<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 {
private:
    vector<int> parent;
    vector<int> rank;

public:
    DisjointSet(int n) : parent(n), rank(n, 0) {
        for (int i = 0; i < n; i++) {
            parent[i] = i;
        }
    }

    int find(int x) {
        if (x == parent[x]) return x;

        return parent[x] = find(parent[x]);
    }
    
    void byRank(int x, int y) {
        x = find(x);
        y = find(y);

        if (rank[x] > rank[y]) {
            parent[y] = x;
        } else if (rank[y] > rank[x]) {
            parent[x] = y;
        } else {
            parent[y] = x;
            rank[x]++;
        }
    }
};

class Solution {
public:
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        DisjointSet ds(n * 2 + 1);
        for (const auto& dislike: dislikes) {
            int x = dislike[0];
            int y = dislike[1];

            if (ds.find(x) == ds.find(y)) {
                return false;
            }

            ds.byRank(x, y + n);
            ds.byRank(y, x + n);
        }

        return true;
    }
};
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