This week, we'll be delving into Graph Theory, which almost always shows up at competitions. It underlies many real-world problems and is almost always directly applicable.
This problem is a good way to whet your appetite on playing with graphs. It will force you to not only build a graph, but to update weights and traverse the graph.
One thing you may want to try is to use different methods of representing graphs when you attempt this problem. Weigh out the pros and cons of each approach and decide which is your prefered method.