You are visiting Hollywood and you have marked your map with certain places you want to...
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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. 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.
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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