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File Algorithms

Algorithms (ISSN 1999-4893; CODEN: ALGOCH), an open access journal of computer science, theory, methods and interdisciplinary applications, data and information systems, software engineering, artificial intelligence, automation and control systems, is published online quarterly by MDPI. | Algorithms Copyright 2006 S. Dasgupta C. H. Papadimitriou and U. V. Vazirani July 18 2006 2 Algorithms Contents Preface 9 0 Prologue 11 0.1 Books and algorithms. 11 0.2 Enter Fibonacci.12 0.3 Big-O notation.15 Exercises.18 1 Algorithms with numbers 21 1.1 Basic arithmetic . 21 1.2 Modular arithmetic.25 1.3 Primality testing .33 1.4 Cryptography .39 1.5 Universal hashing.43 Exercises . 48 Randomized algorithms a virtual chapter 39 2 Divide-and-conquer algorithms 55 2.1 Multiplication.55 2.2 Recurrence relations.58 2.3 Mergesort.60 2.4 Medians.64 2.5 Matrix multiplication.66 2.6 The fast Fourier transform.68 Exercises . 83 3 Decompositions of graphs 91 3.1 Why graphs .91 3.2 Depth-first search in undirected graphs.93 3.3 Depth-first search in directed graphs.98 3.4 Strongly connected components.101 Exercises . 106