山东省赛ACM真题重点.docx

山东省赛ACM真题重点.docx

《山东省赛ACM真题重点.docx》由会员分享，可在线阅读，更多相关《山东省赛ACM真题重点.docx（15页珍藏版）》请在冰豆网上搜索。

山东省赛ACM真题重点

ProblemAPhoneNumber

WeknowthatifaphonenumberAisanotherphonenumberB’sprefix,Bisnotabletobecalled.Foranexample,Ais123whileBis12345,afterpressing123,wecallA,andnotabletocallB.

GivenNphonenumbers,yourtaskistofindwhetherthereexitstwonumbersAandBthatAisB’sprefix.

Input

Theinputconsistsofseveraltestcases.

ThefirstlineofinputineachtestcasecontainsoneintegerN（0

ThenextlinecontainsNintegers,describingthephonenumbers.

Thelastcaseisfollowedbyalinecontainingonezero.

Output

Foreachtestcase,ifthereexitsaphonenumberthatcannotbecalled,print“NO”,otherwiseprint“YES”instead.

SampleInputOutputfortheSampleInput

2

012

012345

2

12

012345

0

NO

YES

ProblemBBalloons

BothSayaandKudolikeballoons.Oneday,theyheardthatinthecentralpark,therewillbethousandsofpeopleflyballoonstopatternabigimage.

Theywereveryinterestedaboutthisevent,andalsocuriousabouttheimage.

Sincetherearetoomanyballoons,itisveryhardforthemtocomputeanythingtheyneed.Canyouhelpthem?

YoucanassumethattheimageisanN*Nmatrix,whileeachelementcanbeeitherballoonsorblank.

SupposeelementAandelementBarebothballoons.Theyareconnectedif:

iTheyareadjacent;

iiThereisalistofelementC1,C2,…,Cn,whileAandC1areconnected,C1andC2areconnected…CnandBareconnected.

Andaconnectedblockmeansthateverypairofelementsintheblockisconnected,whileanyelementintheblockisnotconnectedwithanyelementoutoftheblock.

ToSaya,elementA

andB

isadjacentif

ButtoKudo,elementA

andelementB

isadjacentif

and

Theywanttoknowthatthere’showmanyconnectedblockswiththereowndefinitionofadjacent?

Input

Theinputconsistsofseveraltestcases.

ThefirstlineofinputineachtestcasecontainsoneintegerN（0

EachofthenextNlinescontainsastringwhoselengthisN,representstheelementsofthematrix.Thestringonlyconsistsof0and1,while0representsablockand1representsballoons.

Thelastcaseisfollowedbyalinecontainingonezero.

Output

Foreachcase,printthecasenumber（1,2…andtheconnectedblock’snumberswithSayaandKudo’sdefinition.Youroutputformatshouldimitatethesampleoutput.Printablanklineaftereachtestcase.

SampleInputOutputfortheSampleInput

5

11001

00100

11111

11010

10010

0

Case1:

32

ProblemCClockwise

SayahavealongnecklacewithNbeads,andshesignsthebeadsfrom1toN.ThenshefixesthemtothewalltoshowN-1vectors–vectoristartsfrombeadiandendupwithbeadi+1.

Oneday,KudocomestoSaya’shome,andsheseesthebeadsonthewall.Kudosaysitisnotbeautiful,andletSayamakeitbetter.

Shesays:

“Ithinkitwillbebetterifitisclockwiserotation.Itmeansthattoanyvectori（i-1,itwillhavethesamedirectionwithvectori+1afterclockwiserotateTdegrees,while0≤T<180.”

ItishardforSayatoresetthebeads’places,soshecanonlyremovesomebeads.Tosavingthebeads,althoughsheagreeswithKudo’ssuggestion,shethinkscounterclockwiserotationisalsoacceptable.Acounterclockwiserotationmeanstoanyvectori（i-1,itwillhavethesamedirectionwithvectori+1aftercounterclockwiserotateTdegrees,while0≤180.”

Sayastartstocomputeatleasthowmanybeadssheshouldremovetomakeaclockwiserotationoracounterclockwiserotation.

Sincethenecklaceisvery-verylong,canyouhelphertosolvethisproblem?

Input

Theinputconsistsofseveraltestcases.

ThefirstlineofinputineachtestcasecontainsoneintegerN（2

EachofthenextNlinescontainstwointegerxandy,representsthecoordinateofthebeads.Youcanassumethat0

Thelastcaseisfollowedbyalinecontainingonezero.

Output

Foreachcase,printyouranswerwiththefollowingformat:

Ifitisclockwiserotationwithoutremovinganybeads,pleaseprint“C;otherwiseifitiscounterclockwiserotationwithoutremovinganybeads,print“CC”instead;otherwise,supposeremoveatleastxbeadstomakeaclockwiserotationandremoveatleastybeadstomakeacounterclockwiserotation.Ifx≤y,print“Removexbead（s,C”,otherwiseprint“Removexbead（s,CC”instead.

Youroutputformatshouldimitatethesampleoutput.Printablanklineaftereachtestcase.

SampleInputOutputfortheSampleInput

3

11

22

33

3

p11

22

pspan11p

4

11

22

33

22

0

C

CC

Remove1bead（s,C

ProblemDShopping

SayaandKudogoshoppingtogether.

