<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:
    int find(int i, vector<int> &arr){
        if(arr[i] == i) return i;
        return arr[i] = find(arr[i], arr);
    }
    int unite(int a, int b, vector<int> &arr, vector<int> &rank){
        int p1 = find(a, arr);
        int p2 = find(b, arr);
        if(p1 == p2)return 0;
        if(rank[p1]< rank[p2]){
            arr[p1] = p2;
        }else if(rank[p1]> rank[p2]){
            arr[p2] = p1;
        }else{
            arr[p2] = p1;
            rank[p1]++;
        }
        return 1;
    }
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        vector<int> par(n+1,0);
        vector<int> rank(n+1,0);
        vector<vector<int>> gr(n+1);
        for(int i=0;i<=n;i++){
            par[i] = i;
        }
        for(auto i: dislikes){
            gr[i[0]].push_back(i[1]);
            gr[i[1]].push_back(i[0]);
        }
        for(int i = 0;i<=n;i++){
            for(int j: gr[i]){
                unite(gr[i][0], j, par, rank);
            }
        }
        for(auto i: dislikes){
            if(find(i[0], par) == find(i[1], par))return 0;
        }
        return 1;
    }
};
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