Data Structures and Algorithms in C++

Transcription

1 Data Structures and Algorithms in C++ Second Edition Michael T. Goodrich Department of Computer Science University of California, Irvine Roberto Tamassia Department of Computer Science Brown University David M. Mount Department of Computer Science University of Maryland John Wiley & Sons, Inc.

2 Contents 1 A C++ Primer Basic C++ Programming Elements A Simple C++ Program Fundamental Types Pointers, Arrays, and Structures Named Constants, Scope, and Namespaces Expressions Changing Types through Casting Control Flow Functions Argument Passing Overloading and Inlining Classes Class Structure Constructors and Destructors Classes and Memory Allocation Class Friends and Class Members The Standard Template Library C++ Program and File Organization An Example Program Writing a C++ Program Design Pseudo-Code Coding Testing and Debugging Exercises 60 2 Object-Oriented Design Goals, Principles, and Patterns Object-Oriented Design Goals Object-Oriented Design Principles Design Patterns 70 xv

3 xvi Contents 2.2 Inheritance and Polymorphism Inheritance in C Polymorphism Examples of Inheritance in C Multiple Inheritance and Class Casting Interfaces and Abstract Classes Templates Function Templates Class Templates Exceptions Exception Objects Throwing and Catching Exceptions Exception Specification Exercises 98 3 Arrays, Linked Lists, and Recursion Using Arrays Storing Game Entries in an Array Sorting an Array Two-Dimensional Arrays and Positional Games Ill 3.2 Singly Linked Lists Implementing a Singly Linked List Insertion to the Front of a Singly Linked List Removal from the Front of a Singly Linked List Implementing a Generic Singly Linked List Doubly Linked Lists Insertion into a Doubly Linked List Removal from a Doubly Linked List A C++ Implementation Circularly Linked Lists and List Reversal Circularly Linked Lists Reversing a Linked List Recursion Linear Recursion Binary Recursion Multiple Recursion Exercises Analysis Tools The Seven Functions Used in This Book The Constant Function The Logarithm Function 154

4 Contents xvii The Linear Function The N-Log-N Function The Quadratic Function The Cubic Function and Other Polynomials The Exponential Function Comparing Growth Rates Analysis of Algorithms Experimental Studies Primitive Operations Asymptotic Notation Asymptotic Analysis Using the Big-Oh Notation A Recursive Algorithm for Computing Powers Some More Examples of Algorithm Analysis Simple Justification Techniques By Example The "Contra" Attack Induction and Loop Invariants Exercises Stacks, Queues, and Deques Stacks The Stack Abstract Data Type The STL Stack A C++ Stack Interface A Simple Array-Based Stack Implementation Implementing a Stack with a Generic Linked List Reversing a Vector Using a Stack Matching Parentheses and HTML Tags Queues The Queue Abstract Data Type The STL Queue A C++ Queue Interface A Simple Array-Based Implementation Implementing a Queue with a Circularly Linked List Double-Ended Queues The Deque Abstract Data Type The STL Deque Implementing a Deque with a Doubly Linked List Adapters and the Adapter Design Pattern Exercises 223

5 xviii Contents 6 List and Iterator ADTs Vectors The Vector Abstract Data Type A Simple Array-Based Implementation An Extendable Array Implementation STL Vectors Lists Node-Based Operations and Iterators The List Abstract Data Type Doubly Linked List Implementation STL Lists STL Containers and Iterators Sequences The Sequence Abstract Data Type Implementing a Sequence with a Doubly Linked List Implementing a Sequence with an Array Case Study: Bubble-Sort on a Sequence The Bubble-Sort Algorithm A Sequence-Based Analysis of Bubble-Sort Exercises Trees General Trees Tree Definitions and Properties Tree Functions A C++ Tree Interface A Linked Structure for General Trees Tree Traversal Algorithms Depth and Height Preorder Traversal Postorder Traversal Binary Trees The Binary Tree ADT A C++ Binary Tree Interface Properties of Binary Trees A Linked Structure for Binary Trees A Vector-Based Structure for Binary Trees Traversals of a Binary Tree The Template Function Pattern Representing General Trees with Binary Trees Exercises 310

