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• 2493. Divide Nodes Into the Maximum Number of Groups
  • Approach
  • Python
  • C++

TODO 2493. Divide Nodes Into the Maximum Number of Groups   hard

You are given a positive integer n representing the number of nodes in an undirected graph. The nodes are labeled from 1 to n.

You are also given a 2D integer array edges, where edges[i] = [a_{i, }b_{i}] indicates that there is a bidirectional edge between nodes a_{i} and b_{i}. Notice that the given graph may be disconnected.

Divide the nodes of the graph into m groups (1-indexed) such that:

• Each node in the graph belongs to exactly one group.
• For every pair of nodes in the graph that are connected by an edge [a_{i, }b_{i}], if a_{i} belongs to the group with index x, and b_{i} belongs to the group with index y, then |y - x| = 1.

Return the maximum number of groups (i.e., maximum /~m~) into which you can divide the nodes/. Return -1 if it is impossible to group the nodes with the given conditions.

Example 1:

Input: n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]
Output: 4
Explanation: As shown in the image we:
- Add node 5 to the first group.
- Add node 1 to the second group.
- Add nodes 2 and 4 to the third group.
- Add nodes 3 and 6 to the fourth group.
We can see that every edge is satisfied.
It can be shown that that if we create a fifth group and move any node from the third or fourth group to it, at least on of the edges will not be satisfied.

Example 2:

Input: n = 3, edges = [[1,2],[2,3],[3,1]]
Output: -1
Explanation: If we add node 1 to the first group, node 2 to the second group, and node 3 to the third group to satisfy the first two edges, we can see that the third edge will not be satisfied.
It can be shown that no grouping is possible.

Constraints:

• 1 <= n <= 500
• 1 <= edges.length <= 10^{4}
• edges[i].length == 2
• 1 <= a_{i}, b_{i} <= n
• a_{i} != b_{i}
• There is at most one edge between any pair of vertices.

TODO Approach

Write your approach here.

TODO Python

class Solution:
    def magnificentSets(self, n: int, edges: List[List[int]]) -> int:

TODO C++

class Solution {
public:
    int magnificentSets(int n, vector<vector<int>>& edges) {
        
    }
};