Combinatorial vuto. Losavuta combinatorial mavuto. Mavuto Combinatorial: Zitsanzo

Aphunzitsi a masamu chodzadziŵitsa ophunzira awo ndi mfundo yonena za "vuto combinatorial" akali kalasi lachisanu. Izi ndi zofunika kuonetsetsa kuti iwo anali kupitiriza ntchito ndi zinthu zovuta kwambiri. Mu vuto combinatorial ukhoza kuyamikiridwa mwayi kuthetsa pogwiritsa ntchito kusanja zinthu za akonzedwa amalire.

The chizindikiro chachikulu cha mavuto a dongosolo ili ndi funso, imene zikumveka ngati "mungachite chiyani?" Kapena "Kodi njira? Ambiri" mavuto Combinatorial zikudalira kapena kuwathetsa tanthauzo bwino, ngati iye anali wokhoza molongosoka kanthu kapena njira imene yakhala anafotokoza mu ntchito.

Mmene angathetsere vuto combinatorial?

Nkofunika mukazindikira mtundu wa kugwirizana zikupezeka vuto, koma m'pofunika kufufuza kuti aone ngati akubwereza zinthu ngati zinthu okha kusintha ngati mbali yaikulu ndi ankaimba ndi dongosolo lawo, komanso pa zifukwa zina.

Vuto combinatorial akhoza kukhala ndi chiwerengero cha zofooka kuti akhoza ziletso pa pawiri lapansi. Pankhaniyi, muyenera kuwerenga chisankho chake zonse onani, ngati malamulo ndi asatengere kugwirizana kumene zigawo zikuluzikulu zonse. Ngati mmene kwenikweni kumeneko, muyenera onani chimene iwo anali.

Pati?

Choyamba tiyenera kuphunzira kuthetsa pulayimale mavuto combinatorial. Lophunzira zipangizo yosavuta kulola kuphunzira kumvetsa zinthu zovuta kwambiri. Tikulimbikitsa kuti kuyamba vuto ndi zopinga zimene si amaonanso mu njira yosavuta kwambiri.

Izo analimbikitsanso pofuna kuthetsa mavuto oyambirira amenewa, amene ayenera kuonedwa ochepa zinthu wamba. Kotero inu mukhoza kumvetsa mfundo ya kulenga zitsanzo ndi kuphunzira m'tsogolo okha anawalenga. Ngati ntchito imene kufunika kogwiritsa ntchito combinatorial tichipeza osakaniza angapo chosavuta, izo tikulimbikitsidwa kuti kulikonza ilo ndi mbali.

mavuto Combinatorial

mavuto amenewa ngati chinthu chosavuta mu zochita, koma combinatorics imavuta kwambiri kumene, ena mwa iwo mulibe yankho kwa zaka zapitazi zana. Imodzi mwa ntchito olemekezeka ndi kudziwa chiwerengero cha mabwalo matsenga a ndondomeko yapadera imene nambala N ndi wamkulu kuposa 4.

vuto Combinatorial ndi umafananirako ku chiphunzitso cha Mwina, amene anaonekera mu nthawi akale. Mwina chiyambi cha chochitika makamaka kuchita masamu okha ndi ntchito combinatorics, Pankhaniyi muyenera Njira pakati pa onse a zinthu m'madera ena kuti njira mulingo woyenera.

Kukwaniritsa mavuto

mavuto Combinatorial ndi njira ntchito maphunziro a ophunzira ntchito ndi nkhaniyi. Ngati ife kulankhula ambiri, iwo ayenera kupanga munthu chidwi ndi kufuna kupeza njira wamba. Kuwonjezera masamu, m'pofunika ntchito m'maganizo ndi ntchito akungonena mawu Opeka.

Mu ndondomeko yothetsera mavuto a mwana mudzatha kukhala kuganiza ndi masamu combinatorial mphamvu, zikhoza kwambiri kukhala wofunika kwambiri kwa iye m'tsogolo. Pang'onopang'ono, mlingo wa kuchulukitsa kwa ntchito mukufunika kusintha, tisaiwale chidziwitso alipo ndi kuwonjezera kwa iwo.

Njira 1. Iterate

Njira zothetsera mavuto combinatorial ndi wosiyana kwambiri ndi mzake, koma iwo angagwiritsidwe ntchito mwana ayankhe. Mmodzi wa wamba, koma pa nthawi yomweyo ndi njira yaitali kuti kugwira a. Pamene m'pofunika chabe kuyesera njira zonse zotheka popanda kupanga zithunzi aliyense ndi magome.

Monga ulamuliro, funso ngati vuto kugwirizana ndi njira za chiyambi cha chochitika makamaka, monga: kodi manambala akhoza kupangidwa ndi manambala 2, 4, 8, 9? Ndi kuyesera njira zonse wasenza kuyankha ongokhala osakaniza ndi zotheka. Njira imeneyi imagwira abwino ngati chiwerengero cha options ndi ochepa.

