<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:
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        vector<vector<int>>adj(n);
        unordered_set<int>group1, group2;
        for(int i = 0; i < dislikes.size(); ++i) {
            adj[dislikes[i][0] - 1].push_back(dislikes[i][1] - 1);
            adj[dislikes[i][1] - 1].push_back(dislikes[i][0] - 1);
        }
        vector<bool>visited(n, false);
        for(int i = 0; i < n; ++i) {
            if (visited[i]) continue;
            queue<pair<int, bool>>q;
            q.push({i, false});
            visited[i] = true;
            group1.insert(i);
            while(!q.empty()) { 
                pair<int, bool>top = q.front();
                //cout<<top.first<<endl;
                q.pop();
                for(int j = 0; j < adj[top.first].size(); ++j) {
                    if (visited[adj[top.first][j]]) continue;
                    if (top.second) {
                        group1.insert(adj[top.first][j]);
                    } else {
                        group2.insert(adj[top.first][j]);
                    }
                    visited[adj[top.first][j]] = true;
                    q.push({adj[top.first][j], !top.second});
                }
            }
        }
        // cout<<"sethi1"<<endl;
        // for(auto i = group1.begin(); i != group1.end(); ++i) {
        //     cout<<*i<<endl;
        // }
        // cout<<"sethi"<<endl;
        // for(auto i = group2.begin(); i != group2.end(); ++i) {
        //     cout<<*i<<endl;
        // }
        for(int i = 0; i < dislikes.size(); ++i) {
            if (group1.count(dislikes[i][0]-1) && group1.count(dislikes[i][1]-1)) return false;
            if (group2.count(dislikes[i][0]-1) && group2.count(dislikes[i][1]-1)) return false;
        }
        return true;
    }
};
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