Skip to content

UMPIRE Interview Strategy

Jump to bottom
Samantha He edited this page Oct 13, 2022 · 9 revisions

Time Needed to Inform All Employees

Problem Highlights

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

  • Established a set (2-3) of test cases to verify their own solution later.
  • Established a set (1-2) of edge cases to verify their solution handles complexities.
  • Have fully understood the problem and have no clarifying questions.
  • Have you verified any Time/Space Constraints for this problem?

Solution

  • Can we transform the organization into a tree with each node containing the wait time (before transmitting down to their reports)?
    • This can simplify the problem into traversing the tree from the top node down to the bottom.
  • How is the time calculated while traversing down and comparing and setting the maximum time?
  • Can we avoid repeating the work of calculating how much time it takes for each manager to inform their superiors?
Input: n = 7, headId = 0, manager = [-1, 0, 0, 0, 1, 1, 3]
Output: informTime = [ 4, 2, 0, 3, 0, 0, 0]

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

For graph problems, we want to consider the following approaches:

  • Is this a directed or undirected graph? Directed graph. Direction from manager to employee or employee to manager?
  • Is this BFS or DFS? Similar to root to leaf path. Can be done through DFS

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Use DFS to traverse the graph while calculating time at each step

1. We first convert the list to a graph
2. Then we use DFS to visit every note
3. We keep calculating the notifying time for each employee
4. we update the maximum time at each step

⚠️ Common Mistakes

4: I-mplement

Implement the code to solve the algorithm.

class Solution(object):
    def numOfMinutes(self, n, headID, managers, informTime):
        graph = self.buildGraph(managers)
        self.maxTime = 0
      
        def dfs(source, currentTime):
            # check if the source node is a non-manager
            self.maxTime = max(self.maxTime, currentTime)
            
            # explore the neighbors
            for neighbor in graph[source]:
                dfs(neighbor, currentTime + informTime[source])
        
        dfs(headID, 0)
        return self.maxTime
    
    # we will build a Directed Graph : Manager -> Employee
    def buildGraph(self, managers):
        # Adjacency List
        graph = defaultdict(list)
        for employee, manager in enumerate(managers):
            if manager != -1:
                graph[manager].append(employee)
            
        return graph

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

  • Trace through your code with an input to check for the expected output
  • Catch possible edge cases and off-by-one errors

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

  • Time Complexity: O(n) since we traverse backward on each employee at most once
  • Space Complexity: O(n) since we store the time it takes to inform each employee
Clone this wiki locally