Inkinga combinatorial. Indlela elula izinkinga combinatorial. Izinkinga combinatorial: Izibonelo

Othisha wezibalo tshela abafundi babo kanye umqondo welithi "inkinga combinatorial" namanje osebangeni lesihlanu. Lokhu kuyadingeka ukuqinisekisa ukuthi bakwazi ukuqhubeka nokusebenzisana imisebenzi eminingi. Ngaphansi inkinga combinatorial kungaqondakala ithuba lokuxazulula esebenzisa ukuhlunga izakhi isethi ezilinganiselwe.

Uphawu oyinhloko izinkinga zaleli oda umbuzo kubo, ezwakala njenge- "ongakhetha Yini?" Noma "tingaki tindlela?" Izinkinga combinatorial incike yini noma cha ukuzixazulula okushiwo waqonda, ukuthi uzokwazi ukuba ikuveza isenzo noma inqubo esiye sachazwa lo msebenzi.

Indlela ukuxazulula inkinga combinatorial?

Kubalulekile ayichaze uhlobo uxhumano etholakala inkinga, kodwa kubalulekile ukuba uhlole ukuthi zinjalo yini ke iphindwa izakhi uma izakhi ngokwabo ukushintsha uma indima enkulu udlalwa ngomyalo zabo, kanye nezinye izinto.

Inkinga combinatorial ungaba eziningana ukulinganiselwa ukuthi kungenziwa onikezwe kwakwakhe. Kulokhu, uzodinga ukubala zonke ngesinqumo sakhe ukuhlola, kungakhathaliseki lemithetho zinethonya ngandlela-thile uxhumano kuzo zonke izingxenye. Uma umphumela ukhona ngempela, kudingeka uhlole ukuthi kwakuyini.

Kuphi ukuqala?

Okokuqala kudingeka sifunde ukuze uxazulule izinkinga aphansi combinatorial. Ukuba yingcweti izinto ezilula uvumele ukufunda ukuqonda imisebenzi eminingi. Sincoma ukuthi uqale ukuxazulula inkinga nge izingqinamba ezingenziwanga kucatshangelwe kukho ngaphezulu elula.

It is ibuye Kunconywa ukuzama ukuxazulula lezo zinkinga kuqala, okuyinto kufanele kubhekwe abambalwa izakhi ezivamile. Ngakho ungakwazi ukuqonda isimiso amasampula ukudala futhi ufunde esikhathini esizayo bebodwa ukudala kubo. Uma umsebenzi okuyiwona isidingo ukusebenzisa combinatorial siqukethe inhlanganisela eziningana okulula, kunconywa ukuzixazulula by izingxenye.

izinkinga combinatorial

Izinkinga ezinjalo kungase kubonakale lesilula isinqumo, kodwa combinatorics kuyinto kubenzima ukuthuthukisa, ezinye zazo akudingeki isixazululo minyaka eyikhulu edlule. Munye walemisebenti evelele kunazo zonke iwukuba ukucacisa inombolo izikwele magic nenqubo ekhethekile lapho n inombolo mkhulu kunezinhliziyo 4.

inkinga combinatorial kuyinto eduze ahlobene kuyinkolelo-mbono yokuziphendukela okungenzeka ezavela wenkathi ephakathi. Amathuba umsuka isenzakalo esithile ingabalwa kuphela ukusetshenziswa combinatorics, kulesi simo uzodinga enye phakathi zonke izici kwezinye izindawo ukuze uthole ikhambi elilungile.

Ukuhlangabezana izinselele

izinkinga combinatorial ikhambi osetshenziselwa ukuqeqeshwa kwabafundi abafundi ukusebenza le nto. Uma sikhuluma ngokuvamile, kufanele wenze umuntu kwenzalo isifiso ukuthola isisombululo ezivamile. Ngaphezu izibalo, kubalulekile ukusebenzisa ukucindezeleka kwengqondo futhi usebenzise Ukuqagela.

