Had seen this one before, so the solution came fast.
Model the problem as a directed graph where each bomb is a node and edges represent detonation reachability. Then, find the maximum number of nodes reachable from any starting node, considering that detonations can propagate transitively. Use graph traversal algorithms like DFS/BFS or compute strongly connected components to handle cycles efficiently.
Pro tip: Clarify the blast radius definition (e.g., Manhattan distance vs. Euclidean) and whether bombs detonate simultaneously or sequentially, as this affects the graph construction and traversal. Also, discuss trade-offs between time and space complexity, and consider if the grid is sparse or dense.
Ask about blast radius metric, grid size, number of bombs, and whether detonation is simultaneous or sequential. Confirm if bombs can be detonated in any order and if the goal is to maximize total detonated bombs from a single initial detonation.
Create a directed graph where each bomb is a node, and add a directed edge from bomb A to bomb B if B lies within A's blast radius. This captures the chain reaction potential.
Identify strongly connected components (SCCs) to handle cycles where bombs detonate each other. Condense the graph into a DAG of SCCs, where each component's size is the number of bombs in it.
For each SCC in the condensed DAG, compute the total number of bombs reachable from it (including itself) using dynamic programming or DFS with memoization. The maximum over all SCCs is the answer.
Analyze time and space complexity: building the graph takes O(n^2) in the worst case, SCC computation O(n+m), and DP O(n+m). Discuss potential optimizations like spatial indexing (e.g., k-d tree) for sparse grids.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.