← Instacart Interview Insights
I recognized this as set cover pretty quickly, which felt good, but then I second-guessed myself mid-explanation and started rambling about greedy being optimal when it's obviously not.
Model the problem as a set cover problem where each shopper's product set is a subset of the required products. Since set cover is NP-hard, discuss both exact methods (e.g., bitmask DP for small inputs) and approximation algorithms (e.g., greedy) while clarifying assumptions about input size. Then implement the chosen approach, ensuring to handle the case where no combination covers all products by returning -1.
Pro tip: Explicitly state the problem's NP-hardness and propose a solution that balances optimality and efficiency based on realistic constraints, showing you understand trade-offs in production systems.
Ask about the number of products and shoppers, and whether an exact or approximate solution is needed. Confirm that each shopper can be used at most once and that we need the minimum number of shoppers.
Represent each shopper's products as a set and the required products as the universe. The goal is to select the fewest sets whose union equals the universe.
For small inputs, use bitmask DP or BFS over subsets to find the exact minimum. For large inputs, use a greedy algorithm that repeatedly picks the shopper covering the most uncovered products, and mention its approximation ratio.
Code the chosen algorithm, ensuring to check if the union of all shoppers covers all products; if not, return -1. Also handle empty product list (return 0) and shoppers with no products.
Discuss time and space complexity of the approach, and compare exact vs. approximate methods in terms of optimality, scalability, and practical use in a data science context.
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