<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 DisjointSet {
public:
   vector<int> parent;
   vector<int> rank;

   DisjointSet(int n) {
    parent.resize(n+1,0);
    rank.resize(n+1,0);
    for(int i = 1;  i<=n; i++) {
        parent[i] = i;
    }
   }
 
    int findUParent(int i) {
        if(parent[i] == i) return i;
        return parent[i] = findUParent(parent[i]);
    }

    void findUnion(int u, int v) {
        int upv = findUParent(u);
        int upu = findUParent(v);
        
        if(upv == upu)  return;

        if(rank[upu] < rank[upv]) {
            parent[upv] = upu;
        } else if(rank[upv] < rank[upu]) {
            parent[upu] = upv;
        } else {
            rank[upu]++;
            parent[upu] = upv;
        }
    }
};
class Solution {
public:
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        //vector<vector<int>> matrix(n+1, vector<int>(n+1, 0));
        DisjointSet ds(n);
        vector<int> adj[n+1];
        for(auto it: dislikes) {
            adj[it[0]].push_back(it[1]);
            adj[it[1]].push_back(it[0]);
        }
        for(auto it: adj) {
            if(it.size() == 0) continue;
            vector<int> likers = it;
            int firstLiker = likers[0];
            for(int i = 1; i<likers.size(); i++)
               ds.findUnion(firstLiker,likers[i]);
        }

        for(auto disliker: dislikes) {
            if(ds.findUParent(disliker[0]) == ds.findUParent(disliker[1])) return false;
        }

        return true;
    }
};
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