Graphs 算法竞赛入门经典 刘汝佳.docx

Graphs 算法竞赛入门经典 刘汝佳.docx

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Graphs算法竞赛入门经典刘汝佳

TheGeoSurvCompgeologicsurveycompanyisresponsiblefordetectingundergroundoildeposits.GeoSurvCompworkswithonelargerectangularregionoflandatatime,andcreatesagridthatdividesthelandintonumeroussquareplots.Itthenanalyzeseachplotseparately,usingsensingequipmenttodeterminewhetherornottheplotcontainsoil.

Aplotcontainingoiliscalledapocket.Iftwopocketsareadjacent,thentheyarepartofthesameoildeposit.Oildepositscanbequitelargeandmaycontainnumerouspockets.Yourjobistodeterminehowmanydifferentoildepositsarecontainedinagrid.

Input 

Theinputfilecontainsoneormoregrids.Eachgridbeginswithalinecontainingm and n,thenumberofrowsandcolumnsinthegrid,separatedbyasinglespace.If m =0itsignalstheendoftheinput;otherwise 

 and 

.Followingthisare m linesof n characterseach（notcountingtheend-of-linecharacters）.Eachcharactercorrespondstooneplot,andiseither`*',representingtheabsenceofoil,or`@',representinganoilpocket.

Output 

Foreachgrid,outputthenumberofdistinctoildeposits.Twodifferentpocketsarepartofthesameoildepositiftheyareadjacenthorizontally,vertically,ordiagonally.Anoildepositwillnotcontainmorethan100pockets.

SampleInput 

11

*

35

*@*@*

**@**

*@*@*

18

@@****@*

55

****@

*@@*@

*@**@

@@@*@

@@**@

00

SampleOutput 

0

1

2

2

657-Thedieiscast

InterGamesisahigh-techstartupcompanythatspecializesindevelopingtechnologythatallowsuserstoplaygamesovertheInternet.Amarketanalysishasalertedthemtothefactthatgamesofchanceareprettypopularamongtheirpotentialcustomers.BeitMonopoly,ludoorbackgammon,mostofthesegamesinvolvethrowingdiceatsomestageofthegame.

Ofcourse,itwouldbeunreasonableifplayerswereallowedtothrowtheirdiceandthenentertheresultintothecomputer,sincecheatingwouldbewaytoeasy.So,instead,InterGameshasdecidedtosupplytheiruserswithacamerathattakesapictureofthethrowndice,analyzesthepictureandthentransmitstheoutcomeofthethrowautomatically.

Forthistheydesperatelyneedaprogramthat,givenanimagecontainingseveraldice,determinesthenumbersofdotsonthedice.

Wemakethefollowingassumptionsabouttheinputimages.Theimagescontainonlythreedif-ferentpixelvalues:

forthebackground,thediceandthedotsonthedice.Weconsidertwopixels connected iftheyshareanedge-meetingatacornerisnotenough.Inthefigure,pixelsAandBareconnected,butBandCarenot.

Aset S ofpixelsisconnectedifforeverypair（a,b）ofpixelsin S,thereisasequence 

 in S suchthat a = a1 and b = ak ,and ai and ai+1 areconnectedfor 

.

Weconsiderallmaximallyconnectedsetsconsistingsolelyofnon-backgroundpixelstobedice.`Maximallyconnected'meansthatyoucannotaddanyothernon-backgroundpixelstothesetwithoutmakingitdis-connected.Likewiseweconsidereverymaximalconnectedsetofdotpixelstoformadot.

Input 

Theinputconsistsofpicturesofseveraldicethrows.Eachpicturedescriptionstartswithalinecontainingtwonumberswandh,thewidthandheightofthepicture,respectively.Thesevaluessatisfy 

.

Thefollowing h linescontain w characterseach.Thecharacterscanbe:

``.''forabackgroundpixel,``*''forapixelofadie,and``X''forapixelofadie'sdot.

Dicemayhavedifferentsizesandnotbeentirelysquareduetoopticaldistortion.Thepicturewillcontainatleastonedie,andthenumbersofdotsperdieisbetween1and6,inclusive.

Theinputisterminatedbyapicturestartingwith w = h =0,whichshouldnotbeprocessed.

Output 

Foreachthrowofdice,firstoutputitsnumber.Thenoutputthenumberofdotsonthediceinthepicture,sortedinincreasingorder.

Printablanklineaftereachtestcase.

SampleInput 

3015

..............................

..............................

...............*..............

...*****......****............

...*X***.....**X***...........

...*****....***X**............

...***X*.....****.............

...*****.......*..............

..............................

........***........******.....

.......**X****.....*X**X*.....

......*******......******.....

.....****X**.......*X**X*.....

........***........******.....

..............................

00

SampleOutput 

Throw1

1224

784-MazeExploration

Amazeofrectangularroomsisrepresentedonatwodimensionalgridasillustratedinfigure1a.Eachpointofthegridisrepresentedbyacharacter.Thepointsofroomwallsaremarkedbythesamecharacterwhichcanbeanyprintablecharacterdifferentthan`*',`_'andspace.Infigure1thischaracteris`X'.Alltheotherpointsofthegridaremarkedbyspaces.

