<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>

#include <vector>
using namespace std;

class Solution {
public:
    vector<int> color;

    Solution() : color(2000, -1) {} // Initialize color in the constructor

    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        for (int i = 0; i < n; ++i) { // Ensure all nodes are considered
            if (color[i] == -1) { // Not colored yet
                color[i] = 0; // Start coloring with 0
                if (!coloring(i, dislikes)) {
                    return false; // If coloring fails, return false
                }
            }
        }
        return true; // If all nodes can be colored
    }

    bool coloring(int pos, vector<vector<int>>& dislikes) {
        for (auto& dislike : dislikes) {
            int a = dislike[0] - 1; // Adjust for 0-based index
            int b = dislike[1] - 1; // Adjust for 0-based index
            
            int toColor = (a == pos) ? b : (b == pos) ? a : -1;
            if (toColor == -1) continue; // Skip if neither a nor b is pos

            if (color[toColor] == -1) {
                color[toColor] = !color[pos]; // Color the neighboring node
                if (!coloring(toColor, dislikes)) {
                    return false; // If recursive call fails, return false
                }
            } else if (color[toColor] == color[pos]) {
                return false; // Conflict in coloring
            }
        }
        return true; // Successfully colored
    }
};
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