Build a Top-Down Reporting Forest from Employee-Manager Pairs

You are given a list of reporting relationships. Each person is identified by a positive integer ID, and each pair `[employee, manager]` means that `employee` reports directly to `manager`. Build the reporting structure top-down: every top-level manager, who reports to no one, is the root of a tree, with middle managers below them and employees below those. Together the trees form a forest. Return the forest as an indented org-chart listing: one row `[id, depth]` per person, in the order the people appear in the chart. ### Function Signature ```python def reporting_forest(pairs: list[list[int]]) -> list[list[int]]: ``` ### Rules - A top-level manager is a person who appears in at least one pair but never as the `employee` of a pair. A top-level manager has depth `0`; every other person has the depth of their manager plus `1`. - Every person who appears in any pair appears in the output exactly once. - Order the output as a preorder walk. List the trees in ascending order of their top-level manager's ID. Within a tree, list a person, then the whole subtree of each of their direct reports, taking direct reports in ascending order of ID. - Each output row is a two-element list `[id, depth]` of integers. ### Constraints - `1 <= len(pairs) <= 10**5` - Each pair has exactly two elements, and `1 <= employee, manager <= 10**9`. - In each pair, `employee != manager`. - Each person appears as the `employee` in at most one pair, so everyone has at most one direct manager. - The relationships contain no cycle: following managers upward from anyone always reaches a top-level manager. - A reporting chain can be as long as `len(pairs)`, so depths range from `0` to `len(pairs)`. ### Examples **Example 1** ```text Input: pairs = [[2, 1], [3, 1], [4, 2], [5, 6]] Output: [[1, 0], [2, 1], [4, 2], [3, 1], [6, 0], [5, 1]] ``` `1` and `6` never appear as employees, so they are the two roots, in ascending order. The direct reports of `1` are `2` and `3`, and the whole subtree of `2` (`2`, then `4`) comes before `3`. The tree rooted at `6` comes second even though it contains `5`, because trees are ordered by the ID of their root. **Example 2** ```text Input: pairs = [[9, 7], [7, 3], [4, 3]] Output: [[3, 0], [4, 1], [7, 1], [9, 2]] ``` `3` is the only top-level manager. Its direct reports are ordered by ID (`4` before `7`), not by input order, and `9` sits two levels below `3`. **Example 3** ```text Input: pairs = [[10, 20]] Output: [[20, 0], [10, 1]] ```