Build Friend Recommendations

You are given a social graph and a `User` class that stores a user id and the set of direct friends for each user. Complete a recommendation module with the following parts: 1. Fix `valid_recommend(user, candidate)` so it returns `false` when the candidate is the same as the user or is already a direct friend, and `true` only for valid unseen candidates. 2. Implement `random_recommend(user, k)` to return up to `k` valid recommended users chosen uniformly at random from all valid candidates. 3. Implement `top_k_mutual_friend_recommend(user, k)` that ranks valid candidates by the number of mutual friends with the target user, breaks ties deterministically, and returns the top `k`. Explain the time complexity of your recommendation approach and the data structures you use.