<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>

vector<vector<int>> g;
vector<int> col;
vector<bool> vis;
bool ok = true;
class Solution {
public:
    void dfs(int v){
        vis[v] = true;

        for(auto u:g[v]){
            if(!vis[u]){
                col[u] = !col[v];
                dfs(u);
            }
            else if(col[u] == col[v]) ok = false;
        }
    }
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        ios_base::sync_with_stdio(0), cin.tie(0);
        
        ok = true;
        g.clear();
        g.resize(n+1);
        col.assign(n+1,0);
        vis.assign(n+1,false);

        for(auto friends:dislikes){
           int u = friends[0];
           int v = friends[1];
           g[u].push_back(v);
           g[v].push_back(u);
        }
        for(int i = 1; i <= n; i++){
            if(!vis[i]) dfs(i);
        }

        return ok;
    }
};

auto init = []()
{ 
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    return 'c';
}();
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