Data Structures and Algorithm Analysis in Java

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 Bachelor’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 University’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 University’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).

Table of Contents

Chapter 1 Introduction

1.1 What’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 ADT–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


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 α (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 Dijkstra’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 Prim’s Algorithm
9.5.2 Kruskal’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


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


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