# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement Write a function recommendations(user, ratings) that returns a list of movies to recommend to the given user based on shared preferences. Each rating is a triplet [User Name, Movie Name, Rating] where Rating ∈ {1,2,3,4,5} (strings). Define two users as having similar taste if they have both rated the same movie with a 4 or 5. Recommend a movie to the user if the user has not rated it and any similar-taste user rated it a 4 or 5. Ensure the output contains unique movie names and justify any ordering you choose. ## Recommended Approach Use the string constraints to choose between two pointers, a stack, frequency counts, prefix/suffix state, or dynamic programming. Maintain the invariant that processed characters have already been normalized, counted, or matched according to the operation. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity Most direct string scans are O(n) time. Space ranges from O(1) for two pointers to O(n) for stacks, maps, or DP tables. ## Edge Cases and Tests Empty string, length 1, repeated characters, invalid characters, case sensitivity, Unicode vs ASCII, and very long input.