
ruted aalekh

ganitamadhye, aanee visheshtah aalekh siddhantat, mool aalekh haah eka aalekh aahe jyamadhye eka shirobindu mool mhanoon olakhala gela aahe. mool asalelya aalekhanchya nirdeshit aanee dishaheen asha donhi aavrutyancha abhyas keela gela aahe aanee asha vividh vyakhya dekhil aahet jyaa anek moolanna anumati detat.
ruted aalekh (tyanchya vaparavar avalambun) heey tokdar aalekh kinwa pravah aalekh mhanoon dekhil olakhale jaau shakatat. yaa aalekhanchya kahee upayojananmadhye, sampoorn aalekh mool shirobindupasun pohochata yenyajoga asane aavashyak aahe.
vividhata.
topological graph siddhantat, anek shirobindu kinwa anek kadaa mool mhanoon vicharat ghenyasathi ruted graphachi kalpana vadhavali jaau shakate. yaa sandarbhat pahilya aalekhala, tyanna kathavar rujalelya aalekhapasun vegale karnyasathi, kadhikadhi shirobindu-ruted aalekh mhanatat. mool mhanoon niyukt kelelya anek nodes asalele aalekh dekhil yadruchchik aalekhanchya kshetrat sanyojanshastrat kahee pramanat swarasyapoorn aahet. yaa aalekhanna gunakarit aalekh dekhil mhanatat.
ruted directed graph kinwa ruted degraph yaa sandnyanmadhyehi vyakhyanmadhye farak disato. vishisht nodala mool mhanoon olakhoon mool asalelya degraphcha vichar karane heey spasht pratyaropan aahe. tathapi, sanganak vidnyanat, yaa sandnya samanyatah eka sankuchit kalpanecha sandarbh detat; mhanje, ruted directed graph haah eka vishisht node "aar" asalela eka degraph aahe, jyacha "aar" pasoon "aar" vyatirikt konatyahi nodavar nirdeshit marg aahe. adhik samanya vyakhya denare lekhak 'jodalele' ruted degraph kinwa 'praveshyogya' ruted graph mhanoon sandarbhit karoo shakatat (pahaa).
"sanganak programingchi qalaa" ruted degraphschee thodi adhik vyapakpane vyakhya karate, mhanje, jarr tyat "kiman eka" node asel joou itar serve nodesparyant pohochu shakel tarr nirdeshit graphala ruted mhanatat. noth namood karato qee asha prakare paribhashit keleli kalpana hii majbootpane jodalelya aanee jodalelya degraphchya kalpananmadhil eka prakarcha madhyavarti aahe.
anuprayog.
pravah aalekh.
sanganak vidnyanat, jyaa mool shirobindu itar serve shirobinduparyant pohochu shakatat asha mool aalekhanna pravah aalekh kinwa pravah aalekh mhanatat. kadhikadhi atirikt nirbandh jodale jaatat, jyat pravah aalekhamadhye ekach nirgaman (sink) shirobindu asane aavashyak aahe.
pravah aalekhakade pravah taktyanche amoort swaroop mhanoon pahile jaau shakate, jyamadhye sanrachanatmak ghatak (node samagri aanee prakar) kadhoon takale jaatat. kadachit pravah aalekhancha sarvat prasiddha upvarg mhanje niyantran-pravah aalekh, jeey sankalak aanee karyakram vishleshanat vaparale jaatat. aniyantrit pravah aalekhala pratyek kathavar kadaa aakunchan karoon niyantran-pravah aalekhat rupantarit kele jaau shakate, jee tyachya strotapasun baher jaanari ekmev dhaar aahe aanee tyachya lakshyat yenari ekmev dhaar aahe. samanyatah vaparla jaanara pravah aalekh haah aanakhi eka prakar aahe, coll aalekh, jyamadhye nodes sampoorn subrutinshi sambandhit asatat.
pravah aalekh yaa samanya kalpanela karyakram aalekh mhanatat, parantu teech sandnya keval pravah-niyantran aalekh darshavinyasathi dekhil vaparali gelee aahe. pravah aalekhanna label nasalele pravah aalekh aanee yogya pravah aalekh asehi mhatale gele aahe. heey aalekh kadhikadhi software chachanimadhye vaparale jaatat.
