A company is organizing a meeting and has a list of n employees, waiting to be invited. They have arranged for a large circular table, capable of seating any number of employees.
The employees are numbered from 0 to n - 1. Each employee has a favorite person and they will attend the meeting only if they can sit next to their favorite person at the table. The favorite person of an employee is not themself.
Given a 0-indexed integer array favorite, where favorite[i] denotes the favorite person of the ith employee, return the maximum number of employees that can be invited to the meeting.
Example 1:
Input: favorite = [2,2,1,2] Output: 3 Explanation: The above figure shows how the company can invite employees 0, 1, and 2, and seat them at the round table. All employees cannot be invited because employee 2 cannot sit beside employees 0, 1, and 3, simultaneously. Note that the company can also invite employees 1, 2, and 3, and give them their desired seats. The maximum number of employees that can be invited to the meeting is 3.
Example 2:
Input: favorite = [1,2,0] Output: 3 Explanation: Each employee is the favorite person of at least one other employee, and the only way the company can invite them is if they invite every employee. The seating arrangement will be the same as that in the figure given in example 1: - Employee 0 will sit between employees 2 and 1. - Employee 1 will sit between employees 0 and 2. - Employee 2 will sit between employees 1 and 0. The maximum number of employees that can be invited to the meeting is 3.
Example 3:
Input: favorite = [3,0,1,4,1] Output: 4 Explanation: The above figure shows how the company will invite employees 0, 1, 3, and 4, and seat them at the round table. Employee 2 cannot be invited because the two spots next to their favorite employee 1 are taken. So the company leaves them out of the meeting. The maximum number of employees that can be invited to the meeting is 4.
Constraints:
n == favorite.length2 <= n <= 1050 <= favorite[i] <= n - 1favorite[i] != iThis approach involves detecting cycles in the graph created by the favorite relationships. Each employee can be represented as a node in a graph, and a directed edge from employee i to employee favorite[i]. The problem can then be broken down into finding the longest cycle and managing chain connections to nodes forming such cycles.
In the solution provided, we utilize Depth First Search (DFS) to identify cycles by keeping track of nodes already visited and recurrence depth. The key is recognizing cycles in this graph representation and thus calculating the maximum employees from these cycles. This code is a general template, emphasizing the calculation of cycle lengths.
C++
Time Complexity: O(n) for traversing each node once. Space Complexity: O(n) for storage of visited states and stack sizes.
Another approach is to tackle this problem using dynamic programming. By considering the problem as one on a tree with nodes having specific dependencies (favorite person), we plant roots for our trees where the nodes represent employees and dependencies represent favorites.
The Java solution builds a tree representation using adjacency lists by converting the favorite relationships into a tree structure. Depth-First Search is applied to find the longest paths, while we track each node's depth in a dynamic programming table for efficiency and accuracy.
JavaScript
Time Complexity: O(n), as we perform DFS rooted at each node once. Space Complexity: O(n) for the adjacency list and visited states.
| Approach | Complexity |
|---|---|
| Approach 1: Graph Cycle Detection and Maximum Matching | Time Complexity: O(n) for traversing each node once. Space Complexity: O(n) for storage of visited states and stack sizes. |
| Approach 2: Dynamic Programming on Trees | Time Complexity: O(n), as we perform DFS rooted at each node once. Space Complexity: O(n) for the adjacency list and visited states. |
Maximum Employees to Be Invited to a Meeting - Leetcode 2127 - Python • NeetCodeIO • 12,786 views views
Watch 9 more video solutions →Practice Maximum Employees to Be Invited to a Meeting with our built-in code editor and test cases.
Practice on FleetCode