<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:
    def __init__(self):
        self.visited = []
        self.color = []
        self.flag = True

    def possibleBipartition(self, n: int, dislikes: List[List[int]]) -> bool:
        graph = self.constructGraph(n, dislikes)
        self.visited = [False] * n
        self.color = [False] * n
        for v in range(n):
            if self.flag == False:
                return False
            if self.visited[v]:
                continue
            self.traverse(graph, v)
        return self.flag
    
    def traverse(self, graph, v):
        if self.flag == False:
            return
        
        self.visited[v] = True # target v as visited node

        for neighbour in graph[v]:
            if self.visited[neighbour] == False: # we have never seen this node before
                self.color[neighbour] = not self.color[v]
                self.traverse(graph, neighbour)
            else: # we have seen this node before
                if self.color[neighbour] == self.color[v]:
                    self.flag = False
                    return
        return
        
    def constructGraph(self, n, dislikes):
        graph = [[] for i in range(n)]

        for p1, p2 in dislikes:
            graph[p1-1].append(p2-1)
            graph[p2-1].append(p1-1)
        return graph
        
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