{leetcode}/problems/divide-nodes-into-the-maximum-number-of-groups/[LeetCode - 2493. Divide Nodes Into the Maximum Number of Groups ^]
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<sub>i, </sub>b<sub>i</sub>]
indicates that there is a bidirectional edge between nodes a<sub>i</sub>
and b<sub>i</sub>
. 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<sub>i, </sub>b<sub>i</sub>]
, ifa<sub>i</sub>
belongs to the group with indexx
, andb<sub>i</sub>
belongs to the group with indexy
, 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: <img alt="" src="https://assets.leetcode.com/uploads/2022/10/13/example1.png" style="width: 352px; height: 201px;" />
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 ⇐ 104
-
edges[i].length == 2
-
1 ⇐ a<sub>i</sub>, b<sub>i</sub> ⇐ n
-
a<sub>i</sub> != b<sub>i</sub>
-
There is at most one edge between any pair of vertices.