IntroductiontoAlgorithms - (EPUB全文下载)

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THOMAS H. CORMEN
CHARLES E. LEISERSON
RONALD L. RIVEST CLIFFORD STEIN
INTRODUCTION TO
ALGORITHMS
THIRD EDITION
Introduction to Algorithms
Third Edition
Thomas H. Cormen Charles E. Leiserson Ronald L. Rivest Clifford Stein
Introduction to Algorithms
Third Edition

The MIT Press
Cambridge, Massachusetts London, England
c 2009 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.
For information about special quantity discounts, please email special sales@mitpress.mit.edu. This book was set in Times Roman and Mathtime Pro 2 by the authors.
Printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Introduction to algorithms / Thomas H. Cormen...[etal.].—3rded.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-262-03384-8 (hardcover : alk. paper)—ISBN 978-0-262-53305-8 (pbk. : alk. paper) 1. Computer programming. 2. Computer algorithms. I. Cormen, Thomas H.
QA76.6.I5858 2009 005.1—dc22
2009008593 10 98 765 43 2Contents
Preface xiii
I Foundations
Introduction 3
1 The Role of Algorithms in Computing 5
1.1 Algorithms 5
1.2 Algorithms as a technology 11
2 Getting Started 16
2.1 Insertion sort 16
2.2 Analyzing algorithms 23
2.3 Designing algorithms 29
3 Growth of Functions 43
3.1 Asymptotic notation 43
3.2 Standard notations and common functions 53
4 Divide-and-Conquer 65
4.1 The maximum-subarray problem 68
4.2 Strassen’s algorithm for matrix multiplication 75
4.3 The substitution method for solving recurrences 83
4.4 The recursion-tree method for solving recurrences 88

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4.5 The master method for solving recurrences 93
4.6 Proof of the master theorem 97
5 Probabilistic Analysis and Randomized Algorithms 114
5.1 The hiring problem 114
5.2 Indicator random variables 118

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5.3 Randomized algorithms 122
5.4 Probabilistic analysis and further uses of indicator random variables
130
vi Contents
II Sorting and Order Statistics
Introduction 147
6Heapsort 151
6.1 Heaps 151
6.2 Maintaining the heap property 154
6.3 Building a heap 156
6.4 The heapsort algorithm 159
6.5 Priority queues 162
7 Quicksort 170
7.1 Description of quicksort 170
7.2 Performance of quicksort 174
7.3 A randomized version of quicksort 179
7.4 Analysis of quicksort 180
8 Sorting in Linear Time 191
8.1 Lower bounds f ............

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