Emagrafu e computer science: definition, izinhlobo, izibonelo isicelo. Igrafu theory computer science

Ibala indlela kukhompyutha ukuze ubudlelwano sokunquma ehlangana izakhi. Lezi izinto eziyisisekelo yokufunda igrafu theory.

izincazelo eyisisekelo

Kuyini kugrafu e computer science? Kuhlanganisa sebuningini izinto okuthiwa ISIZINDA noma vertices, ezinye ngazimbili zazo zixhunywe m. N. izimbambo. Ngokwesibonelo, igrafu figure (a) siqukethe ISIZINDA ezine, okhonjiswe A, B, C, D, B okuyinto axhumene abanye abathathu vertices izimbambo, futhi C no-D nazo axhunyiwe. ISIZINDA ezimbili eduze uma uxhunywe onqenqemeni. Lesi sibalo sikhombisa indlela ejwayelekile ye indlela yokwakha emagrafu in computer science. Imibuthano amelela vertices futhi emigqeni yokuxhuma pair of them ngamunye, kukhona izimbambo.

Yini igrafu undirected ibizwa computer science? Yena ubudlelwane phakathi emaphethelweni womabili izimbambo ezithile izinhlangothi zazo ziyalingana. Ubambo umane uxhuma nabo nomunye. Nokho, ezimweni eziningi, kubalulekile ukuveza ubuhlobo quin - ngokwesibonelo, ukuthi A amaphuzu B, kodwa hhayi okuphambene nalokho. Le nhloso kwencazelo igrafu ku computer, lisalokhu lakhiwe iqoqo ISIZINDA iqoqo imiphetho iqondiswe. Ngamunye onqenqemeni ngamakhasimende zihlobene vertices kabani isiqondiso kunenjongo. amagrafu Kuqondiswe zibonisa, njengoba kuboniswe ePhuzwini (b), imiphetho zabo amelwa imicibisholo. Uma ufuna ukugcizelela ukuthi igrafu non-ohlangothini, ibizwa ngokuthi undirected.

inethiwekhi onobuhle

Emagrafu e computer science kukhona imodeli zezibalo kwenethiwekhi izakhiwo. Lesi sibalo elandelayo ikhombisa isakhiwo Inthanethi, wazalela igama ARPANET, ngo-December 1970, lapho eneminyaka engu-amaphuzu 13 kuphela. ISIZINDA kukhona kucutshungulwa izikhungo kanye izimbambo ukuxhuma vertices ezimbili feedforward therebetween. Uma ungenalo unake United States eziphoqelelwe ibalazwe, lonke isithombe igrafu 13-engeyokuqala elifana odlule. Kulokhu, ukuma langempela vertex alibalulekile. Kubalulekile ngazo ISIZINDA axhunyiwe komunye nomunye.

Isicelo emagrafu in computer evumela ukuba ubone ukuthi izinto kungaba ngokomzimba noma ngokunengqondo oxhumene e isakhiwo inethiwekhi. ARPANET 13-engeyokuqala yisibonelo inethiwekhi zokuxhumana lapho amakhompyutha phezulu noma amanye amadivayisi bangadlulisela imilayezo, futhi emaphethelweni bamele umugqa oqondile yokuxhumana lapho ulwazi angadluliselwa.

imizila

Nakuba emagrafu asetshenziswa ezindaweni eziningi ezahlukene, banayo izici ezivamile. Igrafu theory (computer science) kuhlanganisa mhlawumbe ebaluleke kakhulu kubo - ngombono wokuthi izinto ezivame ukuhamba kuwo kanye emaphethelweni, ngokulandelana ukusuka engeyokuqala ku-node, kungaba umgibeli a izindiza ezimbalwa noma ulwazi ngocansi kumuntu nomuntu ngendlela yokuxhumana, noma umsebenzisi ikhompyutha, njalo ukuvakashela eziningana amakhasi ewebhu ngokulandela link.

