<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 clock = 0;

    void dfs(int node, vector<bool>& vis, vector<int>& start, vector<int>& end, vector<int>& lsb, vector<vector<int>>& adj, set<pair<int,int>>& s, int par)
    {
        if(vis[node])
            return;
        vis[node] = true;
        start[node] = clock++;
        for(auto nnode : adj[node])
        {
            if(nnode==par)
                continue;
            if(vis[nnode])
            {
                // found backedge 
                lsb[node] = min(lsb[node], start[nnode]);
                s.insert({min(node, nnode), max(node, nnode)});
            }
            else
            {
                dfs(nnode, vis, start, end, lsb, adj, s, node);
                lsb[node] = min(lsb[node], lsb[nnode]);
                if(lsb[nnode] <= start[node])
                    s.insert({min(node, nnode), max(node, nnode)});
            }
        }
        end[node] = clock++;
    }

    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) 
    {
        vector<vector<int>> adj(n);
        for(auto vec : connections)
        {
            adj[vec[0]].push_back(vec[1]);
            adj[vec[1]].push_back(vec[0]);
        }

        vector<int> start(n, -1), end(n, -1), lowest_succ_bedge(n, INT_MAX), par(n, -1);
        vector<bool> vis(n, false);

        set<pair<int,int>> s;

        dfs(0, vis, start, end, lowest_succ_bedge, adj, s, -1);


        // for(auto i : start)
        //     cout << i << " ";
        // cout << "\n";
        // cout << "-----------------------\n";

        // for(auto i : end)
        //     cout << i << " ";
        // cout << "\n";

        // cout << "-----------------------\n";
        // for(auto i : lowest_succ_bedge)
        //     cout << i << " ";
        // cout << "\n";
        // cout << "-----------------------\n";

        vector<vector<int>> ans;
        for(auto vec : connections)
        {
            if(s.find({min(vec[0], vec[1]), max(vec[0], vec[1])})==s.end())
                ans.push_back(vec);
        }
        return ans;
    }
};
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