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Introduction to Algorithms, Second Edition Thomas H. Cormen Charles E. Leiserson Ronald L. Rivest Clifford Stein The MIT Press Cambridge , Massachusetts London, England McGraw-Hill Book Company Boston Burr Ridge , IL Dubuque , IA Madison , WI New York San Francisco St. Louis Montréal Toronto This book is one of a series of texts written by faculty of the Electrical Engineering and Computer Science Department at the Massachusetts Institute of Technology. It was edited and produced by The MIT Press under a joint production-distribution agreement with the McGraw-Hill Book Company. Ordering Information: North America Text orders should be addressed to the McGraw-Hill Book Company. All other orders should be addressed to The MIT Press. Outside North America All orders should be addressed to The MIT Press or its local distributor. Copyright © 2001 by The Massachusetts Institute of Technology First edition 1990 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. This book was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Introduction to algorithms / Thomas H. Cormen ... [et al.].-2nd ed. p. cm. Includes bibliographical references and index. ISBN 0-262-03293-7 (hc.: alk. paper, MIT Press).-ISBN 0-07-013151-1 (McGraw-Hill) 1. Computer programming. 2. Computer algorithms. I. Title: Algorithms. II. Cormen, Thomas H. QA76.6 I5858 2001 005.1-dc21 2001031277