<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 idx = 0;

public:
    void tarjan(vector<vector<int>>& nbrs, vector<int>& ids, vector<int>& low, vector<int>& inStack, stack<int>& st, vector<vector<int>>& ans, int cur, int pre) {
        ids[cur] = low[cur] = idx++;
        st.push(cur);
        inStack[cur] = 1;
        for(auto nbr: nbrs[cur]) {
            if(nbr == pre) continue;
            if(ids[nbr] == -1) {
                tarjan(nbrs, ids, low, inStack, st, ans, nbr, cur);
            }
            if(low[nbr] < low[cur]) {
                low[cur] = low[nbr];
            }
            if(low[nbr] > ids[cur]) {
                ans.push_back({cur, nbr});
            }
        }
        if(ids[cur] == low[cur]) {
            int tmp;
            for(tmp=st.top();tmp!=cur;tmp=st.top()) {
                low[tmp] = low[cur];
                inStack[tmp] = 0;
                st.pop();
            }
            st.pop();
        }
    }

    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        vector<vector<int>> nbrs(n);
        vector<int>low(n, -1);
        vector<int>ids(n, -1);
        vector<int>inStack(n, 0);
        stack<int>st;
        vector<vector<int>> ans;
        for(auto conn: connections) {
            nbrs[conn[0]].push_back(conn[1]);
            nbrs[conn[1]].push_back(conn[0]);
        }
        for(int i=0;i<n;++i) {
            if(ids[i] == -1) {
                tarjan(nbrs, ids, low, inStack, st, ans, i, -1);
            }
        }
        // for(int i=0;i<n;++i) {
        //     cout<<i<<" "<<low[i]<<endl;
        // }
        return ans;

    }
};
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