[算法-具体数学]Concrete Mathematics

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1、CONCRETEMATHEMATICSSecondEditionDedicatedtoLeonhardEuler(1707{1783)AFoundationforComputerScienceCONCRETEMATHEMATICSSecondEditionRonaldL.GrahamAT&TBellLaboratoriesDonaldE.KnuthStanfordUniversityOrenPatashnikCenterforCommunicationsResearch677ADDISON-WESLEYPUBLISHINGCOMPANYReading,Massachuset

2、tsMenloPark,CaliforniaNewYorkDonMills,OntarioWokingham,EnglandAmsterdamBonnSydneySingaporeTokyoMadridSanJuanMilanParisLibraryofCongressCataloging-in-PublicationDataGraham,RonaldLewis,1935-Concretemathematics:afoundationforcomputerscience/RonaldL.Graham,DonaldE.Knuth,OrenPatashnik.--2nded.x

3、iii,657p.24cm.Bibliography:p.604Includesindex.ISBN0-201-55802-51.Mathematics.2.Computerscience--Mathematics.I.Knuth,DonaldErvin,1938-.II.Patashnik,Oren,1954-.III.Title.QA39.2.G7331994510--dc2093-40325CIPReproducedbyAddison-Wesleyfromcamera-readycopysuppliedbytheauthors.Copyright°c1994,1989

4、byAddison-WesleyPublishingCompany,Inc.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechan-ical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.PrintedintheUnitedStatesofAme

5、rica.12345678910{MA{9897969594PrefaceAudience,level,THISBOOKISBASEDonacourseofthesamenamethathasbeentaughtandtreatment

6、annuallyatStanfordUniversitysince1970.Aboutftystudentshavetakenitadescriptionofeachyear

7、juniorsandseniors,butmostlygraduatestudents

8、andalumnisuchmattersiswhatprefacesare

9、oftheseclasseshavebeguntospawnsimilarcourseselsewhere.Thusthetimesupposedtobeseemsripetopresentthematerialtoawideraudience(includingsophomores).about."ItwasadarkandstormydecadewhenConcreteMathematicswasborn.

10、P.R.Halmos[173]Long-heldvalueswereconstantlybeingquestionedduringthoseturbulentyea

11、rs;collegecampuseswerehotbedsofcontroversy.Thecollegecurriculumitselfwaschallenged,andmathematicsdidnotescapescrutiny.JohnHam-mersleyhadjustwrittenathought-provokingarticleOntheenfeeblementofmathematicalskillsby`ModernMathematics'andbysimilarsoftintellectualt