7.10 Adversary Lower Bounds
- 7.11 Linear-Time Sorts: Bucket Sort and Radix Sort
- 7.12 External Sorting
- 7.12.1 Why We Need New Algorithms
- 7.12.2 Model for External Sorting
- 7.12.3 The Simple Algorithm
- 7.12.4 Multiway Merge
- 7.12.5 Polyphase Merge
- 7.12.6 Replacement Selection

- Summary
- Exercises
- References

- Chapter 8 The Disjoint Set Class
- 8.1 Equivalence Relations
- 8.2 The Dynamic Equivalence Problem
- 8.3 Basic Data Structure
- 8.4 Smart Union Algorithms
- 8.5 Path Compression
- 8.6 Worst Case for Union-by-Rank and Path Compression
- 8.6.1 Slowly Growing Functions
- 8.6.2 An Analysis By Recursive Decomposition
- 8.6.3 An O(M log * N) Bound
- 8.6.4 An O( M Î± (M, N) ) Bound

- 8.7 An Application

- Summary
- Exercises
- References

- Chapter 9 Graph Algorithms
- 9.1 Definitions
- 9.1.1 Representation of Graphs

- 9.2 Topological Sort
- 9.3 Shortest-Path Algorithms
- 9.3.1 Unweighted Shortest Paths
- 9.3.2 Dijkstraâ€™s Algorithm
- 9.3.3 Graphs with Negative Edge Costs
- 9.3.4 Acyclic Graphs
- 9.3.5 All-Pairs Shortest Path
- 9.3.6 Shortest-Path Example

- 9.4 Network Flow Problems
- 9.4.1 A Simple Maximum-Flow Algorithm

- 9.5 Minimum Spanning Tree
- 9.5.1 Primâ€™s Algorithm
- 9.5.2 Kruskalâ€™s Algorithm

- 9.6 Applications of Depth-First Search
- 9.6.1 Undirected Graphs
- 9.6.2 Biconnectivity
- 9.6.3 Euler Circuits
- 9.6.4 Directed Graphs
- 9.6.5 Finding Strong Components

- 9.7 Introduction to NP-Completeness
- 9.7.1 Easy vs. Hard
- 9.7.2 The Class NP
- 9.7.3 NP-Complete Problems

- Summary
- Exercises
- References

- 9.1 Definitions
- Chapter 10 Algorithm Design Techniques
- 10.1 Greedy Algorithms
- 10.1.1 A Simple Scheduling Problem
- 10.1.2 Huffman Codes
- 10.1.3 Approximate Bin Packing

- 10.2 Divide and Conquer
- 10.2.1 Running Time of Divide-and-Conquer Algorithms
- 10.2.2 Closest-Points Problem
- 10.2.3 The Selection Problem
- 10.2.4 Theoretical Improvements for Arithmetic Problems

- 10.3 Dynamic Programming
- 10.3.1 Using a Table Instead of Recursion
- 10.3.2 Ordering Matrix Multiplications
- 10.3.3 Optimal Binary Search Tree
- 10.3.4 All-Pairs Shortest Path

- 10.4 Randomized Algorithms
- 10.4.1 Random Number Generators
- 10.4.2 Skip Lists
- 10.4.3 Primality Testing

- 10.5 Backtracking Algorithms
- 10.5.1 The Turnpike Reconstruction Problem
- 10.5.2 Games

- Summary
- Exercises
- References

- 10.1 Greedy Algorithms
- Chapter 11 Amortized Analysis
- 11.1 An Unrelated Puzzle
- 11.2 Binomial Queues
- 11.3 Skew Heaps
- 11.4 Fibonacci Heaps
- 11.4.1 Cutting Nodes in Leftist Heaps
- 11.4.2 Lazy Merging for Binomial Queues
- 11.4.3 The Fibonacci Heap Operations
- 11.4.4 Proof of the Time Bound

- 11.5 Splay Trees

- Summary
- Exercises
- References

- Chapter 12 Advanced Data Structures and Implementation
- 12.1 Top-Down Splay Trees
- 12.2 Red-Black Trees
- 12.2.1 Bottom-Up Insertion
- 12.2.2 Top-Down Red-Black Trees
- 12.2.3 Top-Down Deletion

- 12.3 Treaps
- 12.4 Suffix Arrays and Suffix Trees
- 12.4.1 Suffix Arrays
- 12.4.2 Suffix Trees
- 12.4.3 Linear-Time Construction of Suffix Arrays and Suffix Trees

- 12.5 k-d Trees
- 12.6 Pairing Heaps

- Summary
- Exercises
- References

#### Index

**Mark Allen Weiss **is Professor and Associate Director for the School of Computing and Information Sciences at Florida International University. He is also currently serving as both Director of Undergraduate Studies and Director of Graduate Studies. He received his Bachelorâ€™s Degree in Electrical Engineering from the Cooper Union in 1983, and his Ph.D. in Computer Science from Princeton University in 1987, working under Bob Sedgewick. He has been at FIU since 1987 and was promoted to Professor in 1996. His interests include data structures, algorithms, and education. He is most well-known for his highly-acclaimed Data Structures textbooks, which have been used for a generation by roughly a million students.

Professor Weiss is the author of numerous publications in top-rated journals and was recipient of the Universityâ€™s Excellence in Research Award in 1994. In 1996 at FIU he was the first in the world to teach Data Structures using the Java programming language, which is now the de facto standard. From 1997-2004 he served as a member of the Advanced Placement Computer Science Development Committee, chairing the committee from 2000-2004. The committee designed the curriculum and wrote the AP exams that were taken by 20,000 high school students annually.

In addition to his Research Award in 1994, Professor Weiss is also the recipient of the Universityâ€™s Excellence in Teaching Award in 1999 and the School of Computing and Information Science Excellence in Teaching Award (2005) and Excellence in Service Award (2007).

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