Recognized it as a variant of a spreadsheet problem I'd practiced before, so I felt decent going in.
Start by clarifying requirements: what formula syntax, error handling, and performance expectations exist. Then propose a design that parses formulas into a dependency graph, uses topological sorting or DFS with memoization for evaluation, and handles cycles. Discuss trade-offs between eager vs lazy evaluation and how to support updates efficiently.
Pro tip: Mention that you would use a directed acyclic graph (DAG) to represent dependencies and detect cycles, and that you'd cache computed values to avoid redundant calculations. This shows you understand both correctness and performance.
Ask about formula syntax, supported operations, error handling, and whether cells can be updated. Confirm if evaluation should be eager or lazy.
Propose storing each cell's raw content (integer or formula) and a dependency graph. Use a map from cell ID to its dependencies and dependents.
Describe parsing formulas, resolving references recursively with memoization, and detecting cycles using DFS with visited states.
Explain how to update a cell and propagate changes: either recompute all dependents or use lazy invalidation with caching.
Compare eager vs lazy evaluation, memory vs computation, and how to handle errors like division by zero or circular references.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the formulas as a directed graph where each cell is a node and dependencies are edges, then detect cycles using DFS with recursion stack or topological sort. Explain the algorithm clearly, discuss trade-offs like time/space complexity, and mention how to handle dynamic updates in a spreadsheet context.
Pro tip: Mention that you can detect cycles incrementally as dependencies are added, which is more efficient than re-checking the entire graph after every change—this shows you think about real-world performance in an interactive system.
Represent each cell as a node and each reference as a directed edge from the referencing cell to the referenced cell. This transforms the problem into cycle detection in a directed graph.
Use DFS with a recursion stack (colors: white, gray, black) or Kahn's topological sort. Both run in O(V+E) time, where V is the number of cells and E is the number of references.
For a live spreadsheet, maintain the graph incrementally: when a formula changes, update edges and re-run cycle detection only on the affected subgraph, or use a union-find structure if dependencies are only added.
Compare DFS vs. topological sort: DFS is simpler for cycle detection, while topological sort also gives evaluation order. Mention self-references (A1 -> A1) and indirect cycles of any length.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.