2. Njira ya Wood chimake

Ena mavuto combinatorial zingathe kuthetsedwa yekha ndi kupanga chiwembu, imene nkhani wachina chilichonse adzakhala kutchulidwa mwatsatanetsatane. Kukafola mtengo mungachite - njira ina kupeza yankho. Ndi abwino njira zothetsera si ntchito yovuta kwambiri, imene ndi chikhalidwe zina.

Chitsanzo cha vutoli:

• Kodi manambala zisanu manambala akhoza kupangidwa kwa manambala ndi 0, 1, 7, 8? Pofuna kuthana ndi chosowa kumanga mtengo wa ma n'kotheka, pamene pali mkhalidwe zina - chiwerengero sangathe kuyambira zikande. Choncho, yankho mudzangokhala a manambala onse kuti adzayamba pa 1, 7 kapena 8.

Mapangidwe Njira 3 matebulo

mavuto Combinatorial angathe kuchitidwa mwa podyerapo. Iwo amafanana mtengo mungachite chifukwa amapereka yankho lomveka bwino kwa zinthu. Kuti tipeze yankho lolondola muyenera jambulani tebulo, ndipo chidzapatsidwa n'zofanana yopingasa ndi zinthu ofukula ali ofanana.

lolondola adzakhala analandira pa mphambano ya mizati ndi mizere. Pankhaniyi, mayankho ku mphambano za mzati ndi mzere sadzalandira deta chomwecho, mphambano ayenera kusamala kwambiri ndi chizindikiro, si kusokonezedwa ndi kukafola mwa ayankhe komaliza. Njira imeneyi si nthawi kumene ophunzira ambiri amakonda mtengo ndi options.

Njira 4. Uchulutsa

Pali njira inanso imene mukhoza kuthetsa mavuto combinatorial - chulutsa ulamuliro. Iye ali wangwiro mu choncho, pamene chikhalidwe Sikuti kuti atchule njira zonse zotheka, inu muyenera kupeza nambala pazipita. Njira imeneyi ndi yekhayo wa mtundu wake, amagwiritsidwa ntchito kwambiri, pamene anakulirakulirabe kuthetsa mavuto combinatorial.

Chitsanzo cha Vutoli motere:

• 6 anthu amayembekezera mu holo mayeso. Kodi njira zambiri angagwiritsidwe ntchito kuziika mu mndandanda? Pakuti Answer m'pofunika mwachindunji angati a iwo akhoza kukhala woyamba, koma pa wachiwiri, ndi wachitatu, ndi zina zotero. D. ayankhe adzakhala chiwerengero 720.

Combinatorics ndi mitundu yake

vuto Combinatorial si zipangizo kusukulu kokha, ophunzira a ku Yunivesite akuphunziranso izo. Mu sayansi, pali mitundu ingapo ya combinatorics, ndipo aliyense wa iwo ali ndi ntchito zake. Combinatorial enumeration muyenera kuganizira mavuto kutengerapo ndi n'kulemba masanjidwe n'zotheka ndi zinthu zina.

Kandalama combinatorics ndi chigawo chimodzi cha pulogalamu sekondale, Ikufotokoza chiphunzitso cha matroids ndi chintchito. combinatorics Oika ukukhudzanso ndi chuma sekondale, ndipo apa ndi zofooka zawo aliyense payekha. gawo lina - Ramsey chiphunzitso ndi kuphunzira dongosolo mu yofanana mwachisawawa zinthu. Palinso combinatorics chinenero, amene akulingalira ngakhale kwa zinthu zina pakati pawo.

Njira kuphunzitsa mavuto combinatorial

Malinga ndi maphunziro, m'badwo wa ophunzirawo, limene lakonzedwa kuti womdziwa koyamba ndi chuma ndi kuthetsa ndi combinatorial vuto - 5 kalasi. Kumeneko kwa nthawi yoyamba nkhaniyi amapatsidwa kwa ophunzira, iwo kupeza bwino chodabwitsa combinatorial ndi kufuna kuthetsa ntchito zawo. Nkofunika kuti njira ntchito mu chiphunzitso cha vuto combinatorial pamene ana zikugwira kupeza mayankho a mafunso.

Mwa zina, kuphunzira nkhaniyi chikanadzakhala chophweka kwambiri kuti atchule mfundo factorial ndi ntchito pothetsa maikwezhoni, ntchito ndi zina zotero. Choncho, combinatorial amagwira ntchito yofunika kwambiri mu maphunziro owonjezereka.

mavuto Combinatorial: nanga chiyani?

Ngati inu mukudziwa chimene mavuto combinatorial, palibe mavuto zochita zawo mudzaona. Njira yothetsera iwo kungakhale kothandiza, ngati n'koyenera, ndandanda, ndandanda ntchito, komanso kuwerengetsera zovuta masamu, amene ntchito si abwino zamakono.