Ngo inqubo ukuxazulula izinkinga ingane uzokwazi ukuthuthukisa umcabango wabo kanye zezibalo umthamo combinatorial, kungaba sina wusizo kuye esikhathini esizayo. Kancane kancane, ezingeni obulukhuni imisebenzi okudingeka uthuthukise, ngeke akukhohlwe ulwazi ekhona bese wengeza kubo.

Indlela 1. ukuhlela

Izindlela ukuxazulula izinkinga combinatorial zihluke kakhulu komunye nomunye, kodwa ingasetshenziswa umfundi impendulo. Omunye elula, kodwa ngesikhathi esifanayo futhi indlela elide kakhulu kumuntu libanjwe. Lapho kubalulekile ukuba umane uzame zonke izixazululo kungenzeka ngaphandle kokwenza noma yiziphi imidwebo amathebula.

Njengomthetho, umbuzo inkinga enjalo elihlobene ne ongakhetha azalelwa isenzakalo esithile, njenge: lokho izinombolo zingase zimiswe ngezinombolo 2, 4, 8, 9? Ngokuzama ngemigudu iyawakha impendulo eyayakhiwa inhlanganisela kunokwenzeka. Le ndlela enhle uma isibalo ongakhetha incane.

2. Indlela Izinkuni samuntu

Ezinye izinkinga combinatorial zingaxazululwa kuphela ngokwenza uhlelo, lapho ulwazi mayelana nephuzu ngalinye izofakwa ohlwini ngokuningiliziwe. Ukudweba esihlahleni ongakhetha - enye indlela yokuthola impendulo. Kuyinto efanelekayo izixazululo hhayi imisebenzi enzima kakhulu, lapho kukhona isimo ezengeziwe.

Isibonelo le nkinga:

• Yini izinombolo idijithi emihlanu-zingase zimiswe kusuka amadijithi 0, 1, 7, 8? Ukuxazulula isidingo ukwakha umuthi zonke inhlanganisela kungenzeka, kuyilapho kukhona isimo eyengeziwe - inombolo ayikwazi ukuqala kabusha. Ngakho, impendulo sizofaka zonke izinombolo ukuthi uzoqala ngo 1, 7 noma-8.

Ukwakhiwa Indlela 3 amathebula

izinkinga combinatorial engenziwa esebenzisa amatafula. Bafana kwesihlahla ongakhetha ngoba unikeza ikhambi sobala isimo. Ukuze uthole impendulo efanele udinga ukudala itafula, futhi uyonikwa walingisa evundla izimo mpo ziyafana.

izimpendulo ezingakhetha izotholwa ezimpambanweni zomgwaqo kanye nemigqa. Kulokhu, izimpendulo empambana ikholomu nomugqa ngeke uthole idatha efanayo, empambana kufanele kube ikakhulukazi uphawu, akumelwe aphanjaniswe no-nokwenziwa kwemigomo imphendvulo yekugcina. Le ndlela akuvamile kakhulu kukhetha abafundi, abaningi bakhetha kwesihlahla ongakhetha.

Indlela 4. Ukubuyabuyelela

Kukhona enye indlela esingathola ngalo ungakwazi ukuxazulula izinkinga combinatorial - ukubuyabuyelela umthetho. Yena uphelele kuleli cala, lapho isimo akudingekile ukuba uhlu zonke izixazululo kunokwenzeka, wena nje kudingeka uthole inani eliphezulu. Le ndlela iyona kuphela into efana nayo, isetshenziswa ngokuvamile kakhulu, uma usanda ukuxazulula izinkinga combinatorial.

Isibonelo le nkinga ingase kanje:

• abantu 6 alindele ehholo ukuhlolwa. Zingaki izindlela ingasetshenziswa uyibeke ohlwini? Ukuze Impendulo kuyadingeka ukuze ucacise bangaki kubo kungenzeka ekuqaleni, kodwa ngosuku lwesibili, eyesithathu, njalonjalo. D. ukusabela kuyoba njani inombolo 720.

