The brute-force part was fine, just iterate over every person-question pair and check tag overlap.
Start by clarifying the problem: define inputs (people with skill tags, questions with required tags), output (matching), and constraints (e.g., one-to-one vs. many-to-many, tag matching semantics). Then present a brute-force solution (e.g., for each person, check all questions) and analyze its time complexity. Finally, optimize using inverted indices, hash maps, or bipartite matching algorithms, discussing trade-offs between time, space, and implementation complexity.
Pro tip: Demonstrate that you consider real-world constraints like tag synonyms, partial matches, and scalability to millions of users; mention that the optimal solution depends on whether you need all matches or just the best ones, and whether matches are exclusive.
Ask questions to understand the problem: Are tags exact matches or can they be hierarchical? Is it one-to-one or many-to-many? What are the sizes of people and questions? Do we need all matches or just top matches?
For each person, iterate through all questions and check if the person's tags cover the question's required tags. Analyze time complexity: O(P * Q * T) where T is average tags per question.
Build an inverted index from tags to questions, then for each person, collect candidate questions via their tags and verify matches. This reduces unnecessary comparisons, especially if tags are sparse.
If matches must be exclusive (each person to at most one question), model as bipartite matching and use Hopcroft-Karp. If many-to-many, use the inverted index approach with efficient set intersections.
Compare approaches: brute-force is simple but slow for large inputs; inverted index is faster but uses more memory; bipartite matching is optimal for exclusive assignments but complex. Mention distributed processing if data is huge.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the problem as a priority-based matching between people and questions, where each person has a set of qualified questions and each question has a priority. Use a greedy algorithm that processes people in order of their best available question, or sort questions by priority and assign each to the highest-priority qualified person, ensuring optimality via exchange argument.
Pro tip: Mention that this is essentially a bipartite matching problem with priorities, and that a greedy approach works if you process questions in descending priority order and assign each to the highest-priority person who qualifies, but be careful about ties and fairness. Also, discuss how to handle dynamic updates efficiently.
Confirm that each person can answer multiple questions but should get exactly one, and that questions have distinct priorities. Ask if people also have priorities or if we need to maximize overall priority sum.
Represent people and questions as nodes in a bipartite graph, with edges indicating qualification. Assign weights to question nodes based on priority.
For maximizing total priority, use a greedy algorithm: sort questions by priority descending, and for each question, assign it to the highest-priority available person who qualifies. Alternatively, use min-cost max-flow if people have preferences.
Argue that the greedy choice is optimal via an exchange argument: if a higher-priority question is assigned to a less suitable person while a lower-priority question is assigned to a more suitable person, swapping assignments doesn't decrease total priority.
Discuss time complexity (e.g., O(Q log Q + E) with sorting and union-find) and how to handle large inputs or dynamic updates (e.g., using priority queues or segment trees).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.