<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:
    vector<list<int>> graph;
    unordered_set<int> visited;
    
    void add_edge(int s, int d, bool dir) {
        graph[s].push_back(d);
        if(dir) graph[d].push_back(s);
    }
    
    void calculate_connected_components(int source, int &total_node) {
        visited.insert(source);
        total_node++;
        for(auto el : graph[source]) {
            if(visited.find(el) == visited.end()) {
                calculate_connected_components(el, total_node);
            }
        }
    }

    long long countPairs(int n, vector<vector<int>>& arr) {
        long long sum = 0;
        vector<int> component_sizes;
        graph.resize(n);
        
        for(int i = 0; i < arr.size(); i++) {
            int s = arr[i][0];
            int d = arr[i][1];
            add_edge(s, d, true);
        }
        
        for(int i = 0; i < n; i++) {
            if(visited.find(i) == visited.end()) {
                int total_node = 0;
                calculate_connected_components(i, total_node);
                component_sizes.push_back(total_node);
            }
        }
        
        long long total_pairs = (long long)n * (n - 1) / 2;
        long long reachable_pairs = 0;
        for(int size : component_sizes) {
            reachable_pairs += (long long)size * (size - 1) / 2;
        }
        
        return total_pairs - reachable_pairs;
    }
};

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