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Wilf presents a structured introduction to key themes in algorithms and computational complexity. The material is organized into chapters covering mathematical preliminaries, recursive algorithms (including Quicksort, fast matrix multiplication, and FFT applications), the network flow problem and its classic max-flow min-cut theory, and number-theoretic algorithmic topics such as primality testing and factoring. 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Wilf  \nUniversity of Pennsylvania  \nPhiladelphia, PA 19104-6395  \nCopyright Notice  \nCopyright 1994 by Herbert S. Wilf. This material may be reproduced for any educational purpose, multiple copies may be made for classes, etc. Charges, if any, for reproduced copies must be just enough to recover reasonable costs of reproduction. Reproduction for commercial purposes is prohibited. This cover page must be included in all distributed copies.  \nInternet Edition, Summer, 1994  \nThis edition of Algorithms and Complexity is available at the web site \u003C[http://www/cis.upenn.edu/ wilf](http://www/cis.upenn.edu/ wilf)>. It may be taken at no charge by all interested persons. Comments and corrections are welcome, and should be sent to [wilf@math.upenn.edu](wilf@math.upenn.edu)  \nCONTENTS  \nChapter 0: What This Book Is About  \n0.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1  \n0.2 Hard vs. easy problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2  \n0.3 A preview     4  \nChapter 1: Mathematical Preliminaries  \n1.1 Orders of magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5  \n1.2 Positional number systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11  \n1.3 Manipulations with series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14  \n1.4 Recurrence relations     16  \n1.5 Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21  \n1.6 Graphs     24  \nChapter 2: Recursive Algorithms  \n2. 1 Introduction     30  \n2.2 Quicksort     31  \n2.3 Recursive graph algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38  \n2.4 Fast matrix multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47  \n2.5 The discrete Fourier transform     50  \n2.6 Applications of the FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56  \n2.7 A review     60  \nChapter 3: The Network Flow Problem  \n3. 1 Introduction     63  \n3.2 Algorithms for the network 􀀍ow problem . . . . . . . . . . . . . . . . . . . . . . . . . 64  \n3.3 The algorithm of Ford and Fulkerson . . . . . . . . . . . . . . . . . . . . . . . . . . 65  \n3.4 The max-􀀍ow min-cut theorem     69  \n3.5 The complexity of the Ford-Fulkerson algorithm . . . . . . . . . . . . . . . . . . . . . 70  \n3.6 Layered networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72  \n3.7 The MPM Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76  \n3.8 Applications of network 􀀍ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77  \nChapter 4: Algorithms in the Theory of Numbers  \n4. 1 Preliminaries     81  \n4.2 The greatest common divisor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82  \n4.3 The extended Euclidean algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 85  \n4.4 Primality testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87  \n4.5 Interlude: the ring of integers modulo n . . . . . . . . . . . . . . . . . . . . . . . . . 89  \n4.6 Pseudoprimality tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92  \n4.7 Proof of goodness of the strong pseudoprimality test . . . . . . . . . . . . . . . . . . . . 94  \n4.8 Factoring and cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97  \n4.9 Factoring large integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99  \n4.10 Proving primality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100  \nChapter 5: NP-completeness  \n5. 1 Introduction     104  \n5.2 Turing machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109  \n5.3 Cook's theorem     112  \n5.4 Some other NP-complete problems     116  \n5.5 Half a loaf     119  \n5.6 Backtracking (I): independent sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 122  \n5.7","cbCaitbBkPPDo3tr","https://ap.wps.com/l/cbCaitbBkPPDo3tr","pdf",1010138,139,"English","# Chapter 0: What This Book Is About\n## 0.1 Background\n## 0.2 Hard vs. easy problems\n## 0.3 A preview\n# Chapter 1: Mathematical Preliminaries\n## 1.1 Orders of magnitude\n## 1.2 Positional number systems\n## 1.3 Manipulations with series\n## 1.4 Recurrence relations\n## 1.5 Counting\n## 1.6 Graphs\n# Chapter 2: Recursive Algorithms\n## 2.1 Introduction\n## 2.2 Quicksort\n## 2.3 Recursive graph algorithms\n## 2.4 Fast matrix multiplication\n## 2.5 The discrete Fourier transform\n## 2.6 Applications of the FFT\n## 2.7 A review\n# Chapter 3: The Network Flow Problem\n## 3.1 Introduction\n## 3.2 Algorithms for the network flow problem\n## 3.3 The algorithm of Ford and Fulkerson\n## 3.4 The max-flow min-cut theorem\n## 3.5 The complexity of the Ford-Fulkerson algorithm\n## 3.6 Layered networks\n## 3.7 The MPM Algorithm\n## 3.8 Applications of network flow\n# Chapter 4: Algorithms in the Theory of Numbers\n## 4.1 Preliminaries\n## 4.2 The greatest common divisor\n## 4.3 The extended Euclidean algorithm\n## 4.4 Primality testing\n## 4.5 Interlude: the ring of integers modulo n\n## 4.6 Pseudoprimality tests\n## 4.7 Proof of goodness of the strong pseudoprimality test\n## 4.8 Factoring and cryptography\n## 4.9 Factoring large integers\n## 4.10 Proving primality\n# Chapter 5: NP-completeness\n## 5.1 Introduction\n## 5.2 Turing machines\n## 5.3 Cook's theorem\n## 5.4 Some other NP-complete problems\n## 5.5 Half a loaf\n## 5.6 Backtracking (I): independent sets\n## 5.7 Backtracking (II): graph coloring\n## 5.8 Approximate algorithms for hard problems\n# Preface","[{\"question\":\"What topics does Chapter 0 introduce?\",\"answer\":\"Chapter 0 explains what the book is about, including background material and the distinction between hard and easy problems, followed by a brief preview of later content.\"},{\"question\":\"Which problems and algorithms are covered in Chapter 2?\",\"answer\":\"Chapter 2 focuses on recursive algorithms, highlighting Quicksort, recursive graph algorithms, fast matrix multiplication, the discrete Fourier transform, and applications of the FFT, along with a review section.\"},{\"question\":\"How does the book approach NP-completeness?\",\"answer\":\"Chapter 5 covers NP-completeness starting from an introduction, then develops concepts through Turing machines and Cook’s theorem, surveys additional NP-complete problems, and discusses backtracking and approximate algorithms for hard problems.\"}]","Algorithms and Complexity - Chapter Outline - Introductory Table of Contents | PDF",350]