<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 Solution {
public:


 void dfs(int node , int p , int c , vector<int>&vis ,  vector<int>&col , vector<vector<int>>&adj , bool &sig ){
    vis[node] = 1 ; 
	col[node] = c ; 

	for(auto nbr : adj[node]){
		 if(vis[nbr] == 0){
			dfs(nbr,node,1-c,vis,col,adj,sig) ; 
		 }else{
			 // colors should be differnct 
			 if(col[nbr] == c){
				 sig = false ; 
			 }
		 }
	}
	return ; 
 }
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        vector<vector<int>>adj(n) ; 
       for(int i = 0 ; i < dislikes.size() ; i++){
          int u = dislikes[i][0] ; 
          int v = dislikes[i][1] ;
          u-- , v-- ; 
          adj[u].push_back(v) ; 
          adj[v].push_back(u) ; 
       }
       vector<int>vis(n,0) ; 
       vector<int>col(n,-1) ; 
       bool sig = true ; 
     for(int i = 0 ; i < n ; i++)
     if(vis[i] ==0)dfs(i,-1,1,vis,col,adj,sig) ; 
     return sig ; 
    }
};
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