Amount of Time for Binary Tree to Be Infected

Infection spreads upward as well as downward, so first traverse the tree to record each node's parent and locate the start node. Then run BFS from start with a visited set. For every dequeued node, consider left child, right child, and parent if present and unvisited. Process one queue level at a time; after expanding a nonempty level, increment minutes, then subtract one at the end or increment only when another level remains. This guarantees the minute count is the maximum number of edges from start to any node. A parent map is essential because ordinary tree traversal has no upward pointer. Each node is visited a constant number of times, so time is O(n). The parent map, visited set, and queue use O(n) space. DFS can compute distances too, but BFS makes the time-layer interpretation direct.