Build a tree from the employee records and compute each manager's team average salary by aggregating salaries of all direct and indirect reports. Use a post-order traversal to compute subtree sums and counts, then evaluate averages for all managers, handling ties by smaller id. Return -1 if no managers exist.
Pro tip: Clarify whether the manager's own salary is included in the team average—typically it's not, but confirming shows attention to detail. Also, mention that you'd handle large datasets by avoiding recursion depth issues with an iterative approach or increasing recursion limit.
Confirm the definition of 'team' (direct and indirect reports only, excluding the manager) and edge cases like no managers, single employee, or multiple roots. Validate that the input forms a valid tree (no cycles, all manager_ids exist).
Create an adjacency list mapping each manager to their direct reports. Identify all managers (nodes with at least one report) and the root(s) of the tree.
Perform a post-order traversal (DFS or BFS) to compute for each node the total salary and count of all descendants. This can be done recursively or iteratively to avoid stack overflow.
For each manager, compute the average salary of their team (total descendant salary / descendant count). Track the manager with the highest average, breaking ties by smaller id.
Return the manager's id or -1 if no managers. Analyze time and space complexity: O(n) time and O(n) space for the tree and aggregates.
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