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

XXXXXXX###X###X###XXX

XXXXX###########XXX

XXXXXXX###X###X###XXX

XXXXXXXXXXXXXXXXXXXXXXXXX#XXX#XXXXXXXXXX

XXXXXXXX###X###X###X###X

XX*XXX###############X

XXXXXXXX###X###X###X###X

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

a）Initialmaze                  b）Paintedmaze

Figure1.Mazesofrectangularrooms

Allroomsofthemazeareequalsizedwithallwalls3pointswideand1pointthickasillustratedinfigure2.Inaddition,awallissharedonitsfulllengthbytheseparatedrooms.Theroomscancommunicatethroughdoors,whicharepositionedinthemiddleofwalls.Therearenooutdoordoors.

door

|

XXXX

X.Xmeasuredfromwithintheroom

door-...--wallsare3pointswide

X.X__

XXXXX|

|___wallsareonepointthick

Figure2.Aroomwith3doors

Yourproblemistopaintallroomsofamazewhichcanbevisitedstartingfromagivenroom,calledthe`startroom'whichismarkedbyastar（`*'）positionedinthemiddleoftheroom.Aroomcanbevisitedfromanotherroomifthereisadooronthewallwhichseparatestherooms.Byconvention,aroomispaintedifitsentiresurface,includingthedoors,ismarkedbythecharacter`#'asshowninfigure1b.

Input 

Theprograminputisatextfilestructuredasfollows:

1.

Thefirstlinecontainsapositiveintegerwhichshowsthenumberofmazestobepainted.

2.

Therestofthefilecontainsthemazes.

Thelinesoftheinputfilecanbeofdifferentlength.Thetextwhichrepresentsamazeisterminatedbyaseparationlinefullofunderscores（`_'）.Thereareatmost30linesandatmost80charactersinalineforeachmaze

Theprogramreadsthemazesfromtheinputfile,paintsthemandwritesthepaintedmazesonthestandardoutput.

Output 

Theoutputtextofapaintedmazehasthesameformatasthatwhichhasbeenreadforthatmaze,includingtheseparationlines.Theexamplebelowillustratesasimpleinputwhichcontainsasinglemazeandthecorrespondingoutput.

SampleInput 

2

XXXXXXXXX

XXX

X*X

XXX

XXXXXXXXX

XX

XX

XX

XXXXX

_____

XXXXX

XX

X*X

XX

XXXXX

_____

SampleOutput 

XXXXXXXXX

X###X###X

X#######X

X###X###X

XXXXXXXXX

XX

XX

XX

XXXXX

_____

XXXXX

X###X

X###X

X###X

XXXXX

_____

705-SlashMaze

Byfillingarectanglewithslashes（/）andbackslashes（ 

）,youcangeneratenicelittlemazes.Hereisanexample:

Asyoucansee,pathsinthemazecannotbranch,sothewholemazeonlycontainscyclicpathsandpathsenteringsomewhereandleavingsomewhereelse.Weareonlyinterestedinthecycles.Inourexample,therearetwoofthem.

Yourtaskistowriteaprogramthatcountsthecyclesandfindsthelengthofthelongestone.Thelengthisdefinedasthenumberofsmallsquaresthecycleconsistsof（theonesborderedbygraylinesinthepicture）.Inthisexample,thelongcyclehaslength16andtheshortonelength4.

Input 

Theinputcontainsseveralmazedescriptions.Eachdescriptionbeginswithonelinecontainingtwointegers w and h （ 

）,thewidthandtheheightofthemaze.Thenext h linesrepresentthemazeitself,andcontain w characterseach;allthesecharacterswillbeeither``/"or``\".

Theinputisterminatedbyatestcasebeginningwith w = h =0.Thiscaseshouldnotbeprocessed.

Output 

Foreachmaze,firstoutputtheline``Maze#n:

'',where n isthenumberofthemaze.Then,outputtheline``kCycles;thelongesthaslength l.'',where k isthenumberofcyclesinthemazeand l thelengthofthelongestofthecycles.Ifthemazedoesnotcontainanycycles,outputtheline``Therearenocycles.".

Outputablanklineaftereachtestcase.

SampleInput 

64

\//\\/

\///\/

//\\/\

\/\///

33

///

\//

\\\

00

SampleOutput 

Maze#1:

2Cycles;thelongesthaslength16.

Maze#2:

Therearenocycles.

439-KnightMoves

Afriendofyouisdoingresearchonthe TravelingKnightProblem（TKP） whereyouaretofindtheshortestclosedtourofknightmovesthatvisitseachsquareofagivensetof n squaresonachessboardexactlyonce.Hethinksthatthemostdifficultpartoftheproblemisdeterminingthesmallestnumberofknightmovesbetweentwogivensquaresandthat,onceyouhaveaccomplishedthis,findingthetourwouldbeeasy.

Ofcourseyouknowthatitisviceversa.Soyouofferhimtowriteaprogramthatsolvesthe"difficult"part.

Yourjobistowriteaprogramthattakestwosquares a and b asinputandthendeterminesthenumberofknightmovesonashortestroutefrom a to b.

InputSpecification

Theinputfilewillcontainoneormoretestcases.Eachtestcaseconsistsofonelinecontainingtwosquaresseparatedbyonespace.Asquareisastringconsistingofaletter（a-h）representingthecolumnandadigit（1-8）representingtherowonthechessboard.

OutputSpecification

Foreachtestcase,printonelinesaying"Togetfrom xx t