This is basically a state compression DP where each state is the current quantity vector of items you still need.
Model the problem as an integer linear program or a shortest path problem where states represent remaining quantities. Use dynamic programming with memoization to compute the minimum cost for each state, considering all possible bundle and individual purchases. Optimize by pruning dominated states and using bounds to limit the search space.
Pro tip: Start by discussing the naive DP and its complexity, then propose optimizations like state compression or A* search to show depth. Mention that in practice, you'd validate with small cases and consider using an ILP solver if constraints are large.
Clarify input sizes, whether quantities are small, and if bundles can overshoot requirements. Discuss if items are distinct or interchangeable.
Define state as the vector of remaining quantities. The cost to reach zero state is the minimum over all actions (buy individual item or apply bundle) of action cost + cost of resulting state.
Use memoization with a map from state to min cost. For each state, iterate over all possible actions, compute new state, and recurse. Base case: all zeros -> cost 0.
Prune states where any quantity is negative (overshoot) if not allowed, or allow overshoot but cap at zero. Use bounds (e.g., greedy solution) to prune branches. Consider A* with admissible heuristic.
Time complexity is O(product of (required_i+1) * number of actions). Discuss trade-offs and test with edge cases like no bundles, bundles more expensive than individual, etc.
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