You are tasked with developing a movie recommendation system. You are given a list of movies (their names) and a list of similarities between movies (pairs of movies that are similar). You are also given a list of user's friends, and for each friend a list of movies that he has already seen. Your system should recommend one movie with the highest discussability and uniqueness. Discussability is the number of friends of user, who have already seen that movie. Uniqueness is 1 divided by the mean number of similar movies that user's friends have already seen. So you should return the film with the highest number: F/S, where F = number of friends who have seen this movie, and S = mean of number of similar movies seen for each friend. Exclude the movies with S = 0. If (a, b) and (b, c) are pairs of similar movies, then (a, c) is a pair of similar movies too. Each movie is not counted in its Uniqueness. Input example. Basically it is up to you to come up with data structure you like or you think easy to work with. In a nutshell you have as an input these parameters (they can be in form of a list/dict etc): movies = ["Parasite","1917","Ford v Ferrari","Jojo Rabbit","Joker"] similarities = [['Parasite","1917"], ["Parasite", "Jojo Rabbit"], ["Joker", "Ford v Ferrari"]] friends = [['Joker"], ["Joker","1917"], ["Joker"], ["Parasite"], ["1917"], ["Jojo Rabbit", "Joker"]] Your code should work, it should be the same time and space complexity as your algorithm (or better, if you have come up with a better solution). It should be clean and easily understandable. Please provide the proof that your algorithm will come up with correct/optimal solution. What is the time complexity of your algorithm? Please provide proof for it. What is the memory complexity of your algorithm? Please provide proof for it.