The Methodology of Teaching Algorithms of Combinatorics: Permutations, Combinations, Arrangements

Abstract

In this article we have described the methodology for teaching the algorithms of combinatorics which are often used when solving tasks of informatics. These are the economic types of tasks in which we need to select different objects, sort selected objects in some order and choose the best selection from all possible selections. The formulas of calculating number of such selections are known from mathematics, but in informatics we are interested not only in number, but also in selections themselves, which can be generated by special algorithms. In general, the number of such selections is quite large, so we need to use optimal algorithms to find the desired answer in real time. The essence of combinatoric objects is explained. It is shown how to find the desired object in optimal way. The samples and description of the corresponding algorithms are presented using the programming language C ++.

Keywords: Combinatorics, Methodology, Permutations, Combinations, Arrangements, Combinatorial object, Selections