You are visiting Hollywood and you have marked your map with certain places you want to visit. These include Hollywood Walk of Fame, Getty center, Sunset Boulevard, etc., to name a few. The map of Hollywood is modeled as a DAG and the nodes corresponding to the places you want to visit are marked as starred (for an example, see the graph on the right). Unfortunately, you only have a day and you cannot visit all these starred places. a) (5 pts) Produce a topological sorting of the DAG. b) (15 pts) Come up with a linear time algorithm that returns a path that contains as many starred nodes as possible. Explain carefully how to do this. Notice that here a general algorithm is expected, not just a path on the example graph. (Description 8 pts, correctness 4 pts, running time 3 pts). Hint: Use the topological sorting of the DAG. Define BEST[i] to be the path towards the sink with the largest number of starred nodes when you start at the i-th node in the topological sort. Then explain how to compute BEST[] recursively for all nodes.