Lo mbono ushukumisa kwencazelo umzila njengoba uchungechunge ISIZINDA zixhunywe emaphethelweni. Ngesinye isikhathi kuyadingeka ukuba ucabangele indlela equkethe hhayi izingxenye kuphela, kodwa futhi ukulandelana imiphetho yokuxhuma kubo. Ngokwesibonelo, ukulandelana vertices MIT, BBN, i-RAND, UCLA kuyinto umzila ku ARPANET internet igrafu. Ukudlula ISIZINDA kanye imiphetho kungase kuphinde kushiwo abanye. Ngokwesibonelo, SRI, USTAN, UCLA, SRI, Utah, MIT futhi umzila. Indlela lapho izimbambo kungukuthi okuphindaphindiwe, ngokuthi neketanga. Uma ISIZINDA okuphindiwe, ibizwa ngokuthi neketanga elula.

imijikelezo

zinhlobo Ikakhulukazi ezibalulekile kwikhompyutha amagrafu - ke imijikelezo amelela isakhiwo indandatho, ezifana ekulandelaneni ISIZINDA LINC, Case, Carn, HARV, BBN, MIT, LINC. Imizila izimbambo okungenani ezintathu, lapho engeyokuqala nesibongo ziyafana, kanti bonke abanye bavela ezahlukene, ukumela amagrafu Zijika computer science.

Izibonelo: umjikelezo SRI, USTAN, UCLA, SRI lifushane, futhi SRI, USTAN, UCLA, i-RAND, BBN, Utah, SRI kakhulu okukhulu.

Cishe zonke onqenqemeni ARPANET igrafu kungokwalabo umjikelezo. Lokhu kwakwenziwa ngamabomu, uma ekhona ehluleka, ngeke kungenzeka ushintsho komunye engeyokuqala kwesinye. Imijikelezo Esekela kwezokuxhumana kanye ezokuthutha izinhlelo abakhona ukuze komsebenzi - zinikeza imizila ngoba omunye endleleni umjikelezo. Zokuxhumana ngokuvamile imijikelezo lubonakale. Uma uthola, ngokwesibonelo, ukuthi umngane esikoleni esekuficile umzala unkosikazi wakho iyasebenza nomfowenu, it is a umjikelezo ukuthi siqukethe wena nomkakho, umzala wakhe, umngani wakhe esikoleni, umsebenzi wakhe (isb. E. Yakho umzalwane), futhi ekugcineni futhi.

igrafu axhunyiwe: definition (computer science)

Kungokwemvelo ukuba sizibuze ukuthi kungenzeka kusukela engeyokuqala ngamunye wakwazi ukuthola isinkwa kunoma iyiphi enye engeyokuqala. Igrafu ixhunyiwe uma kukhona indlela phakathi wonke pair of vertices. Ngokwesibonelo, inethiwekhi ARPANET - exhunywe igrafu. I Kungashiwo okufanayo mayelana iningi zokuxhumana kanye ezokuthutha amanethiwekhi, njengoba injongo yayo ukuqondisa traffic komunye engeyokuqala kwesinye.

Ngakolunye uhlangothi, kuba khona isizathu priori ukulindela ukuthi lezi izinhlobo emagrafu in computer science kugcwele umhlaba wonke. Ngokwesibonelo, e-yokuxhumana akuyona Kunzima ukucabanga abantu ababili abangashadile bahlobene.

izingxenye

Uma kukholamu ayixhunyiwe computer, ngokuvamile zimane awela iqoqo izingcezwana ahlobene, amaqembu ISIZINDA ukuthi sisodwa futhi musa aphambana. Ngokwesibonelo, Figure libonisa izingxenye ezintathu ezingasisiza: owokuqala - A no-B, kwesibili - C, D no E, kanti eyesithathu siqukethe vertices asele.

Izingxenye igrafu ukumela isethi engezansi ISIZINDA, lapho:

• vertex iqeqebana ngamunye has a umzila yimuphi omunye;
• isethi engezansi akuyona ingxenye iqoqo elikhulu lapho engeyokuqala ngamunye has a umzila iyiphi enye.