6 Contents xix 8 Heaps and Priority Queues The Priority Queue Abstract Data Type Keys, Priorities, and Total Order Relations Comparators The Priority Queue ADT A C++ Priority Queue Interface Sorting with a Priority Queue The STL priority.queue Class Implementing a Priority Queue with a List A C++ Priority Queue Implementation using a List Selection-Sort and Insertion-Sort Heaps The Heap Data Structure Complete Binary Trees and Their Representation Implementing a Priority Queue with a Heap C++ Implementation Heap-Sort Bottom-Up Heap Construction ~k Adaptable Priority Queues A List-Based Implementation Location-Aware Entries Exercises Hash Tables, Maps, and Skip Lists Maps The Map ADT A C++ Map Interface The STL map Class A Simple List-Based Map Implementation Hash Tables Bucket Arrays Hash Functions Hash Codes Compression Functions Collision-Handling Schemes Load Factors and Rehashing A C++ Hash Table Implementation Ordered Maps Ordered Search Tables and Binary Search Two Applications of Ordered Maps Skip Lists 402

7 xx Contents Search and Update Operations in a Skip List A Probabilistic Analysis of Skip Lists * Dictionaries The Dictionary ADT A C++ Dictionary Implementation Implementations with Location-Aware Entries Exercises Search Trees Binary Search Trees Searching Update Operations C++Implementation of a Binary Search Tree AVL Trees Update Operations C++ Implementation of an AVL Tree Splay Trees Splaying When to Splay Amortized Analysis of Splaying ~k (2,4) Trees Multi-Way Search Trees Update Operations for (2,4) Trees Red-Black Trees Update Operations C++ Implementation of a Red-Black Tree Exercises Sorting, Sets, and Selection Merge-Sort Divide-and-Conquer Merging Arrays and Lists The Running Time of Merge-Sort C++ Implementations of Merge-Sort Merge-Sort and Recurrence Equations "A" Quick-Sort Randomized Quick-Sort C++ Implementations and Optimizations Studying Sorting through an Algorithmic Lens A Lower Bound for Sorting Linear-Time Sorting: Bucket-Sort and Radix-Sort Comparing Sorting Algorithms 531

8 Contents xxi 11.4 Sets and Union/Find Structures The Set ADT Mergable Sets and the Template Method Pattern Partitions with Union-Find Operations Selection Prune-and-Search Randomized Quick-Select Analyzing Randomized Quick-Select Exercises Strings and Dynamic Programming String Operations The STL String Class Dynamic Programming Matrix Chain-Product DNA and Text Sequence Alignment Pattern Matching Algorithms Brute Force The Boyer-Moore Algorithm The Knuth-Morris-Pratt Algorithm Text Compression and the Greedy Method The Huffman-Coding Algorithm The Greedy Method Tries Standard Tries Compressed Tries Suffix Tries Search Engines Exercises Graph Algorithms Graphs The Graph ADT Data Structures for Graphs The Edge List Structure The Adjacency List Structure The Adjacency Matrix Structure Graph Traversals Depth-First Search Implementing Depth-First Search A Generic DFS Implementation in C Polymorphic Objects and Decorator Values ~k 621

9 xxii Contents Breadth-First Search Directed Graphs Traversing a Digraph Transitive Closure Directed Acyclic Graphs Shortest Paths Weighted Graphs Dijkstra's Algorithm Minimum Spanning Trees Kruskal's Algorithm The Prim-Jarm'k Algorithm Exercises Memory Management and B-Trees Memory Management Memory Allocation in C Garbage Collection External Memory and Caching The Memory Hierarchy Caching Strategies External Searching and B-Trees (a,b) Trees B-Trees External-Memory Sorting Multi-Way Merging Exercises 685 A Useful Mathematical Facts 689 Bibliography 697 Index 702