High school students and their parents often visit college campuses and see an i

Question

High school students and their parents often visit college campuses and see an introductory movie in a lecture room. Suppose the room has 100 seats and the people who came in the same car/bus must watch the movie together. How would you, as the campus visit director, arrange all the people to watch the movie with a minimal number of showings. Suppose c1 , c2 , ..., cm are the numbers of people coming to the campus by the same car/bus, where 0 < ci < 101. One solution is first­come, first­serve: if the next group cannot fit in the lecture hall, then the hall shuts its door and starts the movie. The second solution is best­fit: Always send the largest group that can fit into the hall, until no groups can fit. Unfortunately, both solutions are not optimal. Provide:

A. Counterexamples to show both solutions are not optimal. (10 points)

B. An optimal algorithm with its complexity. (15 points)

Explanation / Answer

Algorithm:

Hence, with the help of this algorithm you will be able to join the show with the minimal numbers of the showing and the people will be gathered in the show together with less problems.Hence, this is the best solution of the algorithm.The complexity of the algorithm is 0(n).

Counterexamples:

Hence,from the above examples it is made sure that both the solutions are not optimal and have loopholes in each of them.

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