Kruskal ka algorithm - o ka hana ana o kekahi e pono ai? Aieao

I ke kakahiaka nui 19th kenekulia geometer Jakob Steiner mai Pelelina i ka hana o ana i ka hoʻohui ekolu mau kauhale no laila, i ko lakou loihi i ka shortest. Ma hope, oia ua hoʻoʻuluʻulu manaʻo i ka pilikia: ka mea, ua koi 'ia e loaʻa kekahi wahi i loko o ka pelane, i ka mamao mai ka mea, a hiki i N nā heluʻai a pau i ka lalo. Ma ka 20th kenekulia, ka mea mau i ka hana ma luna o keia kumuhana. Ua Ua hooholoia e lawe i kekahi mau heluʻai, a hoʻohui iā lākou i loko o ia ke ala i ka mamao ma waena o ia i ka shortest. Kēia a pau He He kūikawā hihia o ka pilikia e? Anoee.

"Kuko" algorithm

Kruskal ka algorithm pili i ka "kuko" algorithm (i kapaʻiaʻano piʻina). Ke ae pā o ka poe - i ka lani kiekie loa lanakila ma luna o kēlā me ka anu u. 'Aʻole manawa, "'īlio" algorithms i ka pono pāʻoihana a hiki i ka pilikia. Aia hoi he kumumanaʻo, hoike mai la ia i loko o kā lākou mau palapala noi i ho'ākāka 'ia i hana ka mea, hāʻawi aku i ka kaʻoi loa pāʻoihana. 'O kēia ka pähola' ana o matroids. Kruskal ka algorithm pili i ia mau pilikia.

Loaa i ka palena iki kupapau kaumaha

Nānā akula au i algorithm? Aiey iauaeoia he a pau e pono maoli helu. Ka pilikia ana o ia mea me penei. Dan undirected kaiapili me ka laua kihi a me ka puka lou, a me ka ahaaina o ka lua penei ua haawiia mai i ke kau paona ana hana w, a waihona o ka helu ana i kēlā me kēia kihi e - ke kaupaonaʻana o ka iwiʻaoʻao - w, (e). Ke kaupaona ana o kēlā me kēia subset o ka ai iiiaanoaa o iwi aoao o ka huina o na paona o kona lua penei. Koi 'ia e' imi i ka iwi o ka uuku kaumaha.

hōʻikeʻano

Kruskal ka algorithm hana. Mua, ua hoonohonoho nā kihi o ka loiloi mua pakuhi ma ka pii mea o ka paona. Initially, ke kino, aole ia i apo ia i kekahi iwi aoao akā, nā mea a pau vertices. Ma hope o ka mea e hiki mai ana ka anu u o ka algorithm a hiki i ke ano e iino? Ieea hapa o ke kino, a hoi i ka spanning ulu lāʻau, i kekahi kihi ua huiia me ka. Ua UaʻAʻole wae ana. A pau i nā kihi o ka pakuhi,ʻaʻole no i ka ponoi, hiki ke kapa ula, he omaomao. Ka luna o kēlāʻulaʻula lua penei nō i loko o ka ia ke keʻena ma lalo o ke kūkulu ulu hoʻolele mokulele, a me ka uliuli mau poʻo, -ʻokoʻa. Nolaila, ina e hookui aku i ka ula maka, aia no he pōʻaiapuni, a ina i ka uliuli - i loaa mai ma hope o keia anu u o ka wahie pili eiiiiiaiou e e emi ma mua o kekahi. Ke'ī mai, ka mea kūpono no? Ieoaeunoaa hiki ole hoʻokomo i ula maka, akā, i kekahi mea uliuli palena hiki ke huiia, e kiʻi i ka ulu lāʻau. A ua kō he omaomao kae me ka palena iki kaumaha. I ka hopena o ka? Aieao i ka palena iki kaumaha.

manaʻo

Kû ke ka papa ululaau F. It ho oka awale i ka huapalapala o vertices i loko o ke kula o ka hoʻolele mokulele (ko laua hoao ana ano F, a me ka mea, e disjoint). Ma nā kihi o ka ulaula vertices ka mea, ka wahaheʻe i loko o hoʻokahi nō nā pepeiao. Part (m) - ke kuleana pili i ia no kela a me keia vertex m, e huli hou i ka hapa o ka inoa, ka mea, no m. Hui pu ia lakou (m, y me) - ke kaʻina hana i kükulu i ka hou paku, oia hoi o ka hoʻohuiʻia māhele o ka m, a y me a pau i nā wahi. E N - helu o ka lua penei. A pau këia mau manaÿo i loko ma ka algorithm o Kruskal. manaʻo:

1. Hooponopono i na kihi o ka pakuhi, mai ka 1st e N-la pii aku paona. (Ai,ʻelua - au me ka apex maka helu).

2. no ka i, = 1 i N hana.

