Match people to questions using tags and priorities

You are building a simplified “Q&A matching” feature.

You have:

• people : N people, where person i has a set of expertise tags P[i] .
• questions : M questions, where question j has a set of tags Q[j] and an integer priority prio[j] (larger means more important).

A person i can be assigned to answer a question j if they share at least one tag:

$P[i] \cap Q[j] \neq \emptyset$

Each person can answer at most one question, and each question can be answered by at most one person.

Task

Compute an assignment of people to questions that:

1. Maximizes the number of answered questions.
2. Subject to (1), maximizes the total priority sum of answered questions.

Return:

• the maximum number of matched (answered) questions
• the maximum achievable total priority under that maximum match count

Input/Output format (you may choose a reasonable one)

• Tags are strings.
• Total number of tags across all people/questions can be large.

Follow-ups

1. Describe a brute-force approach and its complexity.
2. Improve the time complexity using a hash-based index (e.g., tag -> list of people/questions ).
3. If processing questions in priority order, explain how a priority queue could help in your implementation.