Consider the following problem: Design an algorithm to determine the best route for a subway passenger to take from one designated station to another in a well-developed subway system. Map the problem to a shortest path graph-problem. How do you construct the graph for the following 3 cases. Indicate the meaning of vertices and edges. Draw a concrete example. 1 The best route is the route that has the smallest number of stops. 2 The best route is the fastest route. Assume you know the time to travel between stops and ignore the time spent in changing trains. 3 The best route is the fastest route considering also the time to change trains. How does your graph account for the time of changing the train ?