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Model the grid as a weighted graph where each cell is a node and edges connect adjacent cells with weight equal to the spread time from the source cell. The total time to pop all balloons is the maximum over all cells of the minimum time to reach that cell from any initially popped balloon, which can be computed using a multi-source Dijkstra algorithm. Alternatively, if all cells start unpopped and popping spreads from a single source, it's a single-source shortest path problem; clarify the initial condition.
Pro tip: Clarify the problem constraints upfront: whether there are multiple initial popped balloons, whether spread time is per edge or per node, and whether diagonal spread is allowed. This shows attention to detail and avoids solving the wrong problem.
Ask questions to understand the exact mechanics: initial popped balloons, spread time definition (per cell or per edge), movement directions (4 or 8), and whether spread can happen simultaneously.
Represent each cell as a node. Add edges between adjacent cells with weight equal to the spread time from the source cell to the neighbor. If spread time is per cell, the time to enter a cell is the weight of that cell.
If there is a single initially popped balloon, use Dijkstra's algorithm from that source. If multiple, use multi-source Dijkstra by initializing the priority queue with all sources at time 0.
Run the algorithm to find the shortest time to reach each cell. The total time to pop the entire grid is the maximum of these shortest times. If any cell is unreachable, return -1 or infinity.
Discuss time complexity O(N log N) where N is number of cells, and space complexity O(N). Mention edge cases: empty grid, single cell, disconnected components, and large grids.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.