<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 dfs(int root, int &freq, unordered_set<int> &visited, unordered_map<int, vector<int>> &adjList){

        if(visited.find(root) != visited.end()) return; // already visited

        freq++;

        visited.insert(root);

        for(int node: adjList[root]){

            if(visited.find(node) == visited.end())

               dfs(node, freq, visited, adjList);
        }
    }


    long long countPairs(int n, vector<vector<int>>& edges) {
        
        unordered_map<int, vector<int>> adjList;

        for(auto edge : edges){

            adjList[edge[0]].push_back(edge[1]);
            adjList[edge[1]].push_back(edge[0]);
        }

        unordered_set<int> visited;

        long long result = 0;
        int nodes = n;

        for(int i=0; i<n; i++){

            if(visited.find(i) != visited.end()) continue;
            
            int freq = 0;
            
            dfs(i, freq, visited, adjList);

            if(freq != 0){
                
                result += (long long) freq * (nodes - freq);
                nodes -= freq;
            }
        }

        return result;
    }
};
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