英文翻译0615Word文档下载推荐.docx
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西安理工大学高科学院
2012年
英文原文
Diagram
Thediagramisthedatastructurethatismanyrightnessestorelatetomoreofakindofdatachemicalelement,plustheabstractdatatypethatasetofbasicoperationconstitutes.
Thedefinitionofdiagram
Thediagram(Graph)topgotemptybynotgathersVandofthedescriptiontoprelation-gatheringofside(orHu)theEconstitute,itformaldefinitionBE:
G=(V,E)
IfeachsideinthediagramGistohavenodirection,thencallGashavenotothediagram.Havenoisahavingnooftopindiagramtowardthesideindiagramprefaceisaccidentallyright.Havenoprefacetoaccidentallymeantowardsusuallyusingaparenthesis"
()"
.Forexample,topaccidentallyto(vi,vj)thesidethatmeansthattopviandtopvjconnectwitheachother,and(vi,vj)with(vj,vi)meanthesameside.
IfeachsideinthediagramGhasdirectionalof,thencallGforhastowardthediagram.Isahavingoftopindiagramtowardthesideinthediagramprefaceaccidentallyto,thereisprefaceaccidentallytousuallymeanwiththepointbrackets"
<
>
"
.Forexample,topaccidentallyto<
vi,vj>
meanfromoneofthetopvidirectiontopvjandhavetowardtheside;
Amongthem,thetopviiscalledtowardtheside<
ofpointofdeparture,thetopvjiscalledtowardtheside<
ofterminalpoint.AlsobecalledHutotheside;
TotheHu<
say,theviisthepointofdepartureofHu,becalledHutail;
ThevjistheterminalpointofHu,becalledaHuhead.
Thediagramiscomplicateddatastructure,expressatnotonlythedegreeofeachtopcanbedifferent,andthelogicofoftoprelatestoalsocomplex.Canknowfromthedefinitionofdiagram:
Theinformationofadiagramincludestwoparts:
Therelation-sideofortheinformationoftheHuoftheinformationandthedescriptiontopoftopindiagram.Consequentlynomatteradoptwhatmethodtobuildupthesavingstructureofdiagram,allhavetobecompleteandaccuratelyreflectthesetwopartsoftheinformations.InordertobesuitablefortodescribewiththeClanguage,riseatopordinalnumberfromthisstanzafrom0beginning,namelythetopofdiagramgatherofgeneralformBE:
V
ThetimeofthediagramLi
ThetimeLiofdiagramisakindofbasicoperationofdiagram,itistosolveconnectingofdiagramsexproblemandTuotorushtowardtolineupaprefaceandbegthefoundationofcalculatewayslikekeypath,etc.ThetimeofthediagramLiusuallyadoptsdepthtohavetheinitiativetosearch(DepthFirstSearch,DFS)andthewidedegreehavetheinitiativetosearch(BreadthFirstSearch,BFS)twokindsofmethods,thesetwokindsofmethodstothetimethathasnotowardthediagramandhastowardthediagramtheLiallapply.
ThewidedegreeofthediagramtimeLi
WidedegreehavetheinitiativetosearchLidiagramismoresimilarthanatreeofbythelayertimeLi.Widedegreethebasicthoughtthathastheinitiativetosearchis:
Thesometopvsetoutfromthediagram,aftervisitingtopvonebyoneinordervisitedagainmutuallyandabuttinglyhavenevervisitedwithvofrestabutmentsidecrunodev1,v2,…,vk;
Connectdowntovisitaccordingtotheabove-mentionedmethodagainandvonenevervisitingoftheabutmentoverofeachabutmentsidecrunode,andv2nevervisitingoftheabutmentsesoverofeachabutmentsidecrunode,…,andvkabutmentofhavenevervisitedofeachabutmentsidecrunode;
…Keeponpursuingalayerlikethisuntilalltopsinthediagrambevisited.WidedegreethecharacteristicsthathastheinitiativeandsearchesLidiagramisaforerunnerandgoespossiblyhorizontalsearch,namelyandfirstvisitoftopitabutmentsidethecrunodealsovisitfirst,behindvisitoftopitabutmentsidecrunodealsobehindvisit.
ThedepthtimeofthediagramLi
Depth'
shasingtheinitiativetosearchisfirstmoresimilarthanatreetothetimeofthediagramLirootthetimeLiisfirstatreerootakindofexpansionoftimeLi;
Alsonamely,searchingtheorderofsequenceoftopisalongapathdeeplydeveloptotheZongasfaraspossible.Thebasicthoughtthatthedepthhastheinitiativetosearchis:
Supposebeginning'
sstartingstatusisalltopsindiagramhavenevervisited,thedepththenhastheinitiativetosearchcanacertaintopvsetouttonamelyandfirstvisitvfromthediagram,thenonebyoneinorderfromthenevervisitingofthevoveroftheabutmentpointsetoutandcontinuethedepthhavetheinitiativetosearchdiagram,untildiagraminallhavepathwithvthetopsofmutuallybeallvisited;
Iftherewasstillatopbeingnotvisitedinginthediagramatthistime,thenchooseanotheratopthathasnevervisitedasthestartorders,processrepeattheabove-mentioneddepthtohavetheinitiativetosearch,untilalltopsinthediagrambevisited.
Connectingofdiagramuniversality
BEcarryingonlastingtowardshavingnotowardthediagram,toconnectdiagramtoonlyneedtheanytopsetouttocarryondepthtohavetheinitiativetosearchfromthediagramorthewidedegreehavetheinitiativetosearch,canvisittoalltopsinthediagram;
Fordon'
tconnectdiagram,thenneedseveraltopsconnectedbynottostartcarryingontosearch,andeverysetouttocarryonthetopinterviewsearchedtogetintheprocesssequencefromanewtop,bethecontainmentshouldsetouttopoftheconnectweightinofthetopgather.
