Is Graph Bipartite .cpp

/* 
    Solution by Rahul Surana
    
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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.

 



    ***********************************************************
*/



#include <bits/stdc++.h>

class Solution {
public:
     vector<int>vis,col;
    bool dfs(int v, int c, vector<vector<int>>& graph){
        vis[v]=1;
        col[v]=c;
        for(int child:graph[v]){
            if(vis[child]==0){
                // here c^1 is for flipping 1 by 0 or 0 by 1, that is flip the current color
                if(dfs(child,c^1,graph)==false) 
                    return false;
            }
            else{
                if(col[v]==col[child])
                    return false;
            }
        }
        return true;
    }
    
    bool isBipartite(vector<vector<int>>& graph) {
        int n=graph.size();
        vis.resize(n);
        col.resize(n);

        for(int i=0;i<n;++i){
            if(vis[i]==0 && dfs(i,0,graph)==false){ 
                return false;
            }
        }
        
        return true;
    }
};