Kruskal a aligorivimu - yomanga ndi chimango mulingo woyenera

Kumayambiriro 19 m'ma geometer Jakob Steiner ku Berlin anapereka ntchito bwanji kulumikiza midzi atatu kuti kutalika kwake inali yayifupi. Kenako iye mwachidule vuto: izo chofunika kupeza mfundo ndege, mtunda kuchokera ku mfundo N ena otsika. M'zaka za m'ma 20, chikudziwikabe ntchito pa nkhani imeneyi. Anaganiza kutenga mfundo zingapo ndi kugwirizana nawo m'njira yakuti mtunda pakati pa iwo anali yaifupi. Izi zonse ndi nkhani yapadera vuto akuphunziridwa.

"Adyera" aligorivimu

aligorivimu Kruskal umanena za "umbombo" aligorivimu (wochedwanso masinthidwe amtundu). Akamanena za anthu - ndi Nkhata kuposa sitepe iliyonse. Osati nthawi zonse, "umbombo" ma aligorivimu kupereka njira yabwino yothetsera vutolo. Pali chiphunzitso, kusonyeza kuti ntchito zawo kuti ntchito yeniyeni amaika njira akadakwanitsira. Ichi ndi chiphunzitso cha matroids. aligorivimu Kruskal amanena kuti mavuto amenewa.

Kupeza osachepera nyama kulemera

Ankaona aligorivimu yamanga ndi mulingo woyenera chimango kuwerengedwa. Vuto la izo ndi motere. Dan undirected Zithunzi popanda m'mbali kufanana zingwe zopota, ndi ya m'mbali amapatsidwa kulemera ntchito yakumadzulo, amene anapereka chiwerengero aliyense m'mphepete E - kulemera nthiti - yakumadzulo (e). Kulemera kwa aliyense kagawo wa kuchuluka nthiti ndi Uwerenge zolemera za m'mbali ake. Amafuna kupeza mafupa a yaing'ono kulemera.

mafotokozedwe

aligorivimu Kruskal a ntchito. Choyamba, onse m'mbali mwa koyamba Zithunzi imakonzedwa mu akwera dongosolo la zinthu zolemera. Poyamba, chimango ndi lilibe nthiti aliyense koma zikuphatikizapo mfundo zonse. Pambuyo sitepe yotsatira ya aligorivimu mpaka kale inamangidwa ndi nyama, zomwe ndi nkhalango zinatenga, m'mphepete wina anawonjezera. Iwo sadasankhidwe amangosankha. m'mbali zonse Zithunzi, osati za thupi chimango, akhoza kutchedwa ofiira ndi obiriwira. Pamwamba pa chilichonse m'mbali wofiira ndi mu chigawo chimodzi chomwecho pansi zamalumikizidwe yomanga nkhalango, ndipo nsonga wobiriwira - osiyana. Choncho, ngati inu kuwonjezera m'mphepete wofiira, pali mkombero, ndipo ngati wobiriwira - anamlandira pambuyo stepi ino nkhuni chikugwirizana zigawo zikuluzikulu adzakhala n'komwe. Choncho, chifukwa yomanga kuwonjezera palibe m'mphepete ofiira, koma aliyense m'mphepete wobiriwira akhoza kuwonjezeredwa kuti nkhalango. Ndipo anati m'mphepete wobiriwira ndi kulemera osachepera. Chifukwa ndi chimango cha kulemera osachepera.

kukhazikitsa

Potanthauza nkhalango panopa F. Iwo ukugawa ya mfundo m'munda wa zamalumikizidwe (mgwirizano Matupi awo F, ndipo iwo ali disjoint). Pa m'mbali zonse za mfundo wofiira pogona mu chidutswa chimodzi. Part (x) - ntchito kuti aliyense vertex × akubwerera gawo la dzina, iwo uli x. Chingagwirizanitse (×, Y) - ndondomeko imene imalimbitsa kugawa latsopano, wopangidwa mwa kaphatikizidwe mbali ya × ndi Y ndi ziwalo zina zonse. Tiyeni N - chiwerengero cha konsekonse. Zikhulupiriro zonsezi m'gulu aligorivimu Kruskal a. kukhazikitsa:

1. Konzani m'mbali zonse za Zithunzi kwa 1st kwa akwera zolemera N-TH. (Ai, zina kuti adzipeza - Ine ndi pamwamba chiwerengero m'mphepete).

