<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 src,vector<int>&vis,int f,vector<int>&color){
        queue<pair<int,int>>q;//node , color
        q.push({src,f});
        vis[0]=1;
        color[0]=0;

        while(!q.empty()){
            auto it=q.front();
            int node = it.first;
            int col = it.second;
            q.pop();

            for(auto child : adj[node]){
                if(!vis[child]){
                    q.push({child,col^1});
                    color[child]=col^1;
                    vis[child]=1;
                }
                else{
                    if(color[child] == col){
                        return false;
                    }
                }
            }
        }
        return true;
    }

    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        vector<int>adj[n];
        for(auto it : dislikes){
            adj[it[0]-1].push_back(it[1]-1);
            adj[it[1]-1].push_back(it[0]-1);
        }
        vector<int>vis(n,0);
        vector<int>color(n,-1);
        int f=0;
        int ans = true;
        for(int i=0;i<n;i++){
            if(!vis[i]){
                ans=ans & bfs(adj,i,vis,0,color);
            }
        }

        return ans;
      
    }
};
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