My first instinct was BFS and that part was fine.
Model the points as nodes in a graph where edges exist between points with distance < r, then perform BFS/DFS from start to target. Discuss the trade-offs of implicit graph traversal versus explicit edge construction, and consider optimizations like spatial partitioning for large datasets.
Pro tip: Clarify whether the distance function is symmetric and whether the points are static; if not, the graph may be directed or dynamic, affecting the algorithm choice. Also, mention that early termination upon reaching the target can save time.
Ask about the number of points, whether getDistance is symmetric, and if the points are static. This determines if the graph is undirected and if pre-processing is possible.
Decide between building an explicit adjacency list (O(n^2) edges) or using an implicit graph where neighbors are found on-the-fly by checking all points. The latter avoids O(n^2) memory but may be slower.
Use BFS for shortest path in terms of hops or DFS for any path. Both are O(V+E) for explicit graphs; for implicit graphs, each node expansion takes O(n) distance checks.
For large n, use a spatial data structure like a k-d tree or grid to quickly find neighbors within distance r, reducing the number of getDistance calls.
Compare time and space complexity of approaches. Explicit graph: O(n^2) time and space. Implicit with spatial index: O(n log n) average time, O(n) space. Discuss when each is appropriate.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.