The bitwise operations in relation to obtaining Latin squares

The main thrust of the article is to provide interesting example, useful for students of using bitwise operations in the programming languages C ++ and Java. As an example, we describe an algorithm for obtaining a Latin square of arbitrary order. We will outline some techniques for the use of bitwise operations

On an Algorithm for Isomorphism-Free Generations of Combinatorial Objects

In the work are defined the concepts semi-canonical and canonical binary matrix. What is described is an algorithm solving the combinatorial problem for finding the semi-canonical matrices in the set \Lambda_n^k consisting of all n\times n binary matrices having exactly k 1's in every row and every column without perambulating all elements. In the described algorithm bitwise operations are substantially used. In this way it becomes easier to find the solution to the problem for receiving one representative from every equivalence class regarding the introduced in the article equivalence relation in the set \Lambda_n^k . The last problem is equivalent to the problem for finding all canonical matrices in \Lambda_n^k

The Bitwise Operations Related to a Fast Sorting Algorithm

Abstract—in the work we discuss the benefit of using bitwise operations in programming. Some interesting examples in this respect have been shown. What is described in detail is an algorithm for sorting an integer array with the substantial use of the bitwise operations. Besides its correctness we strictly prove that the described algorithm works in time O(n). In the work during the realization of each of the examined algorithms we use the apparatus of the object-oriented programming with the syntax and the semantics of the programming language C++ Keywords—bitwise operations; programming languages C/C++ and Java; sorting algorithm I