Lapho emagrafu in ikhompyutha zihlukaniswe izingxenye zabo, kumane incazelo yokuqala indlela isakhiwo sabo. Le ngxenye ingase bacebe isakhiwo sangaphakathi, kubalulekile nokuchazwa inethiwekhi. Ngokwesibonelo, indlela loluhlelekile nokunquma ukubaluleka engeyokuqala kuyinto ukuthola ukuthi mangaki izingxenye izohlukaniswa ukubala, uma engeyokuqala iyasuswa.

ingxenye Ubuningi

Kukhona indlela ekuhloleni qualitative izingxenye kwenethiwekhi. Ngokwesibonelo, kukhona inethiwekhi emhlabeni wonke nomphakathi nokuxhumana phakathi kwabantu ababili, uma abangane.

Ingabe axhunyiwe? Kungenzeka ukuthi wayengakuqondi. Ukuxhumana - impahla kunalokho iyashesha ukuthinteka, futhi ukuziphatha eyodwa engeyokuqala (noma iqoqo elincane) kunganciphisa nya. Ngokwesibonelo, umuntu olulodwa ngaphandle abangane abahlala wumkhakha ehlanganisa vertex olulodwa, ngakho-ke, ukubala ngeke axhunyiwe. Noma esiqhingini esikude ezishisayo, ehlanganisa abantu abangenandaba ukuxhumana nezwe ngaphandle, uyophinde abe ingxenye encane inethiwekhi, okufakazela incoherence yayo.

Inethiwekhi yomhlabajikelele yama-abangane

Kodwa kukhona enye into. Ngokwesibonelo, umfundi ka incwadi ethandwayo yokuvivinya unabangani ekhulele kwamanye amazwe, futhi kuwenza abe ingxenye. Uma thina acabangele abazali kulaba bangane abadala kanye nabangani babo, bonke laba bantu babe ingxenye efanayo, nakuba babeqala ukuzwa mayelana umfundi, abakhuluma ulimi oluhluke, futhi eduze akukaze. Ngakho, nakuba la Inethiwekhi yomhlabajikelele yama-ubungani - ayixhunyiwe, umfundi azofakwa ingxenye zinkulu kakhulu, engena ukuze zonke izingxenye zomhlaba, okubandakanya abantu bezizinda eziningi ezahlukene, futhi eqinisweni, iqukethe ingxenye enkulu yomphakathi jikelele.

Kwenzeka okufanayo e inethiwekhi amasethi wedatha - ezinkulu, amanethiwekhi eziyinkimbinkimbi ngokuvamile aba ingxenye enkulu, ehlanganisa ingxenye enkulu zonke ISIZINDA. Ngaphezu kwalokho, lapho inethiwekhi kuhlanganisa ingxenye enkulu, kuba pheze njalo eyodwa kuphela. Ukuze uqonde ukuthi kungani, kubalulekile ukuze ubuyele isibonelo kunethiwekhi yomhlaba zobungane uzama ukucabanga khona izingxenye ezimbili esiphezulu, ngamunye okubandakanya izigidi zabantu. Kufanele ubambo olulodwa ezinye ingxenye yokuqala neyesibili ekucineni izingxenye ezimbili benziwe eyodwa. Njengoba onqenqemeni eyodwa kuphela, ezimweni eziningi into ethile cishe ayinakwenzeka ukuthi ayakhekanga, futhi kungakho esiphezulu ababili izingxenye kumanethiwekhi zangempela ze sebenzisa.

Kwezinye izimo ezingavamile, lapho ezimbili izingxenye esiphezulu co-khona isikhathi esithile eside e inethiwekhi real, umshado wabo kwaba ezingalindelekile, amadlingozi, futhi, ekugcineni, kube nemiphumela eyinhlekelele.

