<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:
    int timer;
    Solution()
    {
        timer = 0;
    }
    void DFS(int node, int parent, vector<int> adj[], int discoveryTime[], int lowestDiscoveryTime[], bool visited[], vector<vector<int>> &bridges)
    {
        visited[node] = true;
        timer++;
        discoveryTime[node] = lowestDiscoveryTime[node] = timer;
        for(auto neighbour : adj[node])
        {
            if(neighbour == parent)
                continue;
            if(!visited[neighbour])
            {
                DFS(neighbour, node, adj, discoveryTime, lowestDiscoveryTime, visited, bridges);
                lowestDiscoveryTime[node] = min(lowestDiscoveryTime[node], lowestDiscoveryTime[neighbour]);
                if(lowestDiscoveryTime[neighbour] > discoveryTime[node])
                    bridges.push_back({node, neighbour});
            }
            else
            {  
                lowestDiscoveryTime[node] = min(lowestDiscoveryTime[node], lowestDiscoveryTime[neighbour]);
            }
        }
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& edges) {
        vector<int> adj[n];
        for(int i=0 ; i<edges.size() ; i++)
        {
            adj[edges[i][0]].push_back(edges[i][1]);
            adj[edges[i][1]].push_back(edges[i][0]);
        }
        int discoveryTime[n];
        int lowestDiscoveryTime[n];
        bool visited[n];
        for(int i=0 ; i<n ; i++) visited[i] = false;
        vector<vector<int>> bridges;
        DFS(0, -1, adj, discoveryTime, lowestDiscoveryTime, visited, bridges);
        return bridges;
    }
};
158961