Algorithmic Puzzles

280 Pages·2012·1.57 MB·English

Algorithmic
Puzzles
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ALGORITHMIC
PUZZLES
Anany Levitin
and
Maria Levitin
3
3
OxfordUniversityPress,Inc.,publishesworksthatfurther
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Copyright©2011byOxfordUniversityPress
PublishedbyOxfordUniversityPress,Inc.
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OxfordisaregisteredtrademarkofOxfordUniversityPress
Allrightsreserved.Nopartofthispublicationmaybereproduced,
storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,
electronic,mechanical,photocopying,recording,orotherwise,
withoutthepriorpermissionofOxfordUniversityPress.
LibraryofCongressCataloging-in-PublicationData
Levitin,Anany.
Algorithmicpuzzles/AnanyLevitin,MariaLevitin.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-19-974044-4(pbk.)
1.Mathematicalrecreations. 2.Algorithms.
I.Levitin,Maria. II.Title.
QA95.L4752011
793.74—dc22 2010052043
9 8 7 6 5 4 3 2 1
PrintedintheUnitedStatesofAmerica
onacid-freepaper
To Max with love
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Contents
Preface ix
Acknowledgments xiii
ListofPuzzles xv
TutorialPuzzles xv
MainSectionPuzzles xvi
TheEpigraphPuzzle:Whosaidwhat? xxi
1. Tutorials 3
GeneralStrategiesforAlgorithmDesign 3
AnalysisTechniques 22
2. Puzzles 32
EasierPuzzles(#1to#50) 32
PuzzlesofMediumDifficulty(#51to#110) 45
HarderPuzzles(#111to#150) 60
3. Hints 72
4. Solutions 82
References 241
DesignStrategyandAnalysisIndex 247
IndexofTermsandNames 254
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PrefaceinQuestionsand
Answers
WHAT IS THIS BOOK ABOUT?
Thisbookisacollectionofalgorithmicpuzzles—puzzlesthatinvolve,explicitlyor
implicitly,clearlydefinedproceduresforsolvingproblems.Itisauniquecollection
ofsuchpuzzles.Thebookincludessomeoldclassics,whichhavebecomeapartof
mathematicsandcomputersciencefolklore.Italsocontainsnewerexamples,some
ofwhichhavebeenaskedduringjobinterviewsatmajorcompanies.
Thebookhastwomaingoals:
• Toentertainawiderangeofreadersinterestedinpuzzles
• Topromotedevelopmentofhigh-levelalgorithmicthinking(withno
computerprogramming),supportedbyacarefullydevelopedlistof
generalalgorithmdesignstrategiesandanalysistechniques
Although algorithms do constitute the cornerstone of computer science and
no sensible computer programming is possible without them, it is a common
misconceptiontoequatethetwo.Somealgorithmicpuzzlespredatecomputersby
morethanathousandyears.Itistrue,however,thattheproliferationofcomputers
has made algorithmic problem solving important in many areas of modern life,
fromhardandsoftsciencestoartandentertainment.Solvingalgorithmicpuzzlesis
themostproductiveanddefinitelymostenjoyablewaytodevelopandstrengthen
one’salgorithmicthinkingskills.
WHOM IS THIS BOOK FOR?
There are three large categories of readers who should be interested in this
book:
• Puzzlelovers
• Peopleinterestedindevelopingalgorithmicthinking,includingteachers
andstudents
• Peoplepreparingforinterviewswithcompaniesgivingpuzzlesaswellas
peopleconductingsuchinterviews
All we have to say to puzzle lovers is to reassure them that they could enjoy
this collection as they would a collection not dedicated to any particular theme
or type of puzzle. They will encounter a few all-time favorites, but, hopefully,
will also find a number of little-known puzzle gems. No computing background
ix