Therefore,wanttojudgeonetohavenotowardthediagramwhetherinordertoconnectdiagram,orhaveseveralsconnectweight,thencanincrease1tocounttochangetomeasurecountandestablishitthebeginningbeworthto0andhavetheinitiativetosearchthesecondforcirculationinthecalculatewayDFSTraversefunctioninthedepthin,adjusttouseaDFStoincreaseforcounteachtime1;
Thecountvaluethatiscalculatewayperformancetoendlikethisforedsthepiecethatconnectsweight.
Arriveotheratallpointlytheshortestpathfromasource
GivetosettleonetotakepowertohavetowardthediagramG=(V,E),specifythevofacertaintopwithindiagramGtoorderforsourceandbegfromvtothemostshort-circuitpathofofothereachtops;
Thisproblemiscalledalistsourcetoorderthemostshort-circuitpathproblem.
DiheroSipulls(Dijkstra)especiallyaccordingtoifpressthelengthincreasedorderofsequencebornordervfromthesource0arrivethemostshort-circuitpathofothertops,thenatpresentjustonthebornlythemostshort-circuitpathinadditiontoterminalpointoutside,themostshort-circuitpathofresttopallalreadybornthisthoughtsandputsforwardtopressthepathlengthincreasedorderofsequencetoproducethecalculatewayofthemostshort-circuitpath.(here,pathlengthforpathlastsideorthepowerofHubeworthitand)ThethoughtofDijkstracalculatewayis:
EstablishtwotopstogatherSandTtowardstakingpowerandhavingtowardthediagramG=(V,E),=V-S;
Anywithv0issource'
sorderingtocombineterminalpoints(top)ofmakingsurethemostshort-circuitpathshasalreadyallmergedintotogatherSandgatherSearlyTaiimpliesasourcetoorderv0;
Butthetopthathasn'
tmadesureitsthemostshort-circuitpathallbelongtogatherT,beginningTaigatherTcontainmentinadditiontothesourceordersv0resttops.Accordingtoeachtopandv0mostshort-circuitpathlengthincreasedorderofsequence,graduallyoneortwogatherthetopintheTtojointogathertogointheS,makethepathlengthofeachtopalwaysbenobiggerthanvfromthesourceorderv0togatherS0togatherthepathlengthofeachtopinT.And,gathertojoinanewtopueachtimeintheS,allwanttomodifyasourcetoorderv0togatherthemostshort-circuitpathlengthofsurplustopinT;
Alsonamely,gatheringthelatelythemostshort-circuitpathlengthvalueofeachtopvinTisanoriginallythemostshort-circuitpathlengthvalueoristhemostshort-circuitpathlengthoftoputobeworthagainplusthetopuisworththesetothepathlengthoftopvtwomediumofsmallervalue.ThiskindofgatherthetopintheTtojointogathertheprocessintheScontinuouslyrepeateduntilallofthetopthatgathersTjointogatherSin.
Notice,attogathertoaddtopintheS,alwayskeepthemostshort-circuitpathlengthofeachtoptobenobiggerthanthemostshort-circuitpathlengthofanytopfromthesourceorderv0togatherTfromthesourceorderv0togatherS.Forexample,ifjusttogatheredtoaddintheSofisatopvk,forgathereachtopvuintheT,ifthetopvkarrivedvutohaveaside(establishedthepowervalueasw2),andoriginallyfromthetopv0arrivethepathlength(establishedthepowervalueasw3)oftopvuwasbiggerthanfromthetopv0arrivethepathlength(establishedthepowervalueasw1)ofthetopvkandthepoweroftheside(vk,vu)wereworthw2itand,namelyw3>
ws1+ws2.Thenis0→vksthev→vuthisallthewaythepathisalatelythemostshort-circuitvupath.
译文
图
图是一种数据元素间为多对多关系的数据结构,加上一组基本操作构成的抽象数据类型。
图的定义
图(Graph)是由非空的顶点集合V与描述顶点之间关系——边(或者弧)的集合E组成,其形式化定义为:
如果图G中的每一条边都是没有方向的,则称G为无向图。
无向图中边是图中顶点的无序偶对。
无序偶对通常用圆括号“()”表示。
例如,顶点偶对(vi,vj)表示顶点vi和顶点vj相连的边,并且(vi,vj)与(vj,vi)表示同一条边。
如果图G中的每一条边都是有方向的,则称G为有向图。
有向图中的边是图中顶点的有序偶对,有序偶对通常用尖括号“<
>
”表示。
例如,顶点偶对<
vi,vj>
表示从顶点vi指向顶点vj的一条有向边;
其中,顶点vi称为有向边<
的起点,顶点vj称为有向边<
的终点。
有向边也称为弧;
对弧<
来说,vi为弧的起点,称为弧尾;
vj为弧的终点,称为弧头。
图是一种复杂的数据结构,表现在不仅各顶点的度可以不同,而且顶点之间的逻辑关系也错综复杂。
从图的定义可知:
一个图的信息包括两个部分:
图中顶点的信息以及描述顶点之间的关系——边或弧的信息。
因此无论采取什么方法来建立图的存储结构,都要完整、准确地反映这两部分的信息。
为适于用C语言描述,从本节起顶点序号由0开始,即图的顶点集的一般形式为:
V={v0,v1,…,vn-1}。
图的遍历
图的遍历是图的一种基本操作,它是求解图的连通性问题、拓扑排序以及求关键路径等算法的基础。
图的遍历通常采用深度优先搜索(DepthFirstSearch,DFS)和广度优先搜索(BreadthFirst