How to Solve Divide Nodes Into the Maximum Number of Groups Problem
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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] = [ai, bi] in...
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Problem Statement
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] = [ai, bi] indicates that there is a bidirectional edge between nodes ai and bi. 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 [ai, bi], if ai belongs to the group with index x, and bi 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.
Divide Nodes Into the Maximum Number of Groups
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Examples
n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]4As 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.
n = 3, edges = [[1,2],[2,3],[3,1]]-1If 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 <= 5001 <= edges.length <= 104edges[i].length == 21 <= ai, bi <= nai != biThere is at most one edge between any pair of vertices.How Interview Coder Helps with Leetcode Problems
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