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Algorithms are the heart and soul of computer science. Their applications range from network routing and computational genomics to public-key cryptography and database system implementation. Studying algorithms can make you a better programmer, a clearer thinker, and a master of technical interviews. Algorithms Illuminated is an accessible introduction to the subject---a transcript of what an expert algorithms tutor would say over a series of one-on-one lessons. The exposition is rigorous but emphasizes the big picture and conceptual understanding over low-level implementation and mathematical details. Part 1 of the book series covers asymptotic analysis and big-O notation, divide-and-conquer algorithms and the master method, randomized algorithms, and several famous algorithms for sorting and selection. Preface 7 Introduction 13 Why Study Algorithms? 13 Integer Multiplication 15 Karatsuba Multiplication 18 MergeSort: The Algorithm 24 MergeSort: The Analysis 30 Guiding Principles for the Analysis of Algorithms 38 Problems 45 Asymptotic Notation 48 The Gist 48 Big-O Notation 57 Two Basic Examples 59 Big-Omega and Big-Theta Notation 62 Additional Examples 66 Problems 69 Divide-and-Conquer Algorithms 72 The Divide-and-Conquer Paradigm 72 Counting Inversions in O(n logn) Time 73 Strassen's Matrix Multiplication Algorithm 83 An O(n logn)-Time Algorithm for the Closest Pair 89 Problems 102 The Master Method 104 Integer Multiplication Revisited 104 Formal Statement 107 Six Examples 109 Proof of the Master Method 115 Problems 126 QuickSort 129 Overview 129 Partitioning Around a Pivot Element 133 The Importance of Good Pivots 140 Randomized QuickSort 144 Analysis of Randomized QuickSort 147 Sorting Requires (n logn) Comparisons 157 Problems 163 Linear-Time Selection 167 The RSelect Algorithm 167 Analysis of RSelect 175 The DSelect Algorithm 179 Analysis of DSelect 184 Problems 192 Quick Review of Proofs By Induction 195 A Template for Proofs by Induction 195 Example: A Closed-Form Formula 196 Example: The Size of a Complete Binary Tree 197 Quick Review of Discrete Probability 198 Sample Spaces 198 Events 199 Random Variables 201 Expectation 202 Linearity of Expectation 204 Example: Load Balancing 207 Index 211 "Algorithms are the heart and soul of computer science. Their applications range from network routing and computational genomics to public-key cryptography and database system implementation. Studying algorithms can make you a better programmer, a clearer thinker, and a master of technical interviews. Algorithms Illuminated is an accessible introduction to the subject--a transcript of one-on-one lessons. Part 1 covers asymptotic analysis and big-O notation, divide-and-conquer algorithms and the master method, randomized algorithms, and several famous algorithms for sorting and selection."--Back cover