<p>There are <code>n</code> servers numbered from <code>0</code> to <code>n - 1</code> connected by undirected server-to-server <code>connections</code> forming a network where <code>connections[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> represents a connection between servers <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>. Any server can reach other servers directly or indirectly through the network.</p>

<p>A <em>critical connection</em> is a connection that, if removed, will make some servers unable to reach some other server.</p>

<p>Return all critical connections in the network in any order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/09/03/1537_ex1_2.png" style="width: 198px; height: 248px;" />
<pre>
<strong>Input:</strong> n = 4, connections = [[0,1],[1,2],[2,0],[1,3]]
<strong>Output:</strong> [[1,3]]
<strong>Explanation:</strong> [[3,1]] is also accepted.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2, connections = [[0,1]]
<strong>Output:</strong> [[0,1]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>n - 1 &lt;= connections.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>There are no repeated connections.</li>
</ul>

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using ll = long long;
using ll = long long;
using ll = long long;

using ll = long long;

class Solution
{
public:
    vector<vector<int>> criticalConnections(int n, vector<vector<int>> &connections)
    {
        vector<int> tin(n);
        vector<int> low(n);
        vector<bool> vis(n);
        vector<vector<int>> a(n);

        for (auto &c : connections)
        {
            a[c[0]].push_back(c[1]);
            a[c[1]].push_back(c[0]);
        }

        vector<vector<int>> ans;

        for (int i = 0; i < n; i++)
        {
            if (vis[i] == false)
            {
                int time = 0;
                dfs(tin, low, vis, i, a, n, ans, time, -1);
            }
        }

        return ans;
    }

private:
    void processCriticalEdge(int &to, int &v, vector<vector<int>> &ans)
    {
        ans.push_back({v,to});
    }

    void dfs(vector<int> &tin, vector<int> &low, vector<bool> &vis, int &v, vector<vector<int>> &a, int &n, vector<vector<int>> &ans, int &time, int p = -1)
    {
        vis[v] = true;

        tin[v] = low[v] = time++;

        bool parent_visited = false;

        for (auto &to : a[v])
        {
            if (parent_visited == false && p == to)
            {
                parent_visited = true;
                continue;
            }

            if (vis[to])
            {
                low[v] = min(tin[to], low[v]);
            }
            else
            {
                dfs(tin, low, vis, to, a, n, ans, time, v);
                low[v] = min(low[to], low[v]);

                if (low[to] > tin[v])
                {
                    processCriticalEdge(to, v, ans);
                }
            }
        }
    }
};
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