<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 DisjointSet{
vector<int>rank,parent;
public:
DisjointSet(int n){
    rank.resize(n+1,0);
    parent.resize(n+1,0);
    for(int i=0;i<n;i++){
       parent[i]=i;
    }
}

int findparent(int node){
    if(parent[node]==node){
        return node;
    }
    return parent[node]=findparent(parent[node]);
}
void unionbyrank(int u,int v){
  int ulp=findparent(u);
  int vlp=findparent(v);
  if(ulp==vlp){
    return ;
  }
  else{
    if(rank[ulp]<rank[vlp]){
        parent[ulp]=vlp;
    }
    else{
        if(rank[ulp]==rank[vlp]){
            parent[ulp]=vlp;
            rank[vlp]++;
        }
        else{
        parent[vlp]=ulp;
        }
    }
  }
 return ;
}
};
class Solution {
public:
 bool bfs(unordered_map<int,list<int>>&adj,int node,vector<int>&color){
      queue<int>q;
      q.push(node);
      color[node]=1;
      while(!q.empty()){
         int x=q.front();
         q.pop();
         for(auto it:adj[x]){
            if(color[it]==color[x]){
                return false;
            }
            if(color[it]==-1){
                color[it]=1-color[x];
                q.push(it);
            }
         }
      }
      return true;
   }
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
          vector<int>color(n+1,-1);
          unordered_map<int,list<int>>adj;
          for(int i=0;i<dislikes.size();i++){
             int u=dislikes[i][0];
             int v=dislikes[i][1];
             adj[u].push_back(v);
             adj[v].push_back(u);
          }
          for(int i=1;i<=n;i++){
            if(color[i]==-1){
               if(!bfs(adj,i,color)){
                   return false;
               }
            }
          }
          return true;
    }
};
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