Spent probably five minutes just staring at the problem trying to figure out if it was a tree or a proper DAG.
Start by clarifying requirements and defining data structures for recipes and stock, then design a recursive algorithm that decomposes the requested item into its dependencies, checking availability at each step. Discuss trade-offs like cycle detection, memoization, and handling insufficient quantities, and consider scalability for large dependency graphs.
Pro tip: Mention cycle detection and memoization early to show you anticipate edge cases and optimize for performance, which is crucial for Google-scale systems.
Ask questions to understand constraints: Are recipes fixed or dynamic? Can items be partially produced? Are there cycles? What are the expected scales? This ensures you address the right problem.
Propose structures like a map from item to recipe (list of ingredients with quantities) and a map for stock (item to available quantity). Consider using a graph representation for dependencies.
Outline a function canProduce(item, quantity) that checks stock first, then recursively computes required quantities of ingredients, aggregating needs and verifying against stock. Include base cases for raw ingredients.
Discuss handling cycles (via visited set), memoization to avoid redundant computations, and scaling quantities. Also consider if multiple recipes exist for an item.
Explain time/space complexity, potential bottlenecks, and trade-offs between recursion depth and iterative approaches. Mention how this scales for large graphs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.