Chapter 6 Self-Test 325
Chapter 6 Computer Exercises 326

7 Recurrence Relations 327
7.1 Introduction 327
7.2 Solving Recurrence Relations 338
Problem-Solving Corner: Recurrence Relations 350
7.3 Applications to the Analysis of Algorithms 353
7.4 The Closest-Pair Problem? 365
Chapter 7 Notes 370
Chapter 7 Review 371
Chapter 7 Self-Test 371
Chapter 7 Computer Exercises 372

8 Graph Theory 373
8.1 Introduction 373
8.2 Paths and Cycles 384
Problem-Solving Corner: Graphs 395
8.3 Hamiltonian Cycles and the Traveling Salesperson
Problem 396
8.4 A Shortest-Path Algorithm 405
8.5 Representations of Graphs 410
8.6 Isomorphisms of Graphs 415
8.7 Planar Graphs 422
8.8 Instant Insanity? 429
Chapter 8 Notes 433
Chapter 8 Review 434
Chapter 8 Self-Test 435
Chapter 8 Computer Exercises 436

9 Trees 438
9.1 Introduction 438
9.2 Terminology and Characterizations of Trees 445
Problem-Solving Corner: Trees 450
9.3 Spanning Trees 452
9.4 Minimal Spanning Trees 459
9.5 Binary Trees 465
9.6 Tree Traversals 471
9.7 Decision Trees and the Minimum Time for Sorting 477
9.8 Isomorphisms of Trees 483
9.9 Game Trees? 493
Chapter 9 Notes 502
Chapter 9 Review 502
Chapter 9 Self-Test 503
Chapter 9 Computer Exercises 505

10 Network Models 506
10.1 Introduction 506
10.2 A Maximal Flow Algorithm 511
10.3 The Max Flow, Min Cut Theorem 519
10.4 Matching 523
Problem-Solving Corner: Matching 528
Chapter 10 Notes 529
Chapter 10 Review 530
Chapter 10 Self-Test 530
Chapter 10 Computer Exercises 531

11 Boolean Algebras and Combinatorial
Circuits 532
11.1 Combinatorial Circuits 532
11.2 Properties of Combinatorial Circuits 539
11.3 Boolean Algebras 544
Problem-Solving Corner: Boolean Algebras 549
11.4 Boolean Functions and Synthesis of Circuits 551
11.5 Applications 556
Chapter 11 Notes 564
Chapter 11 Review 565
Chapter 11 Self-Test 565
Chapter 11 Computer Exercises 567

12 Automata, Grammars, and Languages 568
12.1 Sequential Circuits and Finite-State Machines 568
12.2 Finite-State Automata 574
12.3 Languages and Grammars 579
12.4 Nondeterministic Finite-State Automata 589
12.5 Relationships Between Languages and Automata 595
Chapter 12 Notes 601
Chapter 12 Review 602
Chapter 12 Self-Test 602
Chapter 12 Computer Exercises 603

Appendix 605
A Matrices 605
B Algebra Review 609
C Pseudocode 620
References 627
Hints and Solutions to Selected Exercises 633
Index 735

国外计算机科学教材系列离散数学(第8版)(英文版)/(美)RICHARD JOHNSONBAUGH(理查德.约翰逊鲍夫) 作者简介

Richard Johnsonbaugh是美国芝加哥DePaul大学的计算机科学、通信与信息系统的Emeritus教授，并在DePaul大学的从事了20年教学工作，之前曾任莫尔豪斯学院和芝加哥州立大学的数学系教师和系主任一职。Johnsonbaugh教授在耶鲁大学获得数学学士学位、硕士学位，并获得俄勒冈大学的数学博士学位以及伊利诺伊大学的计算机硕士学位。Johnsonbaugh教授近期的研究领域包括模式识别、程序设计语言、算法和离散数学，他也是这些领域众多书籍和文章的作者或合著者。Johnsonbaugh教授的几本专著已被译成各种语言出版，他也是美国数学协会的成员。
Richard Johnsonbaugh是美国芝加哥DePaul大学的计算机科学、通信与信息系统的Emeritus教授，并在DePaul大学的从事了20年教学工作，之前曾任莫尔豪斯学院和芝加哥州立大学的数学系教师和系主任一职。Johnsonbaugh教授在耶鲁大学获得数学学士学位、硕士学位，并获得俄勒冈大学的数学博士学位以及伊利诺伊大学的计算机硕士学位。Johnsonbaugh教授近期的研究领域包括模式识别、程序设计语言、算法和离散数学，他也是这些领域众多书籍和文章的作者或合著者。Johnsonbaugh教授的几本专著已被译成各种语言出版，他也是美国数学协会的成员。

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