The constraint definition wasn't even fully stated in what I saw, which made this extra frustrating to think about after the fact.
Clarify the specific constraint (e.g., sum, length, divisibility) and the input type (array or set) to determine the appropriate algorithmic technique. Then design a solution that not only finds the maximum size but also reconstructs the subset, typically using dynamic programming with parent pointers or a greedy approach with careful tracking. Finally, walk through a small example to validate the logic and discuss time/space complexity.
Pro tip: Always discuss how you would reconstruct the subset, not just compute its size—this is often where candidates fail. Mention that you would store predecessor information during DP or use a separate array to track choices, and be prepared to optimize space if needed.
Ask questions to pin down the exact constraint (e.g., sum equals target, no two adjacent, etc.), input format (array with duplicates? set?), and output requirements (any valid subset or all?).
Based on the constraint, recognize if it's a variation of knapsack, longest increasing subsequence, interval scheduling, or another classic problem. This determines whether DP, greedy, or backtracking is suitable.
For DP, define state and transition, and store parent pointers or choices to rebuild the subset. For greedy, ensure the greedy choice property holds and track selected elements.
Trace the algorithm on a small input to demonstrate correctness and show how the subset is reconstructed step by step.
State time and space complexity, and discuss edge cases like empty input, all elements satisfying constraint, or multiple optimal subsets.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.