<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:

    struct People {
        int group = -1;
        vector<People*> dislike = {};
    };

    bool dfs(People* person, int group) {
        person->group = group;
        for(auto dislike_person: person->dislike) {
            if(dislike_person->group == -1) {
                if(!dfs(dislike_person, (group + 1) % 2)) {
                    return false;
                }
            } else {
                if(dislike_person->group == group) {
                    return false;
                }
            }
        }
        return true;
    }


    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        vector<People> people(n, People());
        for(const auto& edge: dislikes) {
            people[edge[0] - 1].dislike.push_back(&people[edge[1] - 1]);
            people[edge[1] - 1].dislike.push_back(&people[edge[0] - 1]);
        }
        for(auto& person: people) {
            if(person.group == -1) {
                if(!dfs(&person, 0)) {
                    return false;
                }
            }
        }
        return true;
    }
};
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