785. Is Graph Bipartite?

There is an undirected graph with n nodes, where each node is numbered between 0 and n - 1. You are given a 2D array graph, where graph[u] is an array of nodes that node u is adjacent to. More formally, for each v in graph[u], there is an undirected edge between node u and node v. The graph has the following properties:

• There are no self-edges (graph[u] does not contain u).
• There are no parallel edges (graph[u] does not contain duplicate values).
• If v is in graph[u], then u is in graph[v] (the graph is undirected).
• The graph may not be connected, meaning there may be two nodes u and v such that there is no path between them.

A graph is bipartite if the nodes can be partitioned into two independent sets A and B such that every edge in the graph connects a node in set A and a node in set B.

Return true if and only if it is bipartite.

class Solution {
public:
    bool isBipartite(vector<vector<int>>& g) {
        int n = g.size();
        vector<int> gr(n, -1);
        queue<int> q;
        for(int i = 0; i < n; i++) {
            if(gr[i] != -1) continue;
            gr[i] = 0;
            q.push(i);
            while(!q.empty()) {
                auto u = q.front(); q.pop();
                for(auto& v : g[u]) {
                    if(gr[v] == gr[u]) return false;
                    if(gr[v] == -1) {
                        gr[v] = gr[u] ? 0 : 1;
                        q.push(v);
                    }
                }
            }
        }
        return true;
    }
};