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1、Exercise5.1.1Asaset:speed2.662.101.422.803.202.202.001.863.06Average=2.37Asabag:speed2.662.101.422.803.203.202.202.202.002.801.862.803.06Average=2.48Exercise5.1.2Asaset:hd25080320200300160Average=218Asabag:hd2502508025025032020025025030016016080Average=215Exercise5.1.3aAsaset:bore15161418Asabag:bor
2、e1516141615151418Exercise5.1.3bπbore(ShipsClasses)Exercise5.1.4aForbags:Ontheleft-handside:GivenbagsRandSwhereatupletappearsnandmtimesrespectively,theunionofbagsRandSwillhavetupletappearn+mtimes.ThefurtherunionofbagTwiththetupletappearingotimeswillhavetupletappearn+m+otimesinthefinalresult.Ontherig
3、ht-handside:GivenbagsSandTwhereatupletappearsmandotimesrespectively,theunionofbagsRandSwillhavetupletappearm+otimes.ThefurtherunionofbagRwiththetupletappearingntimeswillhavetupletappearm+o+ntimesinthefinalresult.Forsets:Thisisasimilarcasewhendealingwithbagsexceptthetupletcanonlyappearatmostonceinea
4、chset.Thetupletonlyappearsintheresultifallthesetshavethetuplet.Otherwise,thetupletwillnotappearintheresult.Sincewecannothaveduplicates,theresultonlyhasatmostonecopyofthetuplet.Exercise5.1.4bForbags:Ontheleft-handside:GivenbagsRandSwhereatupletappearsnandmtimesrespectively,theintersectionofbagsRandS
5、willhavetupletappearmin(n,m)times.ThefurtherintersectionofbagTwiththetupletappearingotimeswillproducetupletmin(o,min(n,m))timesinthefinalresult.Ontheright-handside:GivenbagsSandTwhereatupletappearsmandotimesrespectively,theintersectionofbagsRandSwillhavetupletappearmin(m,o)times.Thefurtherintersect
6、ionofbagRwiththetupletappearingntimeswillproducetupletmin(n,min(m,o))timesinthefinalresult.TheintersectionofbagsR,SandTwillyieldaresultwheretupletappearsmin(n,m,o)times.Forsets:Thisisasimilarcasewhendealingwithbagsexceptthetupletcanonlyappearatmostonceineachset.Thetupletonlyappearsintheresultifallt
7、hesetshavethetuplet.Otherwise,thetupletwillnotappearintheresult.Exercise5.1.4cForbags:Ontheleft-handside:GiventhattuplerinR,whichappearsmtimes,cansuccessfullyjoinwithtuplesinS,whichappearsntimes,weexpectthe
