Variations for spanning trees

Coursebooks discussing graph algorithms usually have a chapter on minimum spanning trees. It usually contains Prim’s and Kruskal’s algorithms [1, 2] but often lacks other applications. This type of problem is rarely present at informatics competitions or in tests in secondary or higher level informatics education This article is aimed at describing some competition tasks that help us prove that the application of the above algorithms are well-suited for both competition and evaluation purposes. The Hungarian National Informatics Competition for Secondary School Students look back on a history of 20 years and so does the International Olympiad in Informatics. Basically, informatics competitions rely on algoritmization tasks [3, 4], the circle of which is continually developing though showing a surprisingly great constancy at the same time. At both types of competitions there are often tasks connected to graphs or problems that can be reduced to representation of graphs. International competitions nearly lack tasks in connection with minimum spanning trees. On the other hand, at national competitions (Hungarian National Informatics Competitions for Secondary School Students and the Selecting Competition for the International Olympiad) the scientific committees deciding on tasks (mainly Gyula Horváth and László Zsakó) has set this kind of problem several times. You could also have met a similar one for instance at the 11th Lithuanian Olympiad in Informatics (Winter in The Kingdom of Fancy). This article is about the experience gained so far: with the help of the tasks below, we would like to show that their solution is not a simple description of the two classical spanning tree algorithms (Prim’s and Kruskal’s) but their creative application [5, 6].