Time Needed to Inform All Employees
Problem Description
A company has n employees with a unique ID for each employee from 0 to n - 1. The head of the company is the one with headID.
Each employee has one direct manager given in the manager array where manager[i] is the direct manager of the i-th employee, manager[headID] = -1. Also, it is guaranteed that the subordination relationships have a tree structure.
The head of the company wants to inform all the company employees of an urgent piece of news. He will inform his direct subordinates, and they will inform their subordinates, and so on until all employees know about the urgent news.
The i-th employee needs informTime[i] minutes to inform all of his direct subordinates (i.e., After informTime[i] minutes, all his direct subordinates can start spreading the news).
Return the number of minutes needed to inform all the employees about the urgent news.
Example 1:
Input: n = 1, headID = 0, manager = [-1], informTime = [0]
Output: 0
Explanation: The head of the company is the only employee in the company.
Example 2:
Input: n = 6, headID = 2, manager = [2,2,-1,2,2,2], informTime = [0,0,1,0,0,0]
Output: 1
Explanation: The head of the company with id = 2 is the direct manager of all the employees in the company and needs 1 minute to inform them all.The tree structure of the employees in the company is shown.
Constraints:
- 1 <= n <= 105
- 0 <= headID < n
- manager.length == n
- 0 <= manager[i] < n
- manager[headID] == -1
- informTime.length == n
- 0 <= informTime[i] <= 1000
informTime[i] == 0if employeeihas no subordinates.- It is guaranteed that all the employees can be informed.
Solve it on LeetCode
Approaches
1. BFS
Intuition:
Convert the organizational structure into a tree where each node represents an employee. The CEO's id is headID. Using a Breadth First Search (BFS), calculate the total time needed for all direct and indirect employees to receive the information from the CEO.
In a BFS approach, we use a queue to traverse each level of the organization, propagating the information and accumulating the time needed.
Steps:
- Create a list of lists where
subordinates[i]holds all employees directly reporting to employeei. - Initialize a queue and start from the head of the organization (CEO).
- At each employee, traverse their subordinates, adding the time taken to fetch the information and update the maximum time needed.
Code:
- Time Complexity: O(N), where N is the number of employees since each employee is visited once.
- Space Complexity: O(N) for storing the subordinates list and the queue.
2. DFS
Intuition:
Similar to BFS, DFS also helps us traverse the structure of employees, but instead of using a queue, we use recursion. For each employee, we traverse deeper into their subordinates before moving on to the next sibling.
Steps:
- Build a tree representation using adjacency lists for subordinates.
- Use DFS to recursively traverse from the head of the organization.
- At each recursive call, add the inform time particular to an employee and update the maximum time.
Code:
- Time Complexity: O(N), since each employee is visited once.
- Space Complexity: O(N), which is the recursion stack depth in the worst case.
3. DFS with Memoization
Intuition:
This approach recognizes that a problem needs to calculate the time involved recursively but instead of recalculating the time each time, it stores (memoizes) the computed time for each employee to save computational steps.
Steps:
- Same as previous DFS approach, but maintain a memoization array to store the time required to inform each subtree.
- Benefits arise when subtrees are visited multiple times through different paths.
Code:
- Time Complexity: O(N), as we compute each subtree's time once.
- Space Complexity: O(N), owing to recursion space and additional space for the memo array.