Took me a bit to see this wasn't just a greedy problem.
Model the problem as a set cover problem and solve it using dynamic programming over bitmasks of the target items. For each combo, compute the bitmask of target items it covers, then use DP to find the minimum cost to cover each subset. Return the minimum cost for the full target mask, or -1 if unreachable.
Pro tip: During the interview, explicitly discuss the trade-offs between exact DP and greedy/heuristic approaches, especially since set cover is NP-hard. Mention that for large target sets, approximation algorithms or ILP solvers might be needed, but for typical interview constraints, DP is expected.
Ask about the number of target items (n) and combos (m), and whether prices are positive. This determines if bitmask DP is feasible (e.g., n ≤ 20).
Map each target item to a bit position. For each combo, compute a bitmask representing which target items it covers. Discard combos that cover no target items.
Let dp[mask] = minimum cost to cover the subset of target items represented by mask. Initialize dp[0] = 0 and others to infinity. For each combo with mask c and cost p, update dp[new_mask] = min(dp[new_mask], dp[mask] + p) where new_mask = mask | c.
Iterate over all masks from 0 to (1<<n)-1. For each mask, try adding each combo to update dp. Finally, return dp[(1<<n)-1] if finite, else -1.
Time complexity is O(2^n * m). Mention that we can optimize by iterating only over reachable masks or using BFS/Dijkstra on the state graph. Also note that set cover is NP-hard, so for large n, approximation or ILP is needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.