<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 {
  using BigIntTy = long long;
  map<int, vector<int>> graph;
public:
    void dfs(int root, vector<bool>& visited, BigIntTy& count) {
      visited[root] = true;      
      for(auto e : graph[root]) {
        if(!visited[e]) dfs(e, visited, count);
      }
      count = count+1;
    }

    long long countPairs(int n, vector<vector<int>>& edges) {
      if(edges.empty()) {
        BigIntTy cnt = n;
        return (cnt * (cnt-1))/2;
      }

      for(auto el : edges) {
        int u = el[0];
        int v = el[1];
        graph[u].push_back(v);
        graph[v].push_back(u);
      }

      vector<bool> visited(n, false);
      vector<BigIntTy> cc;
      // find number of connected components
      for(int i = 0; i < n && graph.size() > 0; i++) {        
        if(!visited[i]) {
          BigIntTy total = 0;
          dfs(i, visited, total);
          cc.push_back(total);
        }        
      } // end for      
      BigIntTy count = 0;
      for(int i = 0; i < cc.size(); i++) {
        for(int j = i+1; j < cc.size(); j++) {
          count += cc[i] * cc[j];
        }
      }
      return count;
    }
};
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