<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) {
        
        enum COLOR_CONSTANT{
            GREEN = -1,         // -1
            NOT_COLORED,       // 0
            BLUE                // 1
        };
        if( n == 1 || dislikes.size() == 0 ){
            return true;
        }
        unordered_map< int, vector<int> > dislikeTable;
        unordered_map< int, int> colorTable;
        std::function< bool( int, int ) > helper;
        helper = [&]( int personID, int color)->bool{
            colorTable[personID] = color;
            for( const int& theOther : dislikeTable[ personID ] ){
                if( colorTable[theOther] == color ){
                    return false;
                }
                if( colorTable[theOther] == NOT_COLORED && ( !helper(theOther, -color) ) ){
                    return false;
                }
            }
            return true;    
        };
        for( const auto& relation : dislikes ){
            int p1 = relation[0], p2 = relation[1];
            dislikeTable[p1].emplace_back( p2 );
            dislikeTable[p2].emplace_back( p1 );
        }
        for( int personID = 1 ; personID <= n ; personID++){
            if( colorTable[personID] == NOT_COLORED && ( !helper(personID, BLUE) ) ){
                    return false;
            }
        }
        return true;        
    }
};
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