ACM杯比赛往年试题集锦.docx

ACM杯比赛往年试题集锦.docx

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ACM杯比赛往年试题集锦

EscortofDr.WhoHow

TimeLimit:

2000MS

MemoryLimit:

131072K

TotalSubmissions:

1376

Accepted:

266

Description

Thenotoriousringleaderandcyber-criminalDerekWu,betterknownasDr.WhoHow,hasbeenconvictedformultipleabductionsandcyber-fraudsseveralminutesago.Hewillsoonbetransferredfromthecourttotheprisontoservealifesentence.IntelligencefromundercoverofficersinDr.WhoHow’soutlawedgangindicatesapossibleforciblerescueoperationbygangmembersinthecasethatDr.WhoHowisconvicted.Toensureasuccessfulescort,besidesadoptingenhancedsecuritymeasures,thepoliceforcefurtherdesirestominimizetheescorttime—thetimethatthemotorcadeofescorthastospendbetweendeparturefromthecourtandarrivalattheprison.

Thecomplextrafficconditioninthecityimposescomplicationsonthepoliceforce’sescorteffort.Whilethemunicipalgovernmenthasagreedtotemporarilyshutdownafewroadsforexclusivepoliceuse,theshut-downtimewindowsvaryamongroadsandaregenerallynarrowtoavoidexcessivelydisturbingthelifeofthecitizens.Themotorcadeofescortmustpassthroughanyroadentirelywithinitsshut-downtimewindowandnotuseanyroadthatthemunicipalgovernmenthasnotagreedtoshutdown.

Giveninformationaboutallroadsavailabletothepoliceforcefortheescort,determinetheshortestescorttime.

Input

Theinputcontainsasingletestcase.Thefirstlinecontainsfourintegersn,m,sandt（2≤n≤100;0≤m≤1000;1≤s,t≤n;s≠t）.Therearenjunctions,somepairsofwhichareconnectedbymroads.Thecourtandtheprisonarelocatedatthes-thandthet-thjunctions,respectively.Thenextmlineseachcontainfiveintegersx,y,b,eandc（1≤x,y≤n;0≤b

Output

Iftheescortispossible,printtheshortestescorttime;otherwise,print“Impossible”.

SampleInput

4514

12011

12012

13132

24341

34341

SampleOutput

3

Hint

ThesampleisdepictedinFigure1.Eachjunctionisrepresentedbyanumberedspot.Eachroadisrepresentedbyanarrowlabeledwith

itsshut-downtimewindowandpass-throughtime.

Figure1:

Depictionofthesample

Thesecondroadlistedinthesampleisvirtuallyunusableforittakesthemotorcadeofescortlongertimetopassthroughthanitcanstayavailable.Theremainingfourroadsenablethefollowingtwoescortroutes:

1.

2.

（Thelabel

overanarrowindicatesthatthemotorcadepassesthroughthecorrespondingroadbetweentimesandt.）Thefirstroutetakesfourunitsofescorttime,whereasthesecondtakesthree,whichistheshortestpossible.

Source

PKUCampus2008（POJFounderMonthlyContest–2008.05.10）,frkstyc

FullSteinerTopologies

TimeLimit:

1000MS

MemoryLimit:

131072K

TotalSubmissions:

441

Accepted:

187

SpecialJudge

Description

AfullSteinertopologyforagivenpointsetP={p1,p2,…,pn}isanundirectedtreeT=（V,E）whereV={v1,v2,…,vn,vn+1,…,v2n−2}isthesetofvertices,andEisthesetofedges.ThendistinctlylabeledleavesofT,v1,v2,…,vn,correspondtop1,p2,…,pn,respectively;theremainingn−2vertices,vn+1,vn+2,…,v2n−2,calledtheSteinervertices,aremutuallyindistinguishableandeachhaveadegreeofthree.Figure2showstheonlyfullSteinertopologyforP={p1,p2,p3}.Figure3showsallthreedifferentfullSteinertopologiesforP={p1,p2,p3,p4}.

Figure2:

FullSteinertopologyforP={p1,p2,p3}

Figure3:

FullSteinertopologiesforP={p1,p2,p3,p4}

Givenn,thecardinalityofP,computethenumberofdistinctfullSteinertopologies.

Input

Theinputcontainsmultipletestcases.Eachtestcaseconsistsofasingleintegern（3≤n≤107）onaseparateline.TheinputendswhereEOFismet.

Output

Foreachtestcase,printtheansweronaseparateline.Youshallprinttheanswerroundedtofoursignificantdigits.Letm·10ebethescientificformoftheroundedanswer,youshallprint“mEe”,givingallfoursignificantdigitsofmandstrippinganyleadingzeroesbeforee.

SampleInput

3

30

300

3000

30000

300000

3000000

SampleOutput

1.000E0

8.687E36

5.677E697

1.462E10024

1.983E130306

4.215E1603145

7.937E19031556

Source

PKUCampus2008（POJFounderMonthlyContest–2008.05.10）,frkstyc

IlluminatedPlanet

TimeLimit:

1000MS

MemoryLimit:

131072K

TotalSubmissions:

198

Accepted:

45

Description

Aspaceprobeisonamissiontoobserveaplanetarysystem.Itisinstructedtoshootimagesofaplanet,whichorbitsastar,usingitso