Clustering in tasks of the Unified State Exam in informatics

The article presents methodological approaches to solving the data analysis problem included in the Unified State Exam (USE) in informatics since 2025. It is shown that for any shape of clusters, it is possible to separate them by a set of straight lines parallel to the coordinate axes or by inclined lines. an accelerated algorithm for finding cluster centers is proposed, which allows to significantly reduce the computation time and thus to solve the problem for data sets containing more than 10,000 points in an acceptable time. complex versions of the problem, as compared with the demonstration version of the control and measuring materials, are considered: the presence of anomalies that should be ignored when searching for the cluster center, and clusters of complex shape. a comparison of various approaches to dividing data into clusters, including the dbscan algorithm and the k -means method, is carried out.