Detonate the Maximum Bombs

Start by clarifying the exact contract for Detonate Maximum Bombs: input representation, mutation rules, duplicate behavior, and what should happen on invalid or empty input. The core idea is directed reachability graph built from geometric radius checks. Work a tiny example aloud and name the invariant after each step, because that is the proof that the approach stays correct as the input grows.

A dependable implementation plan is to build directed edges using squared distance; traverse from every start; maintain fresh visited set; keep maximum reachable count. Reachability is directed, so undirected union-find loses information. Keep the code aligned with that invariant instead of adding special cases that silently change the contract. Test the smallest input, a normal case, duplicates or ties where relevant, an adversarial boundary, and a case that exercises the failure path. The expected complexity is O(n^3) worst case after O(n^2) graph build. Explain both time and auxiliary memory, including recursion or helper structures; do not hide sorting, copying, or repeated scans. If the title omits critical constraints, say what you need to know before committing to a more specialized solution.