Maitiro ePascal muCombinatorics
Combinatorics ibazi remasvomhu rinoongorora nzira dzekuronga zvinhu. Chimwe chezvishandiso zvinonakidza uye zvinobatsira mubasa iri iPascal's Pattern, inozivikanwawo sePascal's Triangle. Pascal's Triangle itriangle yenhamba dzakavakwa zvichienderana nemitemo yakati uye ine mashandisirwo akawanda muzvikamu zvakasiyana-siyana zvemasvomhu, kusanganisira dzidziso yeprobability, nhamba, uye, zvechokwadi, combinatorics.
Kwakatangira Triangle yaPascal
Triangle yaPascal yakatumidzwa zita raBlaise Pascal, nyanzvi yemasvomhu yekuFrance yemuzana remakore rechi17. Zvisinei, yaizivikanwa nenyanzvi dzemasvomhu dzekuIndia neChina kare Pascal asati avapo. MuIndia, inonzi "Meru-Prastaara," uye muChina inozivikanwa se "Yang Hui Triangle," yakatumidzwa zita raYang Hui, nyanzvi yemasvomhu yekuChina.
Maumbirwo eTriangle yaPascal
Katatu kaPascal kanotanga ne1 pamusoro. Mutsetse wega wega unotevera unoumbwa nekuwedzera nhamba mbiri dziri mumutsara uri pamusoro payo. Mutsetse wekutanga une nhamba imwe chete, 1. Mutsetse wechipiri une nhamba mbiri dziriwo 1. Mutsetse wechitatu une 1s kumagumo ese ne2 pakati pawo, zvichikonzerwa nekuwedzera 1s mbiri kubva mumutsara wekare.
Kazhinji, mutsetse wechitanhatu muPascal's Triangle unogona kunyorwa seizvi:
1, (n-1)C1, (n-1)C2, …, (n-1)C(n-1), 1
Pano, “kC(n)” chiratidzo chemusanganiswa chinoverengwa sekuti “n choose k” kana kuti “n choose k”, inova fomura yemusanganiswa mumasvomhu uye inowanzoshandiswa mudzidziso yeprobability uye linear algebra.
Mashandisirwo muCombinatorics
1. Musanganiswa
Imwe yenzira huru dzekushandisa Pascal's Triangle mu combinatorics ndeyekuverenga misanganiswa. Musanganiswa inzira yekusarudza zvinhu kubva mu seti iyo kurongeka kusingatariswe. Muchirevo chePascal's Triangle, kukosha kuri mumutsara we nth nekoramu ye kth kunomiririra misanganiswa ye n-1Ck-1.
Semuenzaniso, kuti tiverenge musanganiswa we5C2 (tichisarudza 2 kubva pa5), tinogona kutarisa mutsetse wechitanhatu nekoramu yechitatu muPascal's Triangle, iyo inopa kukosha kwe10. Nemamwe mashoko, kune nzira gumi dzekusarudza zvinhu zviviri kubva museti yezvinhu zvishanu.
2. Permutations uye Binomial Coefficients
Pascal's Triangle ine hukama hwakasimba ne binomial coefficients dzinoonekwa mu binomial expansion ye (x + y)^n. Aya ma coefficients ndiwo manhamba atinowana muPascal's Triangle. Semuenzaniso, expansion ye (x + y)^3 ndeiyi:
(x + y)^3 = 1 x^3 + 3 x^2 y + 3 xy^2 + 1 y^3
Pano, ma coefficients 1, 3, 3, uye 1 ndiwo ma values ePascal's Triangle mumutsara wechina.
3. Mutambo Wemikana
Mudzidziso yekufungidzira, Pascal's Triangle inowanzo shandiswa kuona mukana wemhedzisiro dzakasiyana. Semuenzaniso, kana tichikanda mari kana, tinoda kuziva mukana wekuwana misoro miviri. Tichishandisa Pascal's Triangle, tinogona kuwana huwandu hwemisanganiswa inoenderana, iri mumutsara wechishanu nekoramu yechitatu, iyo inotipa kukosha kwe6. Saka, kune nzira nhanhatu dzekuwana misoro miviri mukukanda mari ina.
Zvinhu Zvakakosha zvePascal's Triangle
Katatu kaPascal kane zvinhu zvakasiyana-siyana zvinonakidza uye zvinoshamisa:
1. Kuenzana kwezvikamu
Pascal's Triangle inoratidza kuenzana kwenhamba. Mutsara wechitanhatu wePascal's Triangle wakaenzana, saka nCr = nC(nr).
2. Hukama hweFibonacci
Pascal's Triangle inogona kushandiswawo kurondedzera kurongeka kweFibonacci. Nhamba dzeFibonacci dzinogona kuwanikwa nekuwedzera nhamba dziri pamitsetse yakapatsanurwa inosanganisa mitsara yakati wandei muPascal's Triangle.
3. Kuenzana
Pascal's Triangle inoratidza mapatani anonakidza ekuenzana. Kana tikapenda nhamba dzisina kuenzana uye dzakafanana dziri muPascal's Triangle zvakasiyana, mapatani anonakidza ekuona anobuda, achiwanzogadzira mafractals.
Kushandiswa kwePascal Patterns muProgramming
Pascal's Triangle inoshandiswawo kakawanda mumaalgorithms uye mapurogiramu. Semuenzaniso, tinogona kugadzira Pascal's Triangle tichishandisa mutauro wepurogiramu sePython nekodhi inotevera:
"'python
def generate_pascals_triangle(n):
katatu = [[1]]
ye i iri mu range(1, n):
mutsara = [1]
ye j iri mu range(1, i):
row.append(triangle[i-1][j-1] + triangle[i-1][j])
mutsetse.wedzera(1)
katatu. wedzera (mutsara)
kudzoka katatu
n = 5
katatu = gadzira_pascals_triangle(n)
yemutsara mutriangle:
dhinda (mutsara)
``
Kodhi iri pamusoro apa ichaburitsa mitsara yekutanga kusvika yechishanu yePascal's Triangle, iyo inogona kushandiswa pakubatanidza kwakasiyana-siyana uye mashandisirwo ekuongorora mikana.
Mhedziso
Pascal's Triangle, kana kuti Pascal's Pattern, chishandiso chine simba uye chinoshanda zvakasiyana-siyana mukubatanidza. Kubva pakuverenga misanganiswa uye mikana mumitambo yekufungidzira kusvika pakunzwisisa kuwedzera kwebinomial uye kubatanidza pfungwa dzakasiyana dzemasvomhu, Pascal's Pattern inopa nzira inoshanda uye inonzwisisika yekugadzirisa matambudziko akaomarara. Nemaumbirwo ayo ari nyore asi kudzika kwemasvomhu kunoshamisa, Pattern yaPascal inoramba ichidzidzwa uye ichishandiswa muminda yakasiyana-siyana yemasvomhu nedzimwe sainzi.
