Umkholezima

Ishathi lenqubo yomkholezima ( umkholezima ka- Euclid ) wokuqaqulula isihlukanisi esivamile esikhulu kunazo zonke (gcd) samanani amabili u-a no- b ezigcemeni ezinegama elithi A no-B. Umkholezima iqhubeka ngokususa okulandelanayo ngamaluphu amabili: UMA ukuhlolwa B ≥ A kuveza okuthi "yebo" noma “iqiniso” (ngokunembe kakhudlwana, inombolo engu - b esigcemeni B inkulu noma ilingana nenombolo a endaweni A) BESE, umkholezima ucacisa u-B ← B − A (okusho inombolo b − a ithatha indawo yendala b ).

umkholezima wokuqala ukushicilelwa, umdwebo ka-Ada Lovelace we-"note G"

Kumchazazibalo nakwinzululwazi yesicikizi, umkholezima lunguchungechunge olunomkhawulo lwemiyalezo enembile, evame ukusetshenziswa ukuxazulula izinkinga eziqondile noma ukwenza umcikizo. Imikholezima isetshenziswa njengeziqondiso zokwenza uqaqululo nokudludlunga imininingo. Imikholezima ethe thuthu ingenza izisuso ezihlelelekiwe (ezibizwa ngokuthi inhluzo ehleleliwe) futhi ingasebenzisa njengezivivinyo zomchazazibalo ne-logic ukuphambukisa ukugunundwa komkitizo ngemigudu ehlukene (okubhekiselwa kuyo ngokuthi ukuthatha isigqibo okuhlelekiwe). Ukusebenzisa izici zabantu njengezichazisi zezinguxa ngokomfanekiso noma ukungathekisa kwakuyinto eyayenziwa ngu-Alan Turing ngokusebenzisa amabizo afana nokuthi "inkumbulo", "ukuphequlula" nelithi "imvusi".

Ngokuphambene, insobozelo (heuristic) iwuhlobo lwendlela yokuxazulula izinkinga engacacisiwe ngokuphelele noma engaqinisekise ukuba neziphumo ezingqanda noma ezinembile, ikakhulu ezidlangaleni zezinkinga lapho kungekho khona iziphumo ezingqanda noma ezinembile ezichasiswe kahle.^[1]

Njengendlelasu ephumelelayo, umkholezima ungavezwa ngesamba samazwi esinomkhawulo somkhathi nesikhathi,^[2] kanye nangolimi olusemthethweni oluchasiswe ^[3] ukuze kuqaqululwe insebenzo yomchazazibalo.^[4] Kusukela esimweni esiyisileke nasegalelweni lokuqala,^[5] imiyalezo izochazisa umcikizo ozothi lapho ugunundwa, uqhubeke ngokwenani elinomkhawulo ^[6] lezimo ezichasiswe khake eziwuchunge, kuze kube yilapho ukhiqiza "isphumo" ^[7] futhi ukhawuka esimweni sokugcina esiphelayo . Ushintsho kusuka esimweni esithile kuya kwesilandelayo alunqunyelwe; eminye imikholezima, eyaziwa ngokuthi imikholezima ethukelayo, ihlanganisa igalelo lokwethukela.^[8]

uMlando[hlela | Hlela umthombo]

Imikholezima yasendulo[hlela | Hlela umthombo]

Kusuka enguna, izinkambiso zezinyathelo zokuxazulula izinkinga zomchazazibalo ziye zafakazelwa. Lezi zihlanganisa umchazazibalo waseBhabhiloni (cishe ngowezi-2500 BC), umchazazibalo waseGibhithe (cishe ngowezi-1550 BC), umchazazibalo waseNdiya (cishe ngowezi-800 BC nakamuva), umchazazibalo waseGrisi (cishe ngowezi-240 BC, isb. isihlungo sika-Erathositini nomkholezima ka-Yukulide), kanye nomchazazibalo wase-Arabiya (ngekhulu le-9, isb. imikholezima yomchazanyandla yokugqabula iziguqukezelo esekwe kwesihlaziyo somjingo).

