包邮离散数学:英文版

第1章　组合问题与组合技术引论111　工程完成时间的问题212　匹配问题1013　背包问题1614　算法及其效率23历史注记35补充习题37计算机题39推荐读物40第2章　集合、关系和函数4121　集合运算4122　等价关系47*23　偏序关系5424　函数6525　数学归纳法7626　应用84历史注记93补充习题95计算机题98推荐读物98第3章　编码理论9931　同余10032　欧几里得算法10633　RSA方法11334　检错码和纠错码12235　矩阵码13236　单纠错矩阵码140历史注记147补充习题149计算机题152推荐读物153第4章　图15441　图及其表示15442　通路和回路16443　*短通路和距离18144　图着色19345　有向图和有向多重图202历史注记219补充习题220计算机题226推荐读物227第5章　树22851　树的性质22852　生成树23853　深度优先搜索25354　根树26655　二叉树和遍历27456　*优二叉树和二叉搜索树287历史注记306补充习题308计算机题311推荐读物312第6章　匹配31361　相异代表系31362　图中的匹配31963　匹配算法32764　算法的应用33765　匈牙利方法346历史注记354补充习题355计算机题357推荐读物357第7章　网络流35871　流和割35872　流增广算法36973　*大流*小割定理38274　流和匹配389历史注记397补充习题397计算机题400推荐读物401第8章　计数技术40281　帕斯卡三角形和二项式定理40282　3个基本原理40683　排列和组合41684　允许重复的排列和组合42185　概率428*86　容斥原理434*87　排列和r组合的生成445历史注记452补充习题453计算机题456推荐读物457第9章　递推关系与生成函数45891　递推关系45892　迭代法47093　常系数线性差分方程482*94　用递推关系分析算法的效率49495　用生成函数计数50696　生成函数的代数513历史注记523补充习题524计算机题527推荐读物528第10章　组合电路和有限状态机529101　逻辑门529102　构造组合电路538103　卡诺图546104　有限状态机560历史注记569补充习题570计算机题573推荐读物573附录A　逻辑和证明简介574A1　命题和联结词574A2　逻辑等价583A3　证明的方法587历史注记593补充习题594推荐读物596附录B　矩阵597历史注记604附录C　本书中的算法607参考文献613奇数号习题答案618图片来源658Contents1AN INTRODUCTION TO COMBINATORIAL PROBLEMS AND TECHNIQUES111 The Time to Completea Project 212 A Matching Problem 1013 A Knapsack Problem 1614 Algorithms and Their Efficiency 23Historical Notes 35Supplementary Exercises 37Computer Projects 39Suggested Readings 402 SETS, RELATIONS, AND FUNCTIONS 4121 Set Operations 4122 Equivalence Relations 4723* Partial Ordering Relations 5424 Functions 6525 Mathematical Induction 7626 Applications 84Historical Notes 93Supplementary Exercises 95Computer Projects 98Suggested Readings 983 CODING THEORY 9931 Congruence 10032 The Euclidean Algorithm 10633 The RSA Method 11334 Error-Detecting and Error-Correcting Codes 12235 Matrix Codes 13236 Matrix Codes that Correct All Single-Digit Errors 140Historical Notes 147Supplementary Exercises 149Computer Projects 152Suggested Readings 1534 GRAPHS 15441 Graphs and Their Representations 15442 Pathsand Circuits 16443 Shortest Paths and Distance 18144 Coloringa Graph 19345 Directed Graphs and Multigraphs 202Historical Notes 219Supplementary Exercises 220Computer Projects 226Suggested Readings 2275 TREES 22851 Properties of Trees 22852 Spanning Trees 23853 Depth-First Search 25354 Rooted Trees 26655 Binary Trees and Traversals 27456 Optimal Binary Trees and Binary Search Trees 287Historical Notes 306Supplementary Exercises 308Computer Projects 311Suggested Readings 3126 MATCHING 31361 Sys