Time Needed to Inform All Employees

class Solution {
public:
    int maxInformationTime = INT_MIN;
        
    int calculateMaxInformTime(int totalEmployees, int topManager, vector<int>& managers, vector<int>& notificationTime) {
        vector<int> employees[totalEmployees];
            
        for (int id = 0; id < totalEmployees; id++) {
            if (managers[id] != -1) {
                employees[managers[id]].push_back(id);
            }
        }
            
        queue<pair<int, int>> workQueue;
        workQueue.push({topManager, 0});
            
        while (!workQueue.empty()) {
            pair<int, int> current = workQueue.front();
            workQueue.pop();
                
            int managerID = current.first;
            int currentTime = current.second;
            maxInformationTime = max(maxInformationTime, currentTime);
                
            for (int subordinate : employees[managerID]) {
                workQueue.push({subordinate, currentTime + notificationTime[managerID]});
            }
        }
            
        return maxInformationTime;
    }
};

Calculate the maximum time required to inform all employees in a company using a hierarchical reporting structure with the provided C++ function.

• Understanding the Problem: The company has a hierarchical structure where only one person is the top manager, and each manager (except the top manager) has exactly one direct manager. Each employee, including managers, takes a certain amount of time to pass information to their direct subordinates.

• Approach: The solution utilizes Breadth-First Search (BFS) to propagate the notification from the top manager to all employees. It captures two key information pieces for each employee: their unique ID and the time they would need to notify their direct subordinates.

• Data Structures Used:

  • Vector of vectors: To store the subordinates for each manager. This structure helps in accessing all direct subordinates of any manager efficiently.
  • Queue of pairs: To maintain the current position in the BFS traversal. This stores pairs of (employee_id, notification_time_up_to_this_employee).

• Steps to Implement the Solution:

  1. Initialize the employees vector of vectors to store subordinates for each employee.
  2. Populate this vector using the managers array where each index and value represents an employee and their respective manager.
  3. Use a queue initialized with the top manager and a starting notification time of 0.
  4. Process each element in the queue:
     • Update the maximum information time if the current employee's notification time is greater.
     • Push all subordinates of the current manager into the queue with updated notification times.
  5. The function returns the maximum time taken, which is the time at which the last subordinate is notified.

This solution effectively determines the longest time required to ensure all employees are informed, starting from the top manager and considering the time each manager takes to pass down the information. Use the function by setting up the total number of employees, identifying the top manager, providing each manager's direct manager through an array, and specifying the time each takes to notify their direct subordinates.

class Solution {
    int maximumTime = Integer.MIN_VALUE;
    
    public int totalTimeToInformAll(int numberOfEmployees, int initialID, int[] supervisor, int[] timeToInform) {
        ArrayList<ArrayList<Integer>> employeeTree = new ArrayList<>(numberOfEmployees);
    
        for (int i = 0; i < numberOfEmployees; i++) {
            employeeTree.add(new ArrayList<>());
        }
    
        for (int i = 0; i < numberOfEmployees; i++) {
            if (supervisor[i] != -1) {
                employeeTree.get(supervisor[i]).add(i);
            }
        }
    
        Queue<Pair<Integer, Integer>> queue = new LinkedList<>();
        queue.add(new Pair<>(initialID, 0));
    
        while (!queue.isEmpty()) {
            Pair<Integer, Integer> current = queue.poll();
    
            int supervisorID = current.getKey();
            int accTime = current.getValue();
            maximumTime = Math.max(maximumTime, accTime);
                
            for (int subordinate : employeeTree.get(supervisorID)) {
                queue.add(new Pair<>(subordinate, accTime + timeToInform[supervisorID]));
            }
        }
    
        return maximumTime;
    }
}

The given Java function totalTimeToInformAll is designed to compute the minimum time required to inform all employees in a company. This problem is modeled as a modified breadth-first search (BFS) on a tree structure where nodes represent employees and edges represent the reporting line. Here's how the solution works:

• Initializes an ArrayList of ArrayList<Integer>, employeeTree, which represents a tree of employees where each node (employee) contains a list of its direct reports.

• It populates the employeeTree using the supervisor array where supervisor[i] gives the supervisor of the employee i. Employee i is added to the list of the supervisor's node.

• Implements a Queue of Pair<Integer, Integer> to facilitate the BFS. Each Pair holds an employee’s ID and the cumulative time taken to inform up to that employee.

• Starts the BFS from the employee with ID indicated by initialID with a cumulative time of 0.

• Within the BFS loop, for each employee (node), it checks all direct reports (child nodes), calculates the new accumulated notification time by adding the time taken to inform the current supervisor (timeToInform[supervisorID]), and adds these subordinates to the queue for further traversal.

• Keeps track of the maximumTime taken to inform any employee by comparing and updating it with the accumulated time of the current employee being processed.

• After all employees are processed in the BFS, returns the maximumTime, which will be the total time required to inform all employees.

This approach ensures that the solution accounts for the time taken sequentially through the hierarchy of employees, computing the time efficiently using BFS. The usage of data structures like ArrayList for storing the company structure and Queue for BFS traversal optimally supports the necessary operations for this solution.