Bridges

int dfs_num[mx], dfs_cnt, dfs_low[mx], dfs_parent[mx], n;
vector < pair<int, int> > critical;
vector <int> graph[mx];

void bridges(int u);

void init(){
    memset(dfs_num, 0, sizeof dfs_num);
    dfs_cnt = 1;
    for(int i=1;i<=n;i++){
        if(dfs_num[i]==0){
            bridges(i);
        }
    }
}

void bridges(int u){
    dfs_low[u] = dfs_num[u] = dfs_cnt++;
    for(int i=0;i<graph[u].size();i++){
        if(dfs_num[graph[u][i]]==0){
            dfs_parent[graph[u][i]] = u;
            bridges(graph[u][i]);
            if(dfs_low[graph[u][i]]>dfs_num[u]){
                critical.push_back({min(u, graph[u][i]),max(u, graph[u][i])});
            }
            dfs_low[u] = min(dfs_low[u], dfs_low[graph[u][i]]);
        }
        else if(dfs_parent[u]!=graph[u][i]){
            dfs_low[u] = min(dfs_low[u], dfs_num[graph[u][i]]);
        }
    }
}