2D Points Connected Components by Radius

Given 2D points and radius `r`, connect two points when their distance is at most `r`; connectivity is transitive, and the output is the final number of clusters. The interviewer accepted or preferred a brute-force neighbor scan after discussing optimization ideas. Requirements Input: a list of 2D points and a radius r. Two points are connected if their Euclidean distance is <= r. Connectivity is transitive: if A connects to B and B connects to C, all three belong to the same cluster. Return the number of final clusters. Notes DFS, BFS, or Union-Find all fit the core connected-components model. For many points, discuss how to avoid checking every pair by narrowing neighbor candidates spatially; in this round, the interviewer still preferred the brute-force implementation path. Clarify squared-distance comparison to avoid unnecessary square roots. Preparation Implement connected components once with DFS/BFS and once with Union-Find. Practice stating the O(n^2) brute-force baseline clearly before proposing spatial indexing. Dry-run a case where three points form one cluster only through transitive links.