Abstract <p>The possibilities of using a mathematical apparatus for solving current applied problems related to finding extreme values in areas such as process optimization, data analysis, and technical calculations are shown. Attention is focused on the development of the binary tree concept as a basis for finding extremes and solving problems that require fast and efficient information processing. The development of a software implementation of the proposed mathematical apparatus in the C++ programming language is presented; how the methods and algorithms can be integrated into existing software environments is described; and the advantages of using C++ for working with large amounts of data and high performance requirements are demonstrated.</p>