<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:
    /// use color as attribute to descript dislikeRelationship
    /// if the their color are the same, they can not go to the same group
    enum class COLOR_CONSTANT: int
    {
        GREEN= -1,
        NO_COLOR,
        BLUE,
    };

    bool possibleBipartition(int n, vector<vector<int>>& dislikes) 
    {
        if(n==1 || dislikes.empty()) return true;
        initColor(n);
        initDislikes(dislikes);

        for(int i=1;i<=n;++i)
        {
            if((mColorMap.at(i)==COLOR_CONSTANT::NO_COLOR) && (!checkPossibility(i, COLOR_CONSTANT::GREEN))) return false;
        }

        return true;
    }

    bool checkPossibility(int person, const COLOR_CONSTANT color)
    {
        mColorMap.at(person) = color;
        for(auto dislikePerson:mDislikes[person])
        {
            if(mColorMap.at(dislikePerson)==color) return false;
            auto colorToCheck = static_cast<COLOR_CONSTANT>(-1*static_cast<int>(color));
            if(mColorMap.at(dislikePerson)==COLOR_CONSTANT::NO_COLOR && !checkPossibility(dislikePerson, colorToCheck)) return false;
        }
        return true;
    }

    

    void initDislikes(const vector<vector<int>>& dislikes)
    {
        for(auto relationship:dislikes)
        {
            mDislikes[relationship[0]].push_back(relationship[1]);
            mDislikes[relationship[1]].push_back(relationship[0]);
        }
    }

    void initColor(const int n)
    {
        for(int i=1;i<=n;++i)
        {
            mColorMap[i] = COLOR_CONSTANT::NO_COLOR;
        }
    }


private:
    unordered_map<int, COLOR_CONSTANT> mColorMap; // descript the attribute (color) of each person
    unordered_map<int, vector<int>> mDislikes; // the vector inside contains the people that dislike the person indicated by the key
};
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