08年acm浙江省题目.docx
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08年acm浙江省题目.docx
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08年acm浙江省题目
一、AccuratelySay"CocaCola"!
Timelimit:
1Seconds Memorylimit:
32768K
TotalSubmit:
226 AcceptedSubmit:
132
InapartyheldbyCocaColacompany,severalstudentsstandinacircleandplayagame.
Oneofthemisselectedasthefirst,andshouldsaythenumber1.Thentheycontinuetocountnumberfrom1onebyone(clockwise).Thegameisinterestinginthat,oncesomeonecountsanumberwhichisamultipleof7(e.g.7,14,28,...)orcontainsthedigit'7'(e.g.7,17,27,...),heshallsay"CocaCola"insteadofthenumberitself.
Forexample,4studentsplaythisgame.Atsometime,thefirstonesays25,thenthesecondshouldsay26.Thethirdshouldsay"CocaCola"because27containsthedigit'7'.Thefourthoneshouldsay"CocaCola"too,because28isamultipleof7.Thenthefirstonesays29,andthegamegoeson.Whensomeonemakesamistake,thegameends.
Duringagame,youmayhearaconsecutiveofp"CocaCola"s.Sowhatistheminimumnumberthatcanmakethissituationhappen?
Forexamplep=2,thatmeansthereareaconsecutiveof2"CocaCola"s.Thissituationhappensin27-28asstatedabove.27isthentheminimumnumbertomakethissituationhappen.
Input
Standardinputwillcontainmultipletestcases.ThefirstlineoftheinputisasingleintegerT(1<=T<=100)whichisthenumberoftestcases.AnditwillbefollowedbyTconsecutivetestcases.
Thereisonlyonelineforeachcase.Thelinecontainsonlyoneintegerp(1<=p<=99).
Output
Resultsshouldbedirectedtostandardoutput.Theoutputofeachtestcaseshouldbeasingleintegerinoneline,whichistheminimumpossiblenumberforthefirstofthep"CocaCola"sstandsfor.
SampleInput
2
2
3
SampleOutput
27
70
二、BuildTheElectricSystem
Timelimit:
1Seconds Memorylimit:
32768K
TotalSubmit:
198 AcceptedSubmit:
75
Inlastwinter,therewasabigsnowstorminSouthChina.Theelectricsystemwasdamagedseriously.Lotsofpowerlineswerebrokenandlotsofvillageslostcontactwiththemainpowergrid.Thegovernmentwantstoreconstructtheelectricsystemassoonaspossible.So,asaprofessionalprogrammer,youareaskedtowriteaprogramtocalculatetheminimumcosttoreconstructthepowerlinestomakesurethere'satleastonewaybetweeneverytwovillages.
Input
Standardinputwillcontainmultipletestcases.ThefirstlineoftheinputisasingleintegerT(1<=T<=50)whichisthenumberoftestcases.AnditwillbefollowedbyTconsecutivetestcases.
Ineachtestcase,thefirstlinecontainstwopositiveintegersNandE(2<=N<=500,N<=E<=N*(N-1)/2),representingthenumberofthevillagesandthenumberoftheoriginalpowerlinesbetweenvillages.TherefollowElines,andeachofthemcontainsthreeintegers,A,B,K(0<=A,B Output Foreachtestcaseintheinput,there'sonlyonelinethatcontainstheminimumcosttorecovertheelectricsystemtomakesurethatthere'satleastonewaybetweeneverytwovillages. SampleInput 1 33 015 020 129 SampleOutput 5 三、ColorfulRainbows Timelimit: 1Seconds Memorylimit: 32768K TotalSubmit: 5 AcceptedSubmit: 1 Evelynlikesdrawingverymuch.Today,shedrawslotsofrainbowsonwhitepaperofinfinitesize,eachusingadifferentcolor.Sincethere'retoomanyrainbowsnow,shewonders,howmanyofthemcanbeseen? Forsimplicity,eachrainbowLiisrepresentedasanon-verticallinespecifiedbytheequation: y=aix+bi.ArainbowLicanbeseenifthereexistssomex-coordinatex0atwhich,itsy-coordinateisstrictlygreaterthany-coordinatesofanyotherrainbows: aix0+bi>ajx0+bjforallj! =i. Now,yourtaskis,giventhesetofrainbowsdrawn,figureoutthenumberofrainbowsthatcanbeseen. Input Standardinputwillcontainmultipletestcases.ThefirstlineoftheinputisasingleintegerT(1<=T<=60)whichisthenumberoftestcases.AnditwillbefollowedbyTconsecutivetestcases. There'sablanklinebeforeeverycase.Ineachtestcase,therewillfirstbeanintegern(1<=n<=5000),whichisthenumberofrainbows.Thennconsecutiverealnumberpairsfollow.Eachpaircontainstworealnumbers,aiandbi,representingrainbowLi: y=aix+bi.Notworainbowswillbethesame,thatistosay,havethesameaandb. Output Resultsshouldbedirectedtostandardoutput.Theoutputofeachtestcaseshouldbeasingleinteger,whichisthenumberofrainbowsthatcanbeseen. SampleInput 2 1 11 3 10 20 30 SampleOutput 1 2 四、DifferenceGame Timelimit: 1Seconds Memorylimit: 32768K