<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:
    bool check_bipartite(vector<int> adj[], int src, int color[]) {
        queue<int> q;
        q.push(src);
        color[src] = 1;

        while (!q.empty()) {
            int node = q.front();
            q.pop();

            for (auto adj_node : adj[node]) {
                if (color[adj_node] == -1) {
                    color[adj_node] = 1 - color[node];
                    q.push(adj_node);
                } else if (color[adj_node] == color[node]) {
                    return false;
                }
            }
        }
        return true;
    }

    bool biPartite(vector<int> adj[], int n) {
        int color[n + 1];

        memset(color, -1, sizeof(color));

        for (int i = 1; i <= n; i++) {
            if (color[i] == -1) {
                if (!check_bipartite(adj, i, color)) {
                    return false;
                }
            }
        }
        return true;
    }

public:
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {

        vector<int> adj[n + 1];

        int N = dislikes.size();

        for (int i = 0; i < N; i++) {
            int u = dislikes[i][0];
            int v = dislikes[i][1];

            adj[u].push_back(v);
            adj[v].push_back(u);
        }

        return biPartite(adj, n);
    }
};
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