Imagine you are an avid movie goer and you prepared a list of n movies you are considering watching. As a thorough researcher, you prepared a list of k friends, whose movie advice you trust. You have two ways to evaluate a movie: watch it or ask a friend if it is worth seeing. A movie typically lasts two hours. Usually when you speak with one of your friends, you also spend two hours talking. However, during these two hours, you can discuss multiple movies your friend has seen. Address the dilemma in each of the following two cases: For each movie, you are debating to either see it or speak to all of your friends and hear their recommendations. You only have a total of t hours. You have two choices: a) Design a polynomial-time algorithm for choosing t/2 recommenders, or b) prove that the problem is NP-hard. Decide between the two choices and explain your decision with mathematical rigor. A more efficient approach is to choose between watching the movie and speaking with at least one trusted movie recommender friend. This approach will also take a total of t hours like in the previous case. You have two choices: a) Design a polynomial-time algorithm for choosing t/2 recommenders, or b) prove that the problem is NP-hard. Decide between the two choices and explain your decision with mathematical rigor.

Imagine you are an avid movie goer and you prepared a list of n movies you are considering watching. As a thorough researcher, you prepared a list of k friends, whose movie advice you trust. You have two ways to evaluate a movie: watch it or ask a friend if it is worth seeing. A movie typically lasts two hours. Usually when you speak with one of your friends, you also spend two hours talking. However, during these two hours, you can discuss multiple movies your friend has seen. Address the dilemma in each of the following two cases:

1. For each movie, you are debating to either see it or speak to all of your friends and hear their recommendations. You only have a total of t hours. You have two choices: a) Design a polynomial-time algorithm for choosing t/2 recommenders, or b) prove that the problem is NP-hard. Decide between the two choices and explain your decision with mathematical rigor.
2. A more efficient approach is to choose between watching the movie and speaking with at least one trusted movie recommender friend. This approach will also take a total of t hours like in the previous case. You have two choices: a) Design a polynomial-time algorithm for choosing t/2 recommenders, or b) prove that the problem is NP-hard. Decide between the two choices and explain your decision with mathematical rigor.