<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 {
private:
    void dfs(unordered_map<int,vector<int>>& graph, int node, unordered_set<int>& visited, long* nof_nodes_p){
        if(visited.find(node) != visited.end()){
            return;
        }
        *nof_nodes_p = *nof_nodes_p + 1;
        visited.insert(node);
        for(auto next_node : graph[node]){
            dfs(graph, next_node, visited, nof_nodes_p);
        }
    }

public:
    long long countPairs(int n, vector<vector<int>>& edges) {
        // build graph 
        unordered_map<int,vector<int>> graph;
        for(auto cur_edge : edges){
            for(int i = 0; i < 2; ++i){
                graph[cur_edge[i]].push_back(cur_edge[1-i]);
            }   
        }
        
        // dfs count nof nodes for each isoloated graph
        vector<long> nof_nodes;
        unordered_set<int> visited;
        unordered_map<long, long> nof_nodes_freq; 
        long long pair_nof_nodes = 0;
        for(int node = 0; node < n; ++node){
            if(visited.find(node) == visited.end()){
                long cur_nof_nodes = 0;
                this->dfs(graph, node, visited, &cur_nof_nodes);
                for(auto cur_pair : nof_nodes_freq){
                    int nof_n = cur_pair.first;
                    int cnts = cur_pair.second;
                    pair_nof_nodes += cur_nof_nodes * nof_n * cnts;
                }
                nof_nodes_freq[cur_nof_nodes]++;
            }
        }

        return pair_nof_nodes;
    }
};
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