Combinatorics nezinhlobo zayo

inkinga combinatorial akuyona izinto esikoleni kuphela, abafundi baseyunivesithi nazo nokulifunda. Ngo isayensi, kukhona izinhlobo eziningana combinatorics, futhi ngamunye kubo has umgomo wayo siqu. okubaliwe combinatorial kufanele ucabangele izinkinga ku ukudluliswa kanye isibalo ukucupha zingenzeka izimo ezengeziwe.

combinatorics Bezakhiwe wumkhakha zohlelo esikoleni esiphakeme, ke uhlola ukuthi imfundiso yokuziphendukela matroids namagrafu. combinatorics Extreme futhi ihlobene okusezingeni eliphezulu impahla esikoleni, futhi nazi ukulinganiselwa kwabo ngabanye. Esinye isigaba - Ramsey umbono uwukuthi ekutadisheni amaphethini ukuhlukahluka ongacabangi izakhi. Kukhona combinatorics ngokolimi, okuyinto ucabangela ukuhambisana izakhi ezithile bodwa.

Izindlela lokufundisa izinkinga combinatorial

Ngokwe lwezifundo, engu-abafundi, okuyinto yakhelwe amaziyo kokuqala indaba kanye nokuxazulula inkinga combinatorial - 5 ekilasini. Kwakulapho okokuqala lesi sihloko esinikezwa abafundi, bathola kangcono lo mkhuba combinatorial futhi uzame ukuzixazulula imisebenzi yabo. Kubalulekile kakhulu ukuthi indlela esetshenziswe ekwakhiweni inkinga combinatorial lapho izingane bekwi ekutholeni izimpendulo zemibuzo.

Phakathi kwezinye izinto, ngemva kokufunda le sihloko kungaba lula kakhulu ngenisa umcondvo wekubhalwa ngokwesimo futhi ulisebenzise ukuxazulula zibalo, imisebenzi kanye nokunye. Ngakho, combinatorial udlala indima ebalulekile iqhubekisele phambili imfundo yayo.

izinkinga combinatorial: ziyini na?

Uma wazi ukuthi izinkinga combinatorial, akukho nobunzima isinqumo sabo nawe uzozibonela. Izindlela nokuzixazulula kungaba wusizo, uma kunesidingo, ukuhlela, ukusebenza ngezikhathi, kanye izibalo eziyinkimbinkimbi zezibalo, okuyiwona ukusebenza akuyona zobuchwepheshe efanelekayo.

Etikolweni lapho etadisha ngokujulile wezibalo kanye computer science izinkinga combinatorial kufundvwe okunye, ngoba lena ekhethekile izifundo, iziqondiso, kanye nemisebenzi. Njengomthetho, izinkinga eziningana lolu hlobo kungaba yingxenye le esihlanganisiwe isimo Luhlolo mathematics, ngokuvamile "ocashe" eNgxenyeni C

Indlela ukuxazulula inkinga combinatorial ngokushesha?

Kubalulekile ukwazi ukubona inkinga combinatorial ngokushesha, ngoba kungenzeka ukuba kulotshwe izwi nezwi zigutshuzelwe, kubalulekile ikakhulu lapho ukuthatha ukuhlolwa, lapho zonke ukubalwa ngomzuzu. Bhala eceleni ulwazi ozibona umbhalo yenkinga, ngesikhathi iphepha, bese uzama yihlaziye kusukela iphuzu sicabangela izindlela ezine ezidumile.

Uma ungakwazi ukufaka ulwazi ku-spreadsheet noma enye inhlangano, zama ukuze siyixazulule. Uma thina uhlukanise ke, awukwazi, kulesi simo kungcono ukushiya ke isikhathi esifushane bese sidlulela kweminye imisebenzi, ukuze singathwesi ukuchitha isikhathi esiyigugu. Lesi simo kungagwenywa kusengaphambili poreshat ethile lolu hlobo nkinga.