2. chifukwa ine = 1 N kuchita.

3. ×: = Part (Ai).

4. Y: = Part (zina kuti adzipeza).

5. Ngati × sakutero Y ofanana ndiye Chingagwirizanitse (×, Y), kuti monga ndi chiwerengero m'mphepete F i.

kulondola

Tiyeni T - chimango wa Zithunzi choyambirira anamanga ntchito Kruskal aligorivimu ndi S - chimango ake umasinthasintha. Ife kutsimikizira kuti yakumadzulo (T) sali wamkulu kuposa yakumadzulo (S).

Tiyeni M - kuchuluka zipsepse S, P - ndi kuchuluka kwa zipsepse T. Ngati S si wolingana T, ndiye pali chimango nthiti neri T sitili kuti S. S. neri adjoin kayendedwe ka, umatchedwa C. C kuchotsa es aliyense m'mphepete, otsata S. Ife kupeza chimango watsopano, chifukwa m'mbali ndi mfundo chimodzimodzi. Imatha kulemera sali wamkulu kuposa yakumadzulo (S), kuyambira yakumadzulo (neri) salinso yakumadzulo (es) mu mphamvu Kruskal aligorivimu. opaleshoni (wogwirizira T S nthiti pa nthiti) zidzabwerezedwa bola kulandira T. Kulemera kwa aliyense chimango wotsatira analandira sali wamkulu kuposa kulemera yapita, kutanthauza kuti yakumadzulo (T) sali wamkulu kuposa yakumadzulo (S).

The robustness wa aligorivimu Kruskal a motere kuchokera Lingaliro Lovomerezeka la Rado-Edmonds pa matroids.

Ntchito Zitsanzo Kruskal aligorivimu

Dan Zithunzi ndi mfundo ndi, b, c, anthu d e ndi nthiti (a, b), (a, e), (b, c), (b, e), (c, d), (c, e) , (d, e). The miyeso ya m'mbali amaoneka tebulo ndi maonekedwe. Poyamba, kumanga nkhalango F muli mfundo zonse Zithunzi ndi lilibe nthiti iliyonse. Aligorivimu Kruskal woyamba kuwonjezera nthiti (a, e), kuyambira kulemera anali otsika, ndi mfundo ndi mauthenga ali mu zigawo zosiyana matabwa zamalumikizidwe F (nthiti (a, e) ndi zobiriwira), ndiye nthiti (c, d), chifukwa kuti osachepera ili m'mphepete kulemera kwa m'mbali Zithunzi sitili kuti F, ndipo zobiriwira, kenako kwa zifukwazo accrue m'mphepete (a, b). Koma m'mphepete (b, e) wadutsa, ngakhale ndi kulemera osachepera m'mbali otsala, chifukwa ndi wofiira: ndi mfundo B ndi mauthenga a chigawo womwewo wa zamalumikizidwe nkhalango F, ndiye, ngati ife kuwonjezera F m'mphepete (b, e), aumbike mkombero. Ndiyeno anawonjezera m'mphepete zobiriwira (b, c), wadutsa wofiira m'mphepete (c, e), kenako anthu d, e. Choncho, m'mbali akuwonjezeka sequentially (a, e), (c, d), (a, b), (b, c). Kuyambira nihera mulingo woyenera chimango ndipo imakhala ya Zithunzi pachiyambi. Palembali mozama ndi aligorivimu Kruskal. Chitsanzo kukuonetsedwa.

zimakwana amasonyeza Zithunzi, chomwe zigawo ziwiri zolumikizana. The mizere molimba mtima amasonyeza mulingo woyenera chimango nthiti (obiriwira) anamanga ntchito Kruskal aligorivimu.

The chithunzi pamwamba limasonyeza Zithunzi pachiyambi, ndi pansi - mafupa a thupi kochepa, anamanga kumukopa pogwiritsa ntchito aligorivimu.

The ndondomeko ya nthiti anawonjezera (1.6); (0,3), (2,6) kapena (2,6), (0,3) - si ofunika; (3,4); (0,1), (1,6) kapena (1,6), (0,1), komanso kusamalira (5,6).

aligorivimu Kruskal a wapeza ntchito zothandiza, mwachitsanzo, kuti konza moyenera gasket aya, misewu mu nyumba zina zatsopano zigawo m'madera m'mayiko onsewa, komanso nthawi zina.