This is a simple problem; direct use of finding Bridge algorithm. Given a graph, you have to find all the bridge.
#include <bits/stdc++.h>
using namespace std;
#define mx 1000005
vector<int>grp[mx];
int low[mx], dsc[mx], t;
bool vst[mx];
vector< pair<int,int> >res;
void Bridge(int u,int v){
// cout<<u<<"-->"<<v<<" "<<"is a bridge"<<endl;
res.push_back({min(u,v),max(u,v)});
}
void dfs(int sr,int p = -1){
vst[sr] = true;
t++; low[sr] = dsc[sr] = t;
for(int i=0; i<grp[sr].size(); i++){
int v = grp[sr][i];
if(v == p) continue;
if(vst[v] == true){
low[sr] = min(low[sr], dsc[v]);
}else{
dfs(v, sr);
low[sr] = min(low[sr], low[v]);
if(low[v] > dsc[sr]) Bridge(sr,v);
}
}
}
int main() {
int n;
while(scanf("%d",&n) != EOF){
for(int i=0; i<n; i++){
int u, a; scanf("%d (%d) ",&u,&a);
while(a--){
int v; cin>>v;
grp[u].push_back(v);
grp[v].push_back(u);
}
}
for(int i=0; i<n; i++){
if(vst[i] == false) dfs(i,-1);
}
sort(res.begin(), res.end());
cout<<res.size()<<" critical links"<<endl;
for(int i=0; i<res.size(); i++){
cout<<res[i].first<<" - "<<res[i].second<<endl;
}
cout<<endl;
for(int i=0; i<=n; i++){
grp[i].clear(); low[i] = 0; dsc[i] = 0; vst[i] = false;
}res.clear();
}
}