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Algorithms and Complexity
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上传时间: 2008-11-23
详细说明： Algorithms and Complexity Herbert S. Wilf University of Pennsylvania Philadelphia, PA 19104-6395 CONTENTS Chapter 0: What This Book Is About 0.1Background ......................................1 0.2Hardvs.easyproblems .................................2 0.3Apreview .......................................4 Chapter 1: Mathematical Preliminaries 1.1Ordersofmagnitude ..................................5 1.2Positionalnumbersystems............................... 11 1.3Manipulationswithseries ............................... 14 1.4Recurre ncerelations.................................. 16 1.5Counting ...................................... 21 1.6Graphs ....................................... 24 Chapter 2: Recursive Algorithms 2.1Introduction ..................................... 30 2.2Quicksort ...................................... 31 2.3 Recursive graph algorithms ............................... 38 2.4Fastmatrixmultiplication............................... 47 2.5ThediscreteFouriertransform............................. 50 2.6ApplicationsoftheFFT................................ 56 2.7Areview....................................... 60 Chapter 3: The Network Flow Problem 3.1Introduction ..................................... 63 3.2 Algorithms for the network flow problem ......................... 64 3.3 The algorithm of Ford and Fulkerson .......................... 65 3.4Themax-flowmin-cuttheorem............................. 69 3.5 The complexity of the Ford-Fulkerson algorithm ..................... 70 3.6Layerednetworks................................... 72 3.7 The MPM Algorithm ................................. 76 3.8Applicationsofnetworkflow.............................. 77 Chapter 4: Algorithms in the Theory of Numbers 4.1Preliminaries..................................... 81 4.2Thegreatestcommondivisor.............................. 82 4.3 The extended Euclidean algorithm ........................... 85 4.4Primalitytesting ................................... 87 4.5 Interlude: the ring of integers modulo n ......................... 89 4.6Pseudoprimalitytests ................................. 92 4.7Proofofgoodnessofthestrongpseudoprimalitytest.................... 94 4.8 Factoring and cryptography .............................. 97 4.9 Factoring large integers ................................ 99 4.10Provingprimality...................................100 iii ...展开收缩
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