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Recognized it pretty fast as the rotting oranges problem with a costume on.
Model the grid as a graph where each inflated balloon is a node and edges connect adjacent inflated balloons. The problem reduces to checking if the graph is connected; if so, popping any balloon will eventually pop all, otherwise some remain. Use BFS/DFS to traverse from any inflated balloon and count reachable nodes.
Pro tip: Clarify with the interviewer whether popping is simultaneous or sequential, as this affects the algorithm. Also, mention that if the grid is large, an in-place BFS can save memory.
Ask clarifying questions: Are diagonal adjacencies considered? Does popping propagate only to directly adjacent balloons or also to those popped as a result? Is the grid static or can we choose the order of popping?
Treat each inflated balloon as a vertex. Add edges between adjacent inflated balloons (up, down, left, right). The problem becomes: is this graph connected?
Use BFS or DFS to traverse the graph starting from any inflated balloon. Count the number of visited inflated balloons.
If the number of visited inflated balloons equals the total number of inflated balloons, then all can be popped; otherwise, they cannot.
Discuss time and space complexity (O(R*C) time, O(R*C) space for visited). Handle edge cases: no inflated balloons, all inflated, disconnected components.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.