TotalSubmit: 0 AcceptedSubmit: 0 Nowyouaregoingtoplayaninterestinggame.Inthisgame,youaregiventwogroupsofdistinctintegersandCcoins.Thetwogroups,namedGaandGbrespectively,arenotemptyandcontainthesamenumberofintegersatfirst.Eachtimeyoucanmoveoneintegerinonegrouptotheothergroup.Butamovethatmakesagroupemptyisconsideredasinvalid.Eachmovewillcostyoupcoins,andpequalsthedifferenceofthesizebetweenthetwogroup(taketheabsolutevalue.e.g.movinganumberfromthegroupofsize4tothegroupofsize6willcostyou|4-6|=2coins,andmovinganumberbetweentwogroupwithsamesizewillnotcostanycoins).Youcandoasmanymovesasyouwish,solongasthetotalcostdoesnotexceedC. LetMbetheminimumintegerinGa,andNbethemaximumintegerinGb.Thepurposeofthisgameistoproduceamaximum(M-N). Input Standardinputwillcontainmultipletestcases.ThefirstlineoftheinputisasingleintegerT(1<=T<=60)whichisthenumberoftestcases.AnditwillbefollowedbyTconsecutivetestcases. EachcasebeginwithtwointegersS(1<=S<=20000,indicatingthesizeofGaandGbatfirst)andC(0<=C<=1000000).TwolinesofSintegersfollow,representingthenumbersinGaandGbrespectively.Alltheseintegersaredistinctandarebetween1and50000,bothinclusive. Output Resultsshouldbedirectedtostandardoutput.Theoutputofeachtestcaseshouldbeasingleintegerinoneline,whichisthemaximumpossiblevalueforM-Naftersomemoves. SampleInput 2 110 10 12 210 12 34 SampleOutput -2 1 Hint ForSample1,twogroupsareofsize1,sonomovescanbedonebecauseanymovingwillmakeGaorGbempty,whichisnotvalid.SoM=10,N=12,M-N=-2. ForSample2,onevalidstepsofmovesis: Move1inGatoGb,cost0coins. Move3inGbtoGa,cost2coins. Move4inGbtoGa,cost0coins. ThenGacontains234,Gbcontains1,M=2,N=1,M-N=1.Thisisthemaximumpossiblevalue. 五、EasyTask Timelimit: 1Seconds Memorylimit: 32768K TotalSubmit: 213 AcceptedSubmit: 126 Calculatingthederivationofapolynomialisaneasytask.Givenafunctionf(x),weuse(f(x))'todenoteitsderivation.Weusex^ntodenotexn.Tocalculatethederivationofapolynomial,youshouldknow3rules: (1)(C)'=0whereCisaconstant. (2)(Cx^n)'=C*n*x^(n-1)wheren>=1andCisaconstant. (3)(f1(x)+f2(x))'=(f1(x))'+(f2(x))'. Itiseasytoprovethatthederivationapolynomialisalsoapolynomial. Herecomestheproblem,givenapolynomialf(x)withnon-negativecoefficients,canyouwriteaprogramtocalculatethederivationofit? Input Standardinputwillcontainmultipletestcases.ThefirstlineoftheinputisasingleintegerT(1<=T<=1000)whichisthenumberoftestcases.AnditwillbefollowedbyTconsecutivetestcases. Thereareexactly2linesineachtestcase.ThefirstlineofeachtestcaseisasinglelinecontaininganintegerN(0<=N<=100).ThesecondlinecontainsN+1non-negativeintegers,CN,CN-1,...,C1,C0,(0<=Ci<=1000),whicharethecoefficientsoff(x).Ciisthecoefficientofthetermwithdegreeiinf(x).(CN! =0) Output Foreachtestcasecalculatetheresultpolynomialg(x)alsoinasingleline. (1)Ifg(x)=0justoutputinteger0.otherwise (2)supposeg(x)=Cmx^m+Cm-1x^(m-1)+...+C0(Cm! =0),thenoutputtheintegersCm,Cm-1,...C0. (3)Thereisasinglespacebetweentwointegersbutnospacesafterthelastinteger. SampleInput 3 0 10 2 321 3 10012 SampleOutput 0 62 3001 六、Faster,Higher,Stronger Timelimit: 1Seconds Memorylimit: 32768K TotalSubmit: 205 AcceptedSubmit: 145 Intheyear2008,the29thOlympicGameswillbeheldinBeijing.ThiswillsignifytheprosperityofChinaandBeijingOlympicsistobeafestivalforpeopleallovertheworldaswell. ThemottoofOlympicGamesis"Citius,Altius,Fortius",whichmeans"Faster,Higher,Stronger". Inthisproblem,therearesomerecordsintheOlympicGames.Yourtaskistofindoutwhichoneisfaster,whichoneishigherandwhichoneisstronger. Input Standardinputwillcontainmultipletestcases.ThefirstlineoftheinputisasingleintegerT(1<=T<=50)whichisthenumberoftestcases.AnditwillbefollowedbyTconsecutivetestcases. Eachtestcasehas3lines.Thefirstlineisthetypeoftherecords,whichcanonlybe"Faster""Higher"or"Stronger".ThesecondlineisapositiveintegerNmeaningthenumberoftherecordsinthistestcase.ThethirdlinehasNpositiveintegers,i.e.therecordsdata.Alltheintegersinthisproblemaresmallerthan2008. Output Resultsshouldbedirectedtosta
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