jevha ekach nirgaman aavashyak asate, tevha pravah aalekhamadhye done gunadharm asatat jeey sarvasadharanpane nirdeshit aalekhasah samayik kele jaat naheeh pravah aalekh nested kele jaau shakatat, jeey sabrutin collchya samatulya aahe (jaree passing parameterschi kalpana nahee), aanee pravah aalekh dekhil anukramit kele jaau shakatat, jeey done kodachya tukadyanchya anukramik amalbajavanichya samatulya aahe. "mukhya pravah aalekh" hii pravah aalekh mhanoon paribhashit kelee jaate, jeey uplekhanchya nivadalelya namunyacha vapar karoon, udaharanarth sanrachit programingchya adim paddhatincha vapar karoon, gharate bandhane kinwa anukramanikedware vighatit kele jaau shakat naheet. udaharanarth, nivadak aalekh sanch dilelya mukhya pravah aalekhanche praman nirdharit karnyasathi saiddhantik sanshodhan kele gele aahe.
siddhant tayar qaraa.
pieter ezelane mool nirdeshit aalekh asha prakare vaparale aahet qee pratyek node moodapasoon (jyala too sulabh tokdar aalekh mhanato) pohochanyayogy aahe, jenekarun aaa-susthapit sanch siddhantat ezelcha anty-foundation svayamsiddha tayar karata yeil. yaa sandarbhat, praveshyogya tokdar aalekhatil pratyek shirobindu heey eka (aaa-susthapit) aakarman asalelya (aaa-susthapit) sanch siddhantashi nigadit asate aanee shirobindu 'v' pasoon shirobindu 'w' paryantche eka kamaniche namune jeey 'v' haah 'w' chaa ghatak aahe. ezelchya anty-foundation svayamsiddhatemadhye asey mhatale aahe qee pratyek upalabdh bindu aalekh models (gair-susthapit) yaa prakare seet karatat.
sanyukt khel siddhant.
sanyukt khel dilyas, eka sambandhit ruted nirdeshit aalekh asato jyache shirobindu khelachi sthitee asatat aanee jyanchya kadaa halchali asatat aanee moodapasoon suru honara aalekh traversal game trii tayar karnyasathi vaparla jaato. jarr aalekhamadhye nirdeshit chakr asateel, tarr khelatil sthitee anek vela anant punaravrutti karoo shakate aanee khel anishchit kalasathi suru rahanyapasun rokhanyasathi sahasa niyamanchi aavashyakta asate. anyatha, aalekh haah eka nirdeshit chakriy aalekh aahe aanee jarr too mulancha vruksh nasel tarr khelat sthanantar aahet. haah aalekh aanee tyachi topology khelachya guntaguntichya abhyasat mahattvachi aahe, jithe rajya-jaagechi jatilata hii aalekhatil shirobinduchi sankhya aahe, khelachi sarasari lambi mhanje thet uttaradhikari nasalele moodapasoon shirobinduparyant jaananya shirobinduchi sarasari sankhya aahe aanee khelachya zadachi sarasari shakha ghatak haah aalekhatil sarasari bahya patali aahe.
sanyukt ganana.
1,2 sathee ruted dishaheen aalekhanchi sankhya... nodes 1,2,6,20,90,544 aahet... .
sambandhit sankalpana.
ruchichi eka vishesh baab mhanje mulanchi zaade, vishisht mool shirobindu asaleli zaade. jarr mulanchya degraphmadhil moodapasoon nirdeshit marg atirikt adviteey asanyapurate maryadit asateel, tarr prapt keleli kalpana (mool) arboreschi aahe-mool asalelya zadachya samatulya nirdeshit-aalekh. jarr sampoorn aalekh moodapasoon pohochata aala tarach aanee jarr sanganak shastradnyanni ishtatam arborescence shodhanyachya algoridmik samasyancha abhyas keela asel, tarr mool aalekhamadhye samaan mool asalela arborescence asato.
mool asalele aalekh heey mool asalelya aalekhanchya utpadanacha vapar karoon ekatra kele jaau shakatat.