I knew this was a greedy or sorting problem pretty quickly but fumbled the tie-breaking logic.
First, clarify the problem constraints and edge cases. Then, propose an efficient algorithm: sort sizes, use a min-heap to track available increments, and greedily assign the smallest possible distinct size to each product. Finally, analyze time and space complexity and discuss potential optimizations.
Pro tip: Demonstrate awareness of trade-offs: mention that while a greedy approach with a heap works, a union-find or sorting-based approach might be simpler in some cases. Also, proactively discuss how to handle large inputs and memory constraints.
Ask clarifying questions: Are sizes integers? Can sizes be negative? What are the constraints on array lengths and size ranges? Is the cost array aligned with the sizes array?
Recognize that we need to assign distinct sizes to each product, minimizing total increment cost. This is a variant of the 'minimum increment to make array unique' problem with weighted costs.
Sort products by size. Use a min-heap to track the next available size for each product. For each product in sorted order, if its size is less than the next available, increment it to the next available and add cost; otherwise, set next available to size+1. Update the heap with the new next available.
Time complexity: O(n log n) due to sorting and heap operations. Space complexity: O(n) for the heap. Discuss if we can optimize further.
Walk through a small example to verify correctness, such as sizes=[1,1,2] and costs=[10,20,30]. Show how the algorithm computes the minimum cost.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
BFS to expand the social graph, then aggregate watch counts.
Clarify the problem constraints and helper method signatures, then design a BFS traversal up to depth 2 to collect friends and friends-of-friends. Aggregate movie watch counts using a hash map, sort by frequency, and handle edge cases like cycles and missing data.
Pro tip: Discuss trade-offs between BFS and DFS, and mention how to scale the solution for large social graphs using distributed processing or approximate algorithms.
Ask about the helper methods' behavior, data types, and whether the graph is directed or undirected. Confirm the depth (friends and friends-of-friends) and how to handle cycles or duplicate friends.
Use BFS to explore the social graph up to depth 2, starting from the given user. Keep a visited set to avoid cycles and ensure each friend is processed once.
For each friend and friend-of-friend, fetch their watched movies and increment a count in a hash map keyed by movie title. Exclude the user's own watched movies if required.
Sort the movies by count in descending order, breaking ties alphabetically or by another criterion. Return the sorted list of movie titles.
Discuss time and space complexity (O(F * M) where F is number of friends and M is average movies per friend). Suggest optimizations like early termination or caching for repeated queries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.