<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:
    bool bfs(int s,vector<vector<int>> &adj,vector<int> &vi,vector<int> &color){
        queue<vector<int>> q;
        q.push({s,-1});
        int par =-1;
        while(!q.empty()){
            int s = q.front()[0];
            q.pop();
            for(auto x:adj[s]){
                if(!vi[x]){
                    color[x] = abs(color[s]-1);
                    vi[x]=1;
                    q.push({x,s});
                }
                else{
                    if(color[s]==color[x]){
                        return false;
                    }

                }
            }
        }
        return true;
    }
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        vector<int> color(n+1,-1);
        vector<int> vi(n+1,0);
        vector<vector<int>> adj(n+1);
        for(int i=0;i<dislikes.size();i++){
            adj[dislikes[i][0]].push_back(dislikes[i][1]);
            adj[dislikes[i][1]].push_back(dislikes[i][0]);
        }
        for(int i=1;i<=n;i++){
            if(!vi[i]){
                color[i]=0;
                vi[i]=1;
                if(!bfs(i,adj,vi,color)) return false;
            }
        }
        return true;
        
    }
};
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