Algorithms and Programming Problems and Solutions
"Algorithms and Programming" is primarily intended for a first year undergraduate course in programming. Structured in a problem-solution format, the text motivates the student to think through the programming process, thus developing a firm understa
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Editorial Board
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ABC
Alexander Shen Laboratoire d’Informatique Fondamentale de Marseille (LIF) CNRS, Universit´e de la M´editerran´ee, Universit´e de Provence CMI 39 Rue Joliot-Curie 13453 Marseille Cedex 13 France [email protected] and Russian Academy of Sciences Institute for Information Transmission Problems Bolshoy Karetny per. 19 Moscow, GSP-4, 127994 Russia
Series Editors Jonathan M. Borwein, FRSC Professor Laureate Director Centre for Computer Assisted Research Mathematics and its Applications, CARMA School of Mathematical & Physical Sciences University of Newcastle Callaghan NSW 2308 Australia [email protected]
Helge Holden Department of Mathematical Sciences Norwegian University of Science and Technology Alfred Getz vei 1 NO-7491 Trondheim Norway [email protected]
ISSN 1867-5506 e-ISSN 1867-5514 ISBN 978-1-4419-1747-8 e-ISBN 978-1-4419-1748-5 DOI 10.1007/978-1-4419-1748-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009942420 Mathematics Subject Classification (2000): 65K05, 65Yxx, 90Cxx, 68-01, 68W40 c Birkh¨auser 1997 1st edition: c Birkh¨auser 2008 Reprint of 1st edition in series: ‘Modern Birkh¨auser Classics’ c Springer Science+Business Media, LLC 2010 2nd edition: All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To the memory of Anna Pogossiants
Contents
Preface to the second edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
1
Variables, expressions, assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Problems without arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3 Inductive functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2
Generation of combinatorial objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Permutatio
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