41 research outputs found
Some Combinatorial Problems on Binary Matrices in Programming Courses
The study proves the existence of an algorithm to receive all elements of a
class of binary matrices without obtaining redundant elements, e. g. without
obtaining binary matrices that do not belong to the class. This makes it
possible to avoid checking whether each of the objects received possesses the
necessary properties. This significantly improves the efficiency of the
algorithm in terms of the criterion of time. Certain useful educational effects
related to the analysis of such problems in programming classes are also
pointed out
Calculation of the Number of all Pairs of Disjoint S-permutation Matrices
The concept of S-permutation matrix is considered. A general formula for
counting all disjoint pairs of S-permutation matrices as a
function of the positive integer is formulated and proven in this paper. To
do that, the graph theory techniques have been used. It has been shown that to
count the number of disjoint pairs of S-permutation matrices,
it is sufficient to obtain some numerical characteristics of all
bipartite graphs.Comment: arXiv admin note: text overlap with arXiv:1211.162