Time Needed to Inform All Employees

Time Needed to Inform All Employees

What is this problem about?

In a large corporation, information often flows from the top down. "Time Needed to Inform All Employees" presents a scenario where a manager can inform all their direct reports in a specific amount of time. Each manager has their own "inform time." Given the company's organizational structure (who reports to whom) and the inform times for each manager, find the total time needed to inform every single employee in the company, starting from the head.

Why is this asked in interviews?

This time needed to inform all employees interview question is a tree-based challenge asked by Microsoft, Amazon, and Google. It tests your ability to represent a tree structure using an adjacency list and your proficiency with tree traversal algorithms (BFS or DFS). It evaluates your ability to find the maximum "path length" from the root to the leaves in a weighted tree.

Algorithmic pattern used

This problem follows the Breadth-First Search, Depth-First Search, Tree interview pattern.

1. Build an adjacency list representing the organization tree (manager -> list of reports).
2. Use DFS or BFS to traverse the tree starting from the head manager (ID given).
3. The total time to inform a leaf employee is the sum of inform times of all managers on the path from the head to that leaf.
4. The answer is the maximum of these path sums across all employees.
5. In DFS: max_time(u) = informTime[u] + max(max_time(v) for v in reports[u]).

Example explanation

Head: 2. Structure: 2 -> [0, 1]. InformTime: [0, 0, 5].

1. King (2) takes 5 minutes to inform 0 and 1.
2. Employees 0 and 1 are not managers (informTime 0), so they finish as soon as they are told.
3. Total time = 5. If 0 was a manager for 3 with informTime 10:
4. King (2) tells 0 and 1 at time 5.
5. Manager 0 tells 3 at time 5+10 = 15.
6. Total time = 15.

Common mistakes candidates make

In "Time Needed to Inform All Employees coding problem," a common mistake is assuming that a manager informs their reports sequentially (adding up the times). However, the problem usually implies that all direct reports are told simultaneously, meaning you take the maximum branch time, not the sum of all branches. Another error is not correctly handling the base case for leaf nodes.

Interview preparation tip

Master the art of building adjacency lists from "parent" or "manager" arrays. Once the tree is built, most problems become standard traversals. Practice both BFS and DFS, as they have different trade-offs in terms of memory and implementation simplicity.