How do you solve Maximum Employees to Be Invited to a Meeting on LeetCode?

Maximum Employees to Be Invited to a Meeting (LeetCode #2127) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding cycles in directed graphs is crucial for solving this problem.

What is the time complexity of Maximum Employees to Be Invited to a Meeting?

The optimal solution for Maximum Employees to Be Invited to a Meeting runs in O(n) time and uses O(n) space. This complexity is efficient because we only traverse each employee once during the DFS, leading to a linear time complexity.

What is the brute force solution for Maximum Employees to Be Invited to a Meeting?

The brute force approach for Maximum Employees to Be Invited to a Meeting is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking every possible combination of employees to see if they can sit together according to their preferences. This is straightforward but inefficient, as it requires evaluating many combinations. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Maximum Employees to Be Invited to a Meeting?

Always visualize the problem as a graph to understand relationships. Discuss your thought process clearly; explain how you would approach finding cycles. Practice DFS and graph traversal techniques, as they are common in interview questions.

What are common mistakes when solving Maximum Employees to Be Invited to a Meeting?

Failing to recognize cycles and treating the problem as a simple selection. Not considering that employees outside a cycle cannot be invited.

#2127

Maximum Employees to Be Invited to a Meeting

Hard

ArrayDynamic ProgrammingDepth-First SearchGraph TheoryTopological SortGraph TheoryDepth-First SearchCycle Detection

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal approach involves modeling the problem as a directed graph where each employee points to their favorite. By identifying cycles and chains, we can efficiently determine the maximum number of employees that can be invited.

⚙️

Algorithm

3 steps

1Step 1: Create a graph where each employee points to their favorite employee.
2Step 2: Use DFS to find all cycles in the graph and count the number of employees in each cycle.
3Step 3: For each cycle, add its size to the total count, and also consider employees leading into the cycle.

solution.py26 lines

1def maxEmployees(favorite):
2    n = len(favorite)
3    visited = [False] * n
4    in_cycle = [False] * n
5    max_count = 0
6
7    def dfs(node):
8        nonlocal cycle_size
9        if visited[node]:
10            if in_cycle[node]:
11                return True
12            return False
13        visited[node] = True
14        cycle_size += 1
15        in_cycle[node] = True
16        if dfs(favorite[node]):
17            return True
18        in_cycle[node] = False
19        return False
20
21    for i in range(n):
22        if not visited[i]:
23            cycle_size = 0
24            if dfs(i):
25                max_count += cycle_size
26    return max_count

ℹ

Complexity note: This complexity is efficient because we only traverse each employee once during the DFS, leading to a linear time complexity.

1Understanding cycles in directed graphs is crucial for solving this problem.
2Employees can only be invited if they can sit next to their favorite, which limits valid combinations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.