Felt okay on the BFS/DFS part but fumbled a bit explaining why I'd pick one over the other for this specific case.
Clarify the graph representation and whether the DAG is static or dynamic, then choose traversal algorithms: DFS/BFS for ancestors (following incoming edges) and descendants (following outgoing edges). Discuss time/space complexity and potential optimizations like memoization or precomputation for repeated queries.
Pro tip: Mention that for multiple queries, precomputing transitive closure or using topological order with bitsets can be more efficient, but trade-offs exist; always ask about constraints first.
Ask about graph size, number of queries, whether the graph is static, and if nodes/edges have additional properties. This determines the optimal approach.
For a single query, use DFS or BFS: for ancestors, traverse incoming edges; for descendants, traverse outgoing edges. Ensure no cycles (DAG) so no visited set needed, but still use one to avoid redundant work.
Time: O(V+E) per query. Space: O(V) for visited set and recursion stack. For multiple queries, consider precomputing transitive closure (O(V*(V+E)) or using bitsets) or topological order with dynamic programming.
Consider isolated nodes, self-loops (not in DAG), and large graphs causing stack overflow (use iterative DFS). Discuss whether to return nodes in topological order.
Compare online traversal vs. precomputation. Mention real-world applications like dependency resolution in build systems or package managers, and how Notion might use this for block dependencies.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by acknowledging the read-heavy, write-light workload and propose a caching layer that stores precomputed ancestor/descendant sets for each node. Discuss cache invalidation strategies that leverage the infrequent updates, such as lazy invalidation or versioning, and consider memory trade-offs. Conclude with a concrete design that balances performance, memory, and consistency.
Pro tip: Mention that you would measure the actual read/write ratio and query patterns before committing to a caching strategy, and consider a hybrid approach where hot nodes are cached in-memory while cold nodes use a persistent store.
Ask about the graph size, expected read/write ratio, latency requirements, and consistency needs to tailor the caching solution.
Propose caching precomputed ancestor/descendant lists per node, either in-memory (e.g., Redis) or on disk, and discuss trade-offs between memory usage and query speed.
Since updates are rare, suggest invalidating only affected nodes' caches on writes, using techniques like versioning or lazy invalidation to avoid full rebuilds.
Explain how to handle stale reads, e.g., by using a write-through cache or accepting eventual consistency, and discuss fallback to the database on cache miss.
Compare with other approaches like materialized path, closure table, or on-the-fly computation with memoization, and justify your choice based on the given workload.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clearly state the time and space complexity of both methods in big-O notation, specifying the variables (e.g., n for number of nodes, h for height). Then, briefly explain the reasoning behind each complexity, referencing the data structure and traversal algorithm used. Finally, discuss any trade-offs or optimizations you considered.
Pro tip: Mention that in a typical tree structure, the time complexity for get_ancestors is O(h) and for get_descendants is O(m), where m is the number of descendants, but if the tree is unbalanced, h can be O(n). Also, note that space complexity often depends on recursion depth or auxiliary data structures.
Clarify what n, h, and m represent in your implementation (e.g., n = total nodes, h = height, m = number of descendants). State any assumptions about the tree structure (e.g., balanced vs. unbalanced).
For get_ancestors, explain that it traverses from the node up to the root, so time is O(h). For get_descendants, explain that it traverses the subtree, so time is O(m), where m is the number of nodes in the subtree.
For get_ancestors, if using recursion or a stack, space is O(h); if iterative with a list, O(h) for the output. For get_descendants, space is O(m) for the output, plus O(h) for recursion stack if using DFS.
Mention edge cases like empty tree, node not found, or skewed tree. Discuss possible optimizations like caching or using parent pointers to reduce time.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.