Took me longer than it should have to see this as a graph problem.
Model the problem as a dependency graph where recipes depend on ingredients and other recipes. Use a topological sort or BFS/DFS to iteratively determine which recipes can be made, starting from the initially available supplies. Return all recipes that become makeable.
Pro tip: Clarify edge cases upfront, such as cycles in recipe dependencies or duplicate ingredients, and discuss how your approach handles them. This shows thoroughness and prevents incorrect assumptions.
Ask about input format, whether recipes can depend on each other cyclically, and if ingredients are case-sensitive. Confirm that you need to return all makeable recipes, not just a boolean.
Represent recipes and ingredients as nodes, with directed edges from ingredients to recipes. Use topological sort (Kahn's algorithm) or BFS to process recipes whose dependencies are satisfied.
Maintain a set of available items (initial supplies plus newly made recipes). Use a queue to process recipes whose ingredient counts drop to zero, and add their outputs to the available set.
Check for cycles (unmakeable recipes), recipes with no ingredients, and duplicate ingredients. Test with small examples to ensure correctness.
Time complexity is O(N + E) where N is number of recipes/ingredients and E is total dependencies. Space is O(N + E). Mention potential optimizations like early termination or memoization if needed.
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