Took me a minute to even understand what they were optimizing for.
Clarify the problem constraints (e.g., can cards be reused? are sets disjoint?) and then outline a backtracking algorithm that explores all valid 3-card sets summing to 15, using recursion with pruning to maximize the number of cards used. Discuss time/space complexity and potential optimizations like memoization or sorting to improve efficiency.
Pro tip: Emphasize that backtracking is a natural fit for this combinatorial optimization problem, but also mention that for large inputs, you might need to consider dynamic programming or branch-and-bound to handle the exponential search space. Showing awareness of trade-offs between exactness and efficiency demonstrates maturity.
Ask clarifying questions: Can cards be used in multiple sets? Are sets required to be disjoint? What is the input size? This ensures you understand the exact requirements before designing the algorithm.
Decide on the state representation: which cards are used, current set being built, and the total cards used so far. The goal is to maximize the count of used cards.
At each step, try to form a valid 3-card set summing to 15 from the remaining cards. Recurse with the updated set of used cards, and backtrack by unmarking cards to explore other combinations.
Prune branches that cannot possibly beat the current best (e.g., if remaining cards plus used cards <= best). Sort cards or use frequency counts to avoid duplicate sets and speed up the search.
Discuss worst-case time complexity (exponential) and space complexity (recursion depth). Walk through a small example to verify correctness and consider edge cases like no valid sets.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.