Clarify that the problem is equivalent to finding the height of a tree, then present both recursive DFS and iterative BFS solutions, analyzing their time and space complexities. Emphasize that the maximum depth is the number of edges on the longest path from the root to a leaf, and discuss edge cases such as an empty tree or a single-node tree.
Pro tip: Mention that in a real org chart, the tree could be very deep, so an iterative BFS avoids stack overflow, and you can also discuss how to handle cycles or multiple roots if the data is not guaranteed to be a tree.
Confirm that the org chart is a tree with the CEO as root, and that depth is measured in number of edges. Ask about input format and constraints (e.g., number of employees, whether the tree is balanced).
Decide between recursive DFS (post-order) and iterative BFS (level-order). Explain that both work, but BFS naturally computes depth level by level and avoids recursion limits.
For BFS: use a queue, start with the root at depth 0, and for each node, enqueue its children with depth+1. Track the maximum depth seen. For DFS: recursively compute the depth of each subtree and return 1 + max(child depths).
State that both approaches run in O(n) time and O(n) space in the worst case (queue or recursion stack). Discuss edge cases: empty tree (depth 0 or -1?), single node (depth 0), and skewed tree (depth n-1).
Trace through a small org chart (e.g., CEO -> [VP1, VP2], VP1 -> [Eng1, Eng2]) to verify the algorithm returns the correct maximum depth.
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