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This was a follow-up to the basic spreadsheet problem so I thought I had a head start.
Model the spreadsheet as a directed graph where each cell is a node and dependencies (from SUM formulas) are edges. To detect cycles when setting a formula, perform a DFS from the target cell to see if it can reach itself through existing dependencies; if so, reject the operation. For efficiency, consider incremental cycle detection or topological sorting.
Pro tip: Mention that you can optimize by checking only the affected subgraph and using memoization or a visited set to avoid redundant traversals, and discuss trade-offs between eager and lazy cycle detection.
Confirm the operations (Set, Get, SUM), the definition of a cycle (direct or indirect), and whether formulas can reference ranges or only individual cells. Also discuss error handling and performance expectations.
Represent each cell as a node and each dependency (e.g., cell A depends on B and C) as directed edges from A to B and C. Explain that a cycle in this graph indicates a circular dependency.
When setting a formula, before committing, traverse the dependency graph from the target cell to check if it can reach itself. Use DFS with a visited set to detect cycles efficiently.
If no cycle, update the cell's formula and adjust the graph edges. If a cycle is detected, reject the operation and return an error without modifying the state.
Consider incremental cycle detection, caching, or topological sorting for batch updates. Discuss time/space complexity and alternatives like union-find for undirected cycles (not applicable here).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.