<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;
    int v;

    void add_edge(int src, int dest, bool bi_dir = true) {
        graph[src].push_back(dest);
        if (bi_dir) {
            graph[dest].push_back(src);
        }
    }

    int dfs(int src, unordered_set<int>& visited) {
        visited.insert(src);
        int size = 1;
        for (auto nei : graph[src]) {
            if (!visited.count(nei)) {
                size += dfs(nei, visited);
            }
        }
        return size;
    }

    vector<long long> connected_components() {
        vector<long long> component_sizes;
        unordered_set<int> visited;
        for (int i = 0; i < v; i++) {
            if (!visited.count(i)) {
                int component_size = dfs(i, visited);
                component_sizes.push_back(component_size);
            }
        }
        return component_sizes;
    }

    long long countPairs(int n, vector<vector<int>>& edges) {
        v = n;
        graph.resize(v, list<int>());
        for (int i = 0; i < edges.size(); i++) {
            add_edge(edges[i][0], edges[i][1]);
        }

        vector<long long> component_sizes = connected_components();
        long long k=component_sizes.size();
        vector<long long>suff(k);
        suff[k-1]=component_sizes[k-1];
        for(long long i=k-2;i>0;i--){
            suff[i]=component_sizes[i]+suff[i+1];
        }
        long long ans=0;
        for(long long i=0;i<k-1;i++){
            ans+=(component_sizes[i]*suff[i+1]);
        }
        return ans;
    }
};

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