<p>You are given an integer <code>n</code>. There is an <strong>undirected</strong> graph with <code>n</code> nodes, numbered from <code>0</code> to <code>n - 1</code>. You are given a 2D integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> denotes that there exists an <strong>undirected</strong> edge connecting nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>

<p>Return <em>the <strong>number of pairs</strong> of different nodes that are <strong>unreachable</strong> from each other</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/05/tc-3.png" style="width: 267px; height: 169px;" />
<pre>
<strong>Input:</strong> n = 3, edges = [[0,1],[0,2],[1,2]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no pairs of nodes that are unreachable from each other. Therefore, we return 0.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/05/tc-2.png" style="width: 295px; height: 269px;" />
<pre>
<strong>Input:</strong> n = 7, edges = [[0,2],[0,5],[2,4],[1,6],[5,4]]
<strong>Output:</strong> 14
<strong>Explanation:</strong> There are 14 pairs of nodes that are unreachable from each other:
[[0,1],[0,3],[0,6],[1,2],[1,3],[1,4],[1,5],[2,3],[2,6],[3,4],[3,5],[3,6],[4,6],[5,6]].
Therefore, we return 14.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= edges.length &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>There are no repeated edges.</li>
</ul>

class Solution {
public:

    void bfs(vector<int> adj[],int u,vector<bool> &visited,long long  &comp){
        queue<int> q;
        visited[u]=true;
        q.push(u);
        comp++;
        while(!q.empty()){
            int v=q.front();
            q.pop();
            for(int a:adj[v]){
             if(!visited[a]){
                 q.push(a);
                 visited[a]=true;
                 comp++;
              }
            }
           
        }
    }


    long long countPairs(int n, vector<vector<int>>& edges) {
        
        vector<int> adj[n];
        for(auto it:edges){
            adj[it[0]].push_back(it[1]);
            adj[it[1]].push_back(it[0]);

        }
       vector<bool> visited(n,false);
       long long remainingsize=n;
       long long result=0;
       for(int i=0;i<n;i++){
         
          if(!visited[i]){
             long long componentsize=0;
            bfs(adj,i,visited,componentsize);
            result += componentsize *(remainingsize-componentsize);
            remainingsize -= componentsize;

          }
       }
       return result;
     



    }
};


//    void bfs(int u, unordered_map<int, vector<int>> &adj, vector<bool>& visited, long long &Size) {
        
//         queue<int> que;
//         que.push(u);
        
//         visited[u] = true;
//         Size++;
        
//         while(!que.empty()) {
            
//             int x = que.front();
//             que.pop();
            
//             for(int &v : adj[x]) {
                
//                 if(!visited[v]) {
//                     visited[v] = true;
//                     que.push(v);
//                     Size++;
//                 }
                
//             }
            
//         }
        
//     }
    
//     long long countPairs(int n, vector<vector<int>>& edges) {
        
//         unordered_map<int, vector<int>> adj;
        
//         for(auto &vec : edges) {
            
//             int u = vec[0];
//             int v = vec[1];
            
//             adj[u].push_back(v);
//             adj[v].push_back(u);
            
//         }
        
//         vector<bool> visited(n, false);
        
//         long long remainingNodes = n;
        
//         long long result = 0;
        
//         for(int i = 0; i<n; i++) {
            
//             if(!visited[i]) {
                
//                 long long Size = 0;
                
//                 bfs(i, adj, visited, Size);
                
//                 result += (Size) * (remainingNodes - Size);
                
//                 remainingNodes -= Size;
//             }
            
//         }
        
//         return result;
        
//     }






295166