<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 {
private:
    unordered_map<int, int> parent, constraints;

    int find_parent(const int& a) {
        if(parent[a] == a) return a;
        else return parent[a] = find_parent(parent[a]);
    }
public:
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        if(dislikes.empty()) return true;

        for(auto& dislike : dislikes) {
            int a = dislike[0];
            int b = dislike[1];

            if(parent.find(a) == parent.end()) {
                parent[a] = a;
            } 

            if(parent.find(b) == parent.end()) {
                parent[b] = b;
            }

            if(constraints.find(a) != constraints.end()) {
                parent[b] = find_parent(constraints[a]);
            }

            if(constraints.find(b) != constraints.end()) {
                parent[a] = find_parent(constraints[b]);
            }

            int pa = find_parent(a);
            int pb = find_parent(b);

            if(pa == pb) return false;

            constraints[a] = b;
            constraints[b] = a;
        }

        return true;
    }
};
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