App Elements of Discrete Math

ivan gabrovski

Iqukethe izikhangiso

Mayelana nalolu hlelo lokusebenza

Uhlelo lokusebenza luklanyelwe ukuhlinzeka ngokusebenza okuthile okuhlobene negatsha lezibalo elihlukaniswe njenge-Discrete Mathematics. Uhlelo lokusebenza luhlanganisa ama-algorithms athile, izingxenye zethiyori yezinombolo kanye nokubethela, ukungeniswa kanye nokuphindaphinda, ukuqaliswa kwezindlela zokubala ezithuthukisiwe ezikhethiwe. Izihloko ze-Discrete Mathematics kanye Nezicelo Zazo (Imfundo ye-McGraw-Hill - Kenneth H. Rosen) akunakwenzeka ukuhlanganisa kuhlelo lokusebenza olulodwa, futhi lolu hlelo lokusebenza aluzibeki umsebenzi onjalo.
Ama-algorithms kuhlelo lokusebenza ahlanganisa(Umsebenzi Wama-Algorithms): i-algorithm yokusesha okuqondile nokuhamba kanambambili, ukuhlunga ngendlela yebhamuza nangendlela yokuguqula, ukunquma amapheya axhunyiwe namapheya angagqagqani (isibonelo, imicimbi enesiqalo nesiphetho njengezifundo).
Uhlobo lwebhamuza lungenye yezindlela ezilula zokuhlunga, kodwa hhayi eyodwa esebenza kahle kakhulu. Ibeka uhlu ekuhleleni okwandayo ngokuqhathanisa ngokulandelana izinto eziseduze, ishintshanise uma ilandelana okungeyona. Ukufeza ukuhlunga kwebhamuza, yenza umsebenzi oyisisekelo, okungukuthi, ukushintshanisa into enkulu nencane eyilandelayo, kuqalwe ekuqaleni kohlu, ukuze kudlule ngokugcwele. Iphinda le nqubo kuze kuqedwe ukuhlunga.
Uhlobo lokufaka luqhathanisa i-elementi yesibili ne-elementi yokuqala bese luyifaka ngaphambi kwe-elementi yokuqala uma ingeqi ingxenye yokuqala nangemuva kwe-elementi yokuqala uma idlula isici sokuqala. Kuleli qophelo, izakhi ezimbili zokuqala zilandelana ngendlela efanele. Isici sesithathu sibe sesiqhathaniswa nesici sokuqala, futhi uma sikhulu kunesici sokuqala, siqhathaniswa nesesibili; ifakwe endaweni efanele phakathi kwezakhi ezintathu zokuqala. Inqubo iqhubeka ngendlela efanayo nezakhi ezilandelayo kuze kube sekugcineni kohlu.
Ama-algorithms enza lokho okubonakala kuwukukhetha "okungcono kakhulu" esinyathelweni ngasinye abizwa ngokuthi ama-algorithms ahahayo - lawa ama-algorithms amabili wamapheya axhunyiwe namapheya angadlulelani.
Amapheya angagqagqani angasetshenziswa ekutholeni umzila phakathi kwamasayithi amabili.
Umsebenzi Wokuguqulwa Kwezinombolo kanye Nokubhala Okuyimfihlo kuhlanganisa: - Ukuguqula izinombolo zisuke ohlelweni lwezinombolo ziye kwelinye; nokunye.
Uhlelo lokusebenza lungasetshenziswa lapho uguqula izinombolo zisuka ohlelweni lwezinombolo ziye kolunye(Umsebenzi Wokuguqulwa Kwezinombolo), ekusebenzeni kwe-arithmetic (imisebenzi ye-Arithmetic) enamanani aphelele kumasistimu ezinombolo ahlukene (afakwe kusisekelo esingu-2,3,4,5,6,7,8,9,16). Ukusebenza kwe-arithmetic nokuguqulwa kumasistimu ezinombolo ahlukene kwenziwa ngama-integer ngaphandle komkhawulo ngobude bama-operands, okuthiwa yi-BigInteger.
I-Factorization(Umsebenzi Wokwenza I-Factorization) ihilela ukunquma izici eziyinhloko zenombolo, ukucacisa isihlukanisi esivamile esikhulu kunazo zonke sezinombolo ezimbili, nokunye.
Isizukulwane sezinombolo zomgunyathi ezingahleliwe zohlobo lwe-BigInteger( Izinombolo Ezingahleliwe ze-Pseudo), ezinqunywa ubude bamabhithi.
Ukubethelwa kombhalo(Umsebenzi We-Cryptography) osuselwa kuzinhlamvu zesiLatini(26), ukubethela kwemibhalo ngezinhlamvu zesiCyrillic (izinhlamvu ezingama-30) nokubethela kusetshenziswa indlela ye-RSA kanye nendlela ye-AES. Ngazo zonke izindlela zokubethela, kungenzeka ukugcina amafayela abethelwe kusiqondisi Sokulanda sedivayisi, emagameni okunombhalo othi AppDiscret.
Ku-cryptography kubalulekile ukwazi ukuthola insalela ka-b emandleni n ihlukaniswe ngama-m ngempumelelo ngaphandle kokusebenzisa inkumbulo eningi ngokweqile. Uhlelo lokusebenza luphinde lube nomsebenzi wokuveza imojuli esheshayo(Umsebenzi Wokucacisa Okwemodyuli osheshayo) .
Ukufakwa kwezibalo ekusetshenzisweni kuhlanganisa(Umsebenzi Wokungeniswa Kwezibalo): ukufinyezwa kwezinombolo zokuqala ezingu-N, nokunye.
Imisebenzi yokubala ethuthukisiwe(Umsebenzi Wokubala) ihlanganisa: - Ukubala inani lamagciwane aphindaphindwe ngemva kwesikhathi esithile; - Izinombolo zeFibonacci; - Inani le-disc elinyakazayo kumdlalo weTowers of Hanoi; nokunye.
Cishe kuyo yonke imisebenzi, kukhona usizo oluveza izici ezibaliwe.