<p>We want to split a group of <code>n</code> people (labeled from <code>1</code> to <code>n</code>) into two groups of <strong>any size</strong>. Each person may dislike some other people, and they should not go into the same group.</p>

<p>Given the integer <code>n</code> and the array <code>dislikes</code> where <code>dislikes[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that the person labeled <code>a<sub>i</sub></code> does not like the person labeled <code>b<sub>i</sub></code>, return <code>true</code> <em>if it is possible to split everyone into two groups in this way</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 4, dislikes = [[1,2],[1,3],[2,4]]
<strong>Output:</strong> true
<strong>Explanation:</strong> The first group has [1,4], and the second group has [2,3].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3, dislikes = [[1,2],[1,3],[2,3]]
<strong>Output:</strong> false
<strong>Explanation:</strong> We need at least 3 groups to divide them. We cannot put them in two groups.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 2000</code></li>
	<li><code>0 &lt;= dislikes.length &lt;= 10<sup>4</sup></code></li>
	<li><code>dislikes[i].length == 2</code></li>
	<li><code>1 &lt;= a<sub>i</sub> &lt; b<sub>i</sub> &lt;= n</code></li>
	<li>All the pairs of <code>dislikes</code> are <strong>unique</strong>.</li>
</ul>

class Graph{
private:
    int V;
    list<int>* l;
public:
    Graph(int v){
        V=v;
        l=new list<int>[V];
    }
    void addEdge(int i,int j){
        l[i].push_back(j);
        l[j].push_back(i);
    }
    bool dfs(int node,int* visited,int* color,int nodeColor){
        visited[node]=1;
        color[node]=nodeColor;
        for(auto nbr: l[node]){
            if(!visited[nbr]){
                int c;
                if(nodeColor==1) c=2;
                if(nodeColor==2) c=1;
                bool isProblem = dfs(nbr,visited,color,c);
                if(!isProblem) return false;
            }else if(color[nbr]==nodeColor) return false;
        }
        return true;
    }
    bool isBipartite(){
        int* visited=new int[V]();
        int* color=new int[V]();
        for(int i=0;i<V;i++){
            if(!visited[i]){
                if(!dfs(i,visited,color,1)) return false;
            }
        }
        return true;
    }
};
class Solution {
public:
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        Graph g(n);
        for(auto edge: dislikes){
            g.addEdge(edge[0]-1,edge[1]-1);
        }
        return g.isBipartite();
    }
};
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