<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(vector<int> adj[] , int i,vector<int> &vis,vector<int> &col){
        vis[i] = 1;
        col[i] = 0;
        queue<int> q;
        q.push(i);
        while(!q.empty()){
            int node = q.front();
            q.pop();
            for(auto nbr : adj[node]){
                if(col[nbr] == col[node]) return false;

                if(!vis[nbr]){
                    vis[nbr] = 1;
                    col[nbr] = !col[node];
                    q.push(nbr);
                }
            }
        }   

        return true;
    }    

    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        
        vector<int> adj[n+1];
        for(auto i : dislikes){
            adj[i[0]].push_back(i[1]);
            adj[i[1]].push_back(i[0]);
        }

        vector<int> vis(n+1,0);
        vector<int> col(n+1,-1);

        bool ans = true;
        for(int i = 1; i <= n; i++){
            if(!vis[i]){
                ans &= bfs(adj,i,vis,col);
                if(!ans) return false;
            }
        }

        return true;

    }
};
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