<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:
    vector<int> root, rank;
    int FindRoot(int a) {
        if (a == root[a]) return a;
        root[a] = FindRoot(root[a]);
        return root[a];
    }
    void merge(int a, int b) {
        int rootA = FindRoot(a);
        int rootB = FindRoot(b);
        if (rootA == rootB) return;
        if (rank[rootA] < rank[rootB])
            root[rootA] = rootB;
        else if (rank[rootB] < rank[rootA])
            root[rootB] = rootA;
        else {
            root[rootB] = rootA;
            rank[rootA]++;
        }
    }
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        root = vector<int>(n+1, 0);
        rank = vector<int>(n+1, 0);
        for (int i=0; i<=n; i++)
            root[i] = i;
        map<int, int> mp;

        for (int i=0; i<dislikes.size(); i++) {
            if (FindRoot(dislikes[i][0]) == FindRoot(dislikes[i][1]))
                return false;
            if (mp.find(dislikes[i][0]) == mp.end())
                mp[dislikes[i][0]] = dislikes[i][1];
            else
                merge(dislikes[i][1], mp[dislikes[i][0]]);

            if (mp.find(dislikes[i][1]) == mp.end())
                mp[dislikes[i][1]] = dislikes[i][0];
            else
                merge(dislikes[i][0], mp[dislikes[i][1]]);
        }
        return true;
    }
};
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