Ngingalutholaphi ezinye izibonelo?

Into kuphela ukuthi kuzokusiza ufunde indlela yokuxazulula izinkinga combinatorial - izibonelo. Bona ingatholakala kumaqoqo abalulekile zezibalo, okuyinto edayiswa ezitolo izincwadi zemfundo. Nokho, lapho kungatholakala ulwazi kuphela abafundi esikoleni esiphakeme, abafundi kuyodingeka uthole imisebenzi eyengeziwe bathambekele baye baklama umsebenzi lonke nothisha.

University osolwazi bakholelwa ukuthi abafundi kudingeka baqeqeshe futhi njalo ubaphe izincwadi ezengeziwe zemfundo. Omunye amaqoqo engcono kubhekwe "Izindlela leyehlukene Ukuhlaziywa ekuxazululeni izinkinga combinatorial", ebhalwe ngo-1977 futhi akhiwe ngokuphindaphindiwe ehola ukushicilela izindlu yezwe. Kulapho ungathola imisebenzi ehambisana ngesikhathi futhi okugcinwa kusebenza namuhla.

Yini okumele uyenze uma ufuna ukwenza inkinga combinatorial?

Ngokuvamile umsebenzi combinatorial, wena kumelwe sibe ngabafundisi odinga ukufundisa abafundi ukucabanga unconventionally. Lapha konke kuzoncika ezingaba okudala umsunguli. Kunconywa ukuba banake amaqoqo ekhona bese uzama ukwenza umsebenzi ukuze ihlanganisa izindlela eziningana ukuze siyixazulule, futhi sasihlukile idatha ncwadi.

University othisha kulokhu esikoleni yayisikhululeke kakhudlwana kakhulu, bavame ukunikeza abafundi bami beveza ahambisane nemsebenti lowentiwe, izinkinga combinatorial nezixazululo enemininingwane nezincazelo izindlela. Uma akekho noma nezinye, ungakwazi ukucela usizo kulabo abamazi kahle endaweni, kanye ukuqasha komfundisi yangasese. Omunye ihora zezemfundo kwanele ukwakha imisebenzi eminingana efanayo.

Combinatorics - isayensi esizayo?

Ochwepheshe abaningi emkhakheni mathematics ne-physics bakholelwa ukuthi kuyinto inkinga combinatorial babekwazi kubangele ukuthuthukiswa wesayensi lobuchwepheshe. Engingakusho nje indlela angajwayelekile ukuze ikhambi nezinye izinkinga, bese sikwazi ukuphendula imibuzo ezibe kakade namakhulu eminyaka amaningana uhlupho ososayensi. Ezinye zazo silondoloze sina ukuthi combinatorics iyithuluzi bonke yesayensi yanamuhla, ikakhulukazi ukuhlola umkhathi. Kulula kakhulu ukubala trajectory of the indiza lwemikhumbi usebenzisa izinkinga combinatorial, njengoba eyonquma indawo esiqondile emizimbeni ezithile yasezulwini.

Sekuyisikhathi eside Ukuqaliswa indlela angajwayelekile kuqalile emazweni ase-Asia, lapho abafundi ngisho imisebenzi eyisisekelo zokuphindaphinda, ukususa, kwalokho nokuhlukanisa ukunquma usebenzisa izindlela combinatorial. Lamangala ososayensi amaningi aseYurophu, inqubo esebenza ngempela. izikole European kude kangaka nje waqala ukufunda kokuhlangenwe nakho ozakwabo. Lapho-ke combinatorics ngomunye amagatsha ezinkulu wezibalo, ukuthi iqalise nzima. Manje isayense ufundwa ososayensi ehamba phambili emhlabeni abafuna popularize ke.