Combinatorial Problem of Optimal Completing of Sets

U ovom radu opisan je kombinatorni problem kompletiranja setova i dan je primjer primjene. Obrađene su metode koje se koriste za njegovo rješavanje. Analizom problema zaključeno je da ne postoji bolja metoda od postojećih. Programski izvedena metoda primjenjivala se nad različitim ulazima da bi se rezultatima potvrdila ispravnost zaključaka. Nakon analize rezultata, donesen je zaključak da su dane metode optimalne. Dodatno, grafički su prikazani rezultati nakon primjene svake od metoda. Gledajući vizualni prikaz rezultata, razlike među ishodima metoda jasne su i lako uočljive, a opravdanje se pronalazi u poznavanju logike koja stoji iza svake od njih.This paper describes the combinatorial problem of completing the sets and gives the example of its application. Methods used for solving the problem are elaborated as well. After analysing the problem, no better methods were found then the ones that already exist. Methods were implemented in code and applied across different inputs to confirm the correctness of the conclusions. After the analysis of the results, a conclusion was that given methods are optimal. Additionally, the results after method appliance are graphically displayed. Looking at those results makes differences between methods obvious and easy to explain if one knows the logic that stands behind each one of them