3. m: = Part (ʻai).

4. y me: = Part (ʻelua).

5. Inā m i ole like y me laila, hui pu iho la (m, y me), e hookomo i ka maka F ke helu.

pono

E T - haka ai o ka palapala pakuhi kūkulu ka hoʻohana 'ana i ka Kruskal algorithm a me S - kona ākeʻakeʻa kumu maoli. Mākou i ke hooiaio i ka w, (T) mea i oi aku mamua o W (S).

E M - iiiaanoaa o ka haloʻole S, P - he iiiaanoaa o ka haloʻole T. Inā S mea,ʻaʻole like ia T, alaila, he mea i kapiliia iwiaoao ¶ T,ʻaʻole no ka S. S. listen pili ana ma ka pōʻaiapuni, ka mea, ua kapaia o C. C wehe mai kekahi kaʻe es, no S. mākou loaa i ka hou maoli, no ka mea, na kihi a me vertices o ka ia. Kona kaumaha mea i oi aku mamua o W (S), no ka w, (listen) hou w, (es) i loko o ka mana Kruskal algorithm. Kēia hana (hope iwi aoao S ma na kihi o T) e e hai hou no ka like loa me mākou kiʻi T. ke kau paona ana o kela a me keia hope loaa kapiliia mea ole hou ka mua kau paona ana, i hoʻohuʻu i ka w, (T) mea i oi aku mamua o W (S).

Ke robustness o Kruskal ka algorithm ma hope mai o ka theorem o Rado-Edmonds ma matroids.

Noi ano he kumu hoʻohālike Kruskal algorithm

Ua haawiia i kekahi pakuhi me vertices ka, e, pela aku, n, E a me ka iwi aoao (i, b), (ka, e), (b, c), (b, e), (c, d), (c, e) , (d, e). Nā paona o ke kihi a i ike ia ma ka papaʻaina, a me ka huahelu. Initially,? Ieoaeunoai ulu F kekahi mau a pau na vertices o ka pakuhi a me ka malama ole no i kekahi iwi aoao. Algorithm Kruskal hoʻohui mua iwiaoao (ka, e), mai ke kaumaha i ka lalo, a me nā vertices ka a, e ka mea i loko o kekahi eiiiiiaiou laau hoʻolele mokulele F (i, e iwiaoao () mea uliuli), a laila, i ka iwiʻaoʻao (c, d), no ka mea, mea ma ka liʻiliʻi loa keia kihi paona o ka pakuhi kihi,ʻaʻole no ia F, a me ia mea uliuli, alaila, no ka mea ia kumu accrue palena (he, b). Akā, i ka maka (b, e) ua lilo akula, a hiki nae ia, a me ka palena iki ke kaumaha o ka mea i koe iho kihi, no ka mea, ka mea, ua ulaula mai: ka vertices b., A, e pili ana i na mea e pili ana ke keʻena o ka ululaau F,ʻo ia hoʻi, inā mākou e hoʻokomo ai i F ka maka (b, e), i hanaia pōʻaiapuni. A laila, pākuʻi uliuli palena (b, c), ua hala ula palena (c, e), a laila, n, e ka. Penei, penei i pākuʻi sequentially (ka, e), (c, d), (he, b), (b, c). Mai nihera a pau e pono maoli, a he o ka palapala pakuhi. No laila, i loko o keia hihia ka mea hana i algorithm Kruskal. An kumu ua hōʻike.

Me ke kiʻi E hoike mai i ka pakuhi iloko olaila a mau pili ana eiiiiiaiou. Ka wiwo ole laina hōʻike i ka pono maoli iwi aoao (uliuli) kūkulu ka hoʻohana 'ana i ka Kruskal algorithm.

Ka luna kiʻiʻelua i ka palapala pakuhi, a me ka lalo - he iwi o ka palena haʻahaʻa ke kaupaonaʻana, kūkulu ai ia ia ma ka hoʻohana 'ana i ka algorithm.

Ke kaʻina o ka hoʻohuiʻia iwi aoao (1.6); (0,3), (2,6) 'ole (2,6), (0,3) - mea ole nui; (3,4); (0,1), (1,6) 'ole (1,6), (0,1), i malama (5,6).

Kruskal ka algorithm loaa e pili ana, no kekahi laʻana, e hoʻoikaika i ka gasket palapala, alanui i loko o hou neo? Aaiiai? Koikoi localities i loko o kēlā me kēia aupuni, e like me ma ka 'ē aʻe hihia.