U-Al-khwarizim nebizo umkholezima[hlela | Hlela umthombo]

Cishe ngonyaka wama-825, uMuhammad ibn Musa al-Khwarizmi waloba i-kitāb al-ḥisāb al-hindī ("INcwadi yoMcikizo waseNdiya") kanye ne-kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ("UkweNgeza nokuPhunguza kwizibalonqangi zaseNdiya"). Yombili lemibhalo yahlulukwa ngolimi lesi-Arab sendabuko. (Kodwa enye incwadi yakhe ye-algebra isasekhona.)

Ekuqaleni kwekhulu le-12, kwavela izihumusho zesiLathini zemibhalo ka-al-Khwarizim ebandakanya izimiso zezibalonani nesibalonqangi zesiHindu nesi-Arabiya: Liber Alghoarismi de practica arismetrice (eyahunyishwa ngu-John of Seville) kanye ne- Liber Algorismi de numero Indorum (eyahunyushwa ngu-Adelard of Bath). Kanjalo, elithi alghoarismi noma algorismi kwaba yindlela yesiLathini yokuthi Al-Khwarizmi; ngesiZulu elithi 'umkholezima' cishe lazwakala ngokufana nalo, kodwa linomsuka ohlukile.

Imithombo[hlela | Hlela umthombo]

↑ David A. Grossman, Ophir Frieder, Information Retrieval: Algorithms and Heuristics, 2nd edition, 2004, Template:Isbn
↑ "Any classical mathematical algorithm, for example, can be described in a finite number of English words" (Rogers 1987:2).
↑ Well defined with respect to the agent that executes the algorithm: "There is a computing agent, usually human, which can react to the instructions and carry out the computations" (Rogers 1987:2).
↑ "an algorithm is a procedure for computing a function (with respect to some chosen notation for integers) ... this limitation (to numerical functions) results in no loss of generality", (Rogers 1987:1).
↑ "An algorithm has zero or more inputs, i.e., quantities which are given to it initially before the algorithm begins" (Knuth 1973:5).
↑ "A procedure which has all the characteristics of an algorithm except that it possibly lacks finiteness may be called a 'computational methodTemplate:'" (Knuth 1973:5).
↑ "An algorithm has one or more outputs, i.e. quantities which have a specified relation to the inputs" (Knuth 1973:5).
↑ Whether or not a process with random interior processes (not including the input) is an algorithm is debatable. Rogers opines that: "a computation is carried out in a discrete stepwise fashion, without the use of continuous methods or analogue devices ... carried forward deterministically, without resort to random methods or devices, e.g., dice" (Rogers 1987:2).

[1] David A. Grossman, Ophir Frieder, Information Retrieval: Algorithms and Heuristics, 2nd edition, 2004, Template:Isbn

[2] "Any classical mathematical algorithm, for example, can be described in a finite number of English words" (Rogers 1987:2).

[3] Well defined with respect to the agent that executes the algorithm: "There is a computing agent, usually human, which can react to the instructions and carry out the computations" (Rogers 1987:2).

[4] "an algorithm is a procedure for computing a function (with respect to some chosen notation for integers) ... this limitation (to numerical functions) results in no loss of generality", (Rogers 1987:1).

[5] "An algorithm has zero or more inputs, i.e., quantities which are given to it initially before the algorithm begins" (Knuth 1973:5).

[6] "A procedure which has all the characteristics of an algorithm except that it possibly lacks finiteness may be called a 'computational methodTemplate:'" (Knuth 1973:5).

[7] "An algorithm has one or more outputs, i.e. quantities which have a specified relation to the inputs" (Knuth 1973:5).

[8] Whether or not a process with random interior processes (not including the input) is an algorithm is debatable. Rogers opines that: "a computation is carried out in a discrete stepwise fashion, without the use of continuous methods or analogue devices ... carried forward deterministically, without resort to random methods or devices, e.g., dice" (Rogers 1987:2).

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