<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 {

private:
    int mark = 1;

public:
    void bridges(int node, vector<vector<int>>& ans,
                 unordered_map<int, list<int>>& adj, vector<int>& visited,
                 vector<int>& larg, vector<int>& small, int parent) {
        visited[node] = 1;
        small[node] = mark;
        larg[node] = mark;
        mark++;
        for (auto neighbour : adj[node]) {
            if (neighbour == parent) {
                continue;
            }
            if (visited[neighbour] == 0) {

                bridges(neighbour, ans, adj, visited, larg, small, node);

                small[node] = min(small[node], small[neighbour]);
                if (larg[node] < small[neighbour]) {

                    ans.push_back({neighbour, node});
                }
            } else {
                small[node] = min(small[node], small[neighbour]);
            }
        }
    }

public:
    vector<vector<int>> criticalConnections(int n,
                                            vector<vector<int>>& connections) {
        unordered_map<int, list<int>> adj;

        for (int i = 0; i < connections.size(); i++) {
            int u = connections[i][0];
            int v = connections[i][1];

            adj[u].push_back(v);
            adj[v].push_back(u);
        }

        vector<vector<int>> ans;
        vector<int> visited(n, 0);
        vector<int> larg(n);
        vector<int> small(n);

        bridges(0, ans, adj, visited, larg, small, -1);
        return ans;
    }
};
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