<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>

class Solution {
public:
        void dfs(vector<vector<int>> &graph, vector<int> &visited, int node, int parent, vector<int>& disc,       vector<int>& low, stack<int>& s, vector<int>& instack, int& time, vector<vector<int>>& bridges)
        {
            visited[node] = 1;
            s.push(node);
            disc[node] = ++time;
            low[node] = disc[node];
            instack[node] = 1;
            for (int i = 0; i < graph[node].size(); i++)
            {
                if (visited[graph[node][i]] && instack[graph[node][i]] && graph[node][i] != parent)
                {
                    low[node] = min(low[node], disc[graph[node][i]]);
                    continue;
                }
                if(visited[graph[node][i]])
                    continue;
                dfs(graph, visited, graph[node][i], node, disc,  low, s, instack, time,bridges);
                low[node] = min(low[node], low[graph[node][i]]);
                if(low[graph[node][i]] > disc[node])
                    bridges.push_back({node, graph[node][i]});
            }

        }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        vector<int> visited(n, 0);
        vector<int> disc(n, -1);
        vector<int> low(n , INT_MAX);
        vector<int> instack(n , 0);
        vector<vector<int>> bridges;
        stack<int> s;
        int time = 0;
        vector<vector<int>> graph(n + 1);
        int m = connections.size();
        for (int i = 0; i < m; i++)
        {
            
            graph[connections[i][0]].push_back(connections[i][1]);
            graph[connections[i][1]].push_back(connections[i][0]);
        }
        for(int i = 0 ; i < n ; i++)
        {
            if(visited[i])
                continue;
            dfs(graph, visited, i, i, disc, low, s, instack, time, bridges);
        }
        return bridges;
    }
};
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