Mu masukulu ndi kuphunzira mozama za masamu ndi sayansi kompyuta mavuto combinatorial ndi kuphunzira zambiri, pakuti ichi ndi wapadera maphunziro, zolemba ndi ntchito. Monga ulamuliro, mavuto angapo wa mtundu uwu kukhala mbali ya boma Kupenda logwirizana mu masamu, iwo amakhala "zobisika" mu Gawo C.

Mmene angathetsere vuto combinatorial msanga?

Nkofunika kuona vuto combinatorial msanga, chifukwa akhoza ophimbidwa mawu, ndikofunikira pamene mukumwa mayeso, pamene aliyense udindo yokha. Lembani payokha mfundo zimene mukuona lemba la vuto, pa pepala, ndiyeno kuyesera kuchifotokoza icho kuchokera amazionera njira zinayi wotchuka.

Ngati mungathe kuika zambiri mu spreadsheet kapena chilli zina, yesetsani kuthetsa izo. Ngati ife m'kagulu izo, inu simungakhoze, mu nkhani iyi ndi bwino kusiya kwa nthawi yochepa ndi kupitiriza kwa ntchito zina, kuti tiziwononga nthawi wapatali. Zimenezi zikhoza kupewedwa pasadakhale poreshat kuchuluka kwa mtundu wa vuto.

Kodi ndingapeze zitsanzo?

Chinthu chokha chimene kudzakuthandizani kudziwa mmene angathetsere mavuto combinatorial - zitsanzo. Angapezeke mu zopereka wapadera masamu, omwe amagulitsidwa ku masitolo mabuku maphunziro. Komabe, pali angapezeke mudziwe yekha kwa ophunzira akusekondale, ophunzira ayenera kupeza ntchito zina amakonda kuti anatulukira ntchito ena aphunzitsi.

University aphunzitsi kukhulupirira kuti ophunzirawo afunika kuphunzitsa ndi tipereke mabuku zina maphunziro. Mmodzi wa zopereka bwino kuti "Njira apawokha Analysis kuthetsa mavuto combinatorial", wolembedwa mu 1977 ndipo chopangidwa ndi mobwerezabwereza kutsogolera yosindikiza nyumba za dziko. Ndiko kumene mungapeze ntchito amene ali okhudzidwa pa nthawi ndi chomveka lero.

Kodi kuchita ngati mukufuna kuti vuto combinatorial?

Nthawi zambiri ntchito combinatorial, muyenera kukhala aphunzitsi amene ayenera kuphunzitsa ophunzira kuganiza unconventionally. Apa zonse zimadalira angathe kulenga ya woyambitsa wa. Ndi bwino kulabadira zopereka alipo ndipo yesetsani kuchita ntchito moti Chili njira zambiri kulikonza ilo, ndipo anali osiyana pazimene buku.

University aphunzitsi pankhaniyi kwambiri womasuka sukulu, nthawi zambiri iwo ophunzira wanga kuti abwere ndi ntchito ndi mavuto combinatorial ndi njira zambiri ndi mafotokozedwe a njira. Ngati ndinu palibe mmodzi kapena ena, mukhoza kupempha thandizo kwa anthu amene akudziwa deralo, komanso ganyu namkungwi payekha. Mmodzi ola maphunziro ndi zotha kupanga ntchito zambiri zofanana.

Combinatorics - nzeru za m'tsogolo?

Akatswiri ambiri m'munda wa masamu ndi sayansi amakhulupirira kuti combinatorial vuto hule chitukuko cha sayansi ndi luso. Wokwanira njira sanali muyezo kwa yankho la mavuto ena, ndiyeno ife tikhoza kuyankha mafunso amene kale zaka zingapo zikuvutitsa asayansi. Ena mwa iwo kwambiri kusungabe combinatorics ndi chida cha zonse sayansi masiku ano, makamaka malo kufufuza. Zimakhala zosavuta kuwerengetsa njira yodutsamo la ndege la zombo ntchito mavuto combinatorial, monga iwo adzaona malo enieni a matupi zina zakuthambo.

Kukhazikitsa sanali muyezo njira akhala atayamba m'mayiko Asian, pamene ophunzira ngakhale ntchito yaikulu ya chulutsa, wochotsera, Kuwonjezera ndi kugawikana kusankha ntchito njira combinatorial. Chodabwitsa asayansi ambiri European luso la amathandizadi. sukulu European mpaka nditangoyamba kumene kuphunzira pa chitsanzo cha anzawo. Pamene combinatorics kukhala m'nthambi zikuluzikulu za masamu, kuganiza kovuta. Tsopano sayansi kuphunzira ndi asayansi atongi wa dziko amene akufuna popularize izo.