Ingozi ingxenye ekubumbaneni

Ngokwesibonelo, ngemva kokufika kwabakhi lapho abahloli bamazwe baseYurophu e impucuko kakhulu eNtshonalanga Nenkabazwe cishe uhhafu esikhathini seminyaka eyikulungwana eyadlulako, kwakukhona enhlekeleleni yembulunga yonke. Kusukela umbono we inethiwekhi, kubukeka kanje: iminyaka ayizinkulungwane ezinhlanu yokuxhumana emhlabeni wonke, cishe lalinabashumayeli ingxenye amabili amakhulu - oyedwa amazwekazi aseNyakatho naseNingizimu Melika, kanye nezinye - eYurophu nase-Asia. Ngenxa yalesi sizathu, ubuchwepheshe uye savela ngokuzimela ku izingxenye ezimbili, futhi, kuba kubi nakakhulu uma, njengoba athuthukiswe futhi isifo womuntu, nokunye. D. Lapho izingxenye ezimbili ekugcineni Waxhumana ubuchwepheshe kanye nesifo ngokushesha futhi disastrously kuyachichima yesibili.

American Isikolo samabanga aphezulu

Umqondo we ingxenye enkulu kuyasiza ukucabanga mayelana namanethiwekhi ku aluhileli ubunzima obunjengalobu. Isibonelo ezithakazelisayo kuyinto igrafu efanekisa ubuhlobo e-US esikoleni esiphakeme ngenxa izinyanga ezingama-18. Iqiniso abaqukethwe ingxenye enkulu kubalulekile uma kuziwa ukusabalala kwezifo, ezifweni ezithathelwana ngobulili, okungukufa Ihloso yesifundo. Kungenzeka ukuthi abafundi baba umlingani oyedwa kuphela ngaleso sikhathi, kodwa, nokho, enganakile, bebelokhu beyingxenye yezingxenye we esiphezulu, futhi ngenxa yalokho, ingxenye imizila eminingi engaba yokudlulisela. Lezi zakhiwo zibonisa ubuhlobo eziye ezide yaphela, kodwa ukuxhuma abantu ngamaketanga eside kakhulu, ukuze zibe isihloko kokuhlolisisa okukhulu nokuhleba. Noma kunjalo, zingokoqobo: indlela amaqiniso yezenhlalakahle azibonakali, kodwa macrostructures nezisho kwavela njengoba umkhiqizo wobulamuli ngabanye.

Ibanga lobubanzi-lokuqala search

Ngaphezu ulwazi mayelana nokuthi ISIZINDA ezimbili axhunyiwe umzila, igrafu theory computer science ikuvumela ukuba ufunde mayelana ubude bayo - kwezokuthutha, zokuxhumana noma ukusabalalisa izindaba nezifo, kanye noma ngabe egcina iphakama eziningana noma amaningi.

Ukuze wenze lokhu, ichaze obuphelele umzila ilingane enanini izinyathelo abaqukethwe kusukela ekuqaleni kuze kube sekugcineni, isb. E. Inani emaphethelweni e ukulandelana okungukuthi. Ngokwesibonelo, MIT, BBN, i-RAND, UCLA umzila has a ubude 3, futhi-MIT, Utah - 1. Ukusebenzisa ubude indlela, singasho ukuthi uma ISIZINDA ezimbili ahlelwe kukholamu eduze ibanga nomunye noma kude phakathi iziqongo ezimbili kuchazwa njenganoma ubude indlela emfushane phakathi kwazo. Ngokwesibonelo, ibanga phakathi LINC futhi SRI 3 Nokho, ukuqinisekisa lokhu, kubalulekile ukuqinisekisa ukungabi khona obuphelele elilingana 1 noma 2, therebetween.

Ububanzi-lokuqala search algorithm

Ukuze encane igrafu ibanga phakathi ezimbili ISIZINDA ukubala kalula. Kodwa eziyinkimbinkimbi kukhona isidingo indlela ehlelekile yokunquma amabanga.

Indlela yemvelo kakhulu ukwenza lokhu, futhi ngenxa yalokho, ephumelela kunazo iyona (isibonelo, i-Inethiwekhi yomhlabajikelele yama-abangane) ezilandelayo:

• Bonke abangani kuthiwa sise ibanga 1.
• Zonke babangani (singabali le sekushiwo) imenyezelwa at ibanga 2.
• Ngisho nabangani babo (futhi, singabali abantu esinelebuli) umemezele ibanga kude 3.

