算法謎題（算法謎題）

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1、AlgorithmicPuzzlesThispageintentionallyleftblankALGORITHMICPUZZLESAnanyLevitinandMariaLevitin33OxfordUniversityPress,Inc.,publishesworksthatfurtherOxfordUniversity’sobjectiveofexcellenceinresearch,scholarship,andeducation.OxfordNewYorkAucklandCapeTownDaresSalaamHongKongKarachiKualaLumpur

2、MadridMelbourneMexicoCityNairobiNewDelhiShanghaiTaipeiTorontoWithof?cesinArgentinaAustriaBrazilChileCzechRepublicFranceGreeceGuatemalaHungaryItalyJapanPolandPortugalSingaporeSouthKoreaSwitzerlandThailandTurkeyUkraineVietnamCopyright?2011byOxfordUniversityPressPublishedbyOxfordUniversityP

3、ress,Inc.198MadisonAvenue,NewYork,NewYork10016www.oup.comOxfordisaregisteredtrademarkofOxfordUniversityPressAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,witho

4、utthepriorpermissionofOxfordUniversityPress.LibraryofCongressCataloging-in-PublicationDataLevitin,Anany.Algorithmicpuzzles/AnanyLevitin,MariaLevitin.p.cm.Includesbibliographicalreferencesandindex.ISBN978-0-19-974044-4(pbk.)1.Mathematicalrecreations.2.Algorithms.I.Levitin,Maria.II.Title.Q

5、A95.L4752011793.74—dc222010052043987654321PrintedintheUnitedStatesofAmericaonacid-freepaperToMaxwithloveThispageintentionallyleftblankContentsPrefaceixAcknowledgmentsxiiiListofPuzzlesxvTutorialPuzzlesxvMainSectionPuzzlesxviTheEpigraphPuzzle:Whosaidwhat?xxi1.Tutorials3GeneralStrategiesfor

6、AlgorithmDesign3AnalysisTechniques222.Puzzles32EasierPuzzles(#1to#50)32PuzzlesofMediumDif?culty(#51to#110)45HarderPuzzles(#111to#150)603.Hints724.Solutions82References241DesignStrategyandAnalysisIndex247IndexofTermsandNames254ThispageintentionallyleftblankPrefaceinQuestionsandAnswersWHAT

7、ISTHISBOOKABOUT?Thisbookisacollectionofalgorithmicpuzzles—puzzlesthatinvolve,explicitlyorimplicitly,clearlyde?nedproceduresforsolvingproblems.Itisauniquecollectionofsuchpuzzles.Thebookincludessomeoldclassics,whichhavebecomeapartofmathematicsandcomputersciencefolklore.Ital