Youcanassumethestreetasastraightline,whiletheshopsaresomepointsontheline.

Theyparktheircarattheleftmostshop,visitalltheshopsfromlefttoright,andgobacktotheircar.

Yourtaskistocalculatethelengthoftheirroute.

Input

Theinputconsistsofseveraltestcases.

ThefirstlineofinputineachtestcasecontainsoneintegerN（0

ThenextlinecontainsNintegers,describingthesituationoftheshops.Youcanassumethatthesituationsoftheshopsarenon-negativeintegerandsmallerthan2^30.

Thelastcaseisfollowedbyalinecontainingonezero.

Output

Foreachtestcase,printthelengthoftheirshoppingroute.

SampleInputOutputfortheSampleInput

4

24138937

6

73041143942

0

152

70

Explanationforthefirstsample:

Theyparktheircaratshop13;gotoshop24,37and89andfinallyreturntoshop13.Thetotallengthis（24-13+（37-24+（89-37+（89-13=152

ProblemEEmergency

Kudo’srealnameisnotKudo.HernameisKudryavkaAnatolyevnaStrugatskia,andKudoisonlyhernickname.

Now,sheisfacinganemergencyinherhometown:

Hermotherisdevelopinganewkindofspacecraft.Thisplancostsenormousenergybutfinallyfailed.What’smore,becauseofthefailedproject,thegovernmentdoesn’thaveenoughresourcetakemeasuretotherisingsealevelscausedbyglobalwarming,leadtoanislandfloodedbythesea.

Dissatisfiedwithhermother’sspacecraftandthegovernment,civilwarhasbrokenout.Thefoewantstoarrestthespacecraftproject’sparticipantsandthe“Chiefcriminal”–Kudo’smother–DoctorT’sfamily.

Atthebeginningofthewar,allthecitiesareoccupiedbythefoe.Butastimegoesby,thecitiesrecapturedonebyone.

Topreventfromthefoe’sarrestandboostmorale,Kudoandsomeotherpeoplehavetodistractfromacitytoanother.Althoughtheycanusesomeothermeanstotransport,themostconvenientwayisusingtheinter-cityroads.Assumingthecityasanodeandaninter-cityroadasanedge,youcantreatthemapasaweighteddirectedmultigraph.Aninter-cityroadisavailableifbothitsendpointisrecaptured.

Herecomestheproblem.

Giventhetrafficmap,andtherecapturedsituation,canyoutellKudowhat’stheshortestpathfromonecitytoanotheronlypassingtherecapturedcities?

Input

Theinputconsistsofseveraltestcases.

ThefirstlineofinputineachtestcasecontainsthreeintegersN（0

EachofthenextMlinescontainsthreeintegerx,yandz,representsthereisaninter-cityroadstartsfromx,endupwithyandthelengthisz.Youcanassumethat0

EachofthenextQlinescontainstheoperationswiththefollowingformat:

a0x–meanscityxhasjustbeenrecaptured.

b1xy–meansaskingtheshortestpathfromxtoyonlypassingtherecapturedcities.

Thelastcaseisfollowedbyalinecontainingthreezeros.

Output

Foreachcase,printthecasenumber（1,2…first.

Foreachoperation0,ifcityxisalreadyrecaptured（thatis,thesame0xoperationappearsagain,print“Cityxisalreadyrecaptured.”

Foreachoperation1,ifcityxoryisnotrecapturedyet,print“Cityxoryisnotavailable.”otherwiseifKudocangofromcityxtocityyonlypassingtherecapturedcities,printtheshortestpath’slength;otherwiseprint“Nosuchpath.”

Youroutputformatshouldimitatethesampleoutput.Printablanklineaftereachtestcase.

SampleInputOutputfortheSampleInput

336

011

121

023

102

00

02

102

120

02

000

Case1:

City0or2isnotavailable.

3

Nosuchpath.

City2isalreadyrecaptured.

ProblemFFairytale

Itissaidthatinaschool’sunderground,thereisahugetreasurewhichcanmeetanydesireoftheowner.

TheSpyUnion（SUisveryinterestinthislegend.Aftermuchinvestigation,SUfinallygettheanswerandlettheyoungestspysneakintotheschool.That’swhySayaisnowhere.

Today,Sayafoundtheentranceeventually.

Sheenterstheentrance,andfoundherinafairy-taleworld.

“Welcome!

”saysafairy,“IamIvan.Myresponsibilityistoprotectthetreasure,andgiveittotheonewhohavetheabilitytoownit.”

ThenIvangivesSayathreeproblems.

Withyourhelp,Sayafinishedthefirstandthesecondproblem（ProblemHandI.Herecomesthethird.IfSayacansolvethisproblem,thetreasurebelongstoher.

Thereisabigmazeprotectingthetreasure.YoucanassumethemazeasanN*NmatrixwhileeachelementinthematrixmightbeN（North,S（South,W（WestorE（East.Atfirst,Sayaisattheelement（1,1–thenorth-westcorner,andthetreasureisat（N,N–thesouth-eastcorner.

Thedesignerhaveenchanttothismatrix,sothatthetreasuremightmovefromtimetotimerespectingthefollowingrules:

Supposethetreasureisinanelementwhichmarked