Ukuqhubeka ngale ndlela, search wenziwa izingqimba okwalandela, ngalinye elikwazi - kwi unit okwedlule. ugqinsi ngalunye entsha yakhiwa ISIZINDA eziye bengahlanganyelanga esedlule, nokuthi iwe onqenqemeni kusukela vertex ungqimba odlule.

Le nqubo ibizwa ngokuthi search ububanzi-lokuqala, njengoba yena efuna kukholamu aphume engeyokuqala kokuqala, ngokuyinhloko ukumboza esilandelayo. Ngaphezu kokunikeza indlela yokunquma amabanga, ingaba kanye nohlaka ewusizo lomqondo ukuhlela isakhiwo igrafu kanye indlela yokwakha igrafu ikhompyutha, kokuba iphakama esekelwe ibanga zabo kusuka esinqunyiwe yekucala.

search Ububanzi-lokuqala singasetshenziswa hhayi kuphela kwinethiwekhi abangane, kodwa futhi kunoma igrafu.

izwe Encane

Uma ubuyela emuva kumuntu Inethiwekhi yomhlabajikelele yama-abangane, ungabona ukuthi i-agumenti ukuthi uchaza okuqondene ingxenye enkulu avumela ngempela okuthile okwengeziwe: hhayi kuphela umfundi has imizila kubangani, ubumxhumanisa nge ingxenye enkulu yomphakathi jikelele, kodwa lezi imizila kuyamangaza okufutshane .

Lo mbono ubizwa ngokuthi "ngumkhuba ezincane emhlabeni": izwe libonakala encane, uma ucabanga ngalokho umzila iDemo uxhuma kunoma iyiphi abantu ababili.

Imfundiso yokuziphendukela "nokuxhawulana eziyisithupha" yaqale Ucwaningo liphenywa Stanley Milgram nozakwabo ngawo-1960. Ingenabantwana iqoqo idatha yokuxhumana, futhi nge budget ka $ 680, wanquma hlola umqondo ethandwa. Kuze kube yimanje, wabuza 296 ezintweni ngezikhathi ezikhethiwe azame ukuthumela incwadi eya wamasheya, owayehlala emaphethelweni edolobha lase-Boston. Initiators banikwa okunye ulwazi lomuntu siqu mayelana nenjongo (kufaka phakathi ikheli le nasezinkolelweni), futhi kwadingeka ukuba athumele incwadi kumuntu ababengabazi ngegama, nge imiyalo efanayo, ukuze befinyelela umgomo ngokushesha ngangokunokwenzeka. Incwadi ngayinye odabule ezandleni eziningi abangane bakha uchungechunge uvala i-stock wabathengi ngaphandle laseBoston.

Phakathi amaketanga 64 ukuthi Usufike target, ubude obuphakathi yayingamakhulu ayisithupha, eqinisekisa inani okuthiwa emashumini amabili ngaphambili play Dzhona kaGera isihloko.

Naphezu kwakho konke ukushiyeka yalolu cwaningo, ukuhlola kwabonisa omunye ebaluleke kakhulu lapho ukuqonda kwethu ukuxhumana nomphakathi. Eminyakeni eyalandela kusukela senziwa isiphetho ebanzi: ukuxhumana nomphakathi bavame ukuba nemizila esifushane kakhulu phakathi ngazimbili ngokungadingekile abantu. Futhi ngisho noma enjalo uxhumano engaqondile nge nabaholi bamabhizinisi kanye nabarholi bezepolotiki bamshaya bona nsuku zonke, ukuba khona kwalezi imizila iDemo kunendima enkulu e ijubane ukusabalalisa ulwazi, isifo kanye nezinye izinhlobo ukutheleleka emphakathini, kanye nokufinyelela amathuba zokuxhumana inikeza abantu ngempela izimfanelo okuphambene.