My first instinct was BFS, which is fine, but I fumbled a bit explaining why I didn't need to build the full adjacency list upfront.
Model the points as a graph where edges connect points within distance r, then use BFS or DFS to check connectivity from start to end. Alternatively, use a union-find data structure to efficiently merge connected components and check if start and end are in the same component. Discuss trade-offs between explicit graph construction and on-the-fly neighbor queries, especially for large point sets.
Pro tip: Mention that for large datasets, spatial indexing (like KD-trees or grid-based partitioning) can drastically reduce neighbor search time, and that union-find with path compression is often the most efficient for connectivity queries.
Ask about the number of points, distribution, threshold r, and whether the distance function is a metric. This informs the choice of algorithm and data structures.
Decide between graph traversal (BFS/DFS) and union-find. Consider if you need just a yes/no answer or also the path.
If points are many, propose using spatial indexing (e.g., KD-tree, ball tree, grid) to avoid O(n^2) pairwise distance checks.
Discuss time and space complexity of your approach, including the cost of building the index and performing queries.
Relate to ML applications like clustering (DBSCAN) or similarity graphs, and discuss scalability for distributed systems.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where I actually blanked for a second.
Start by clarifying the problem context: what is the goal (e.g., nearest neighbor search, clustering, anomaly detection)? Then propose spatial indexing structures like KD-trees or ball trees to prune the search space, and discuss approximate methods (e.g., LSH) when exact results are not required. Emphasize caching and batching to reduce expensive distance calls.
Pro tip: Mention that the choice of index depends on the dimensionality of the data: KD-trees degrade in high dimensions, so for high-dimensional data, consider approximate methods like LSH or HNSW. Also, highlight that sometimes a cheap pre-filter (e.g., using a cheaper distance proxy) can eliminate many candidates before calling the expensive distance function.
Ask about the goal (e.g., nearest neighbors, clustering), data dimensionality, and whether approximate results are acceptable. This determines the appropriate algorithmic approach.
Propose tree-based structures (KD-tree, ball tree) for low-dimensional data, or hashing-based methods (LSH) for high-dimensional data. These avoid checking all pairs by pruning the search space.
Cache distance computations to avoid recomputation, and batch calls to the expensive distance function to amortize overhead. Use memoization if the same pairs are queried repeatedly.
If exact results are not required, use approximate nearest neighbor algorithms (e.g., LSH, HNSW). Alternatively, use a cheap pre-filter (e.g., Euclidean distance on a subset of dimensions) to eliminate obvious non-candidates before calling the expensive distance function.
Discuss the trade-offs between accuracy, speed, and memory. Suggest validating the chosen approach on a sample of the data to ensure it meets performance requirements.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.