"Find the Way" is a serious game we developed with the intention to help mainly university students but also all interested persons to understand the Minimum Spanning Tree (MST) problem and familiarize with the application of the algorithms suggested by R. Prim and J. Kruskal. Both algorithms are discussed as part of the curriculum in the context of courses on Introduction to Algorithms and are used in a wide range of practical real-world applications.

In the context of Graph Theory, a graph is a collection of vertices (i.e., points) and edges (i.e., lines connecting points). Vertices correspond to entities. An edge between two vertices implies that the corresponding entities are somehow related. Edges can bear weights which reflect some sort of cost required for their establishment. Weights can reflect physical or conceptual distance, time, budget and so on. Trees are special cases of graphs which are acyclic and connected. A Spanning Tree for a given graph is a tree containing all vertices of this graph. When weights are assigned to the edges of a graph, a Minimum Spanning Tree (MST) for this graph is a spanning tree of minimum total edge-cost. The MST problem aims at finding spanning trees of minimum total (edge) cost for given (connected) graphs and has many practical applications. Imagine for example that graph vertices correspond to houses, airports, close by islands, gates, and we seek for minimum-cost solutions for keeping all of them connected. Given a connected graph, we can efficiently (i.e., fast) compute a Minimum Spanning Tree for this graph using two well-known algorithms from the literature, one suggested initially by Vojtěch Jarník and later by Robert Prim and one suggested by Joseph Kruskal, which return similar results though in a slightly different fashion.

In "Find the Way", players can either create or are presented with a newly created village where pavements must be constructed so that all houses are connected with the lower possible budget. Only the minimum-cost proposals are qualified for funding. Players can engineer their proposal about which houses must be connected with a pavement so that all houses are eventually connected at a minimum total budget using one of two available methods, Prim's algorithm or Kruskal's algorithm. According to the method suggested by Prim, players are given the house where the work will start and the cost for all individual pavements between any two houses in the village. Then, players build their proposal by gradually adding houses connected by minimum-cost pavements to houses already included in their solution so far until all houses are connected. According to the method suggested by Kruskal, players are given the cost for all individual pavements between any two houses in the village. Then, players build their proposal by gradually adding to their proposal minimum-cost pavements until all houses are connected. Player scores are calculated for each method taking into account elapsed time until the submission of their proposal, village size (i.e., number of vertices in the given graph) and possible pavements (i.e., number of edges in the given graph) and appear under player profiles.

"Find the Way" is a responsive application, currently supporting greek and english; it was developed using state-of-the art web technologies and software including html, css and javascript for the front-end as well as the node.js run time environment and the express.js framework for the back-end.

Keywords: Serious game, educational web app, responsive, Minimum Spanning Tree (MST) problem, Prim's algorithm, Kruskal's algorithm, node, js, express, js, html, css, javascript.