1192. Critical Connections in a Network

class Solution:
    def criticalConnections(self, n: int, connections: List[List[int]]) -> List[List[int]]:
        """tc O(V+E) sc O(V+E) 
        """
        g = collections.defaultdict(list)
        for u,v in connections:
            g[u].append(v)
            g[v].append(u)
        low = [-1] * n
        dfn = [-1] * n
        self.timestamp = 0 
        res = [] 
        def dfs(cur, parent):
            if dfn[cur] == -1:
                dfn[cur] = self.timestamp
                low[cur] = self.timestamp 
                self.timestamp += 1 
            
            for nei in g[cur]:
                if parent!= None and nei == parent:
                    continue
                elif dfn[nei] == -1:
                    dfs(nei, cur)
                    low[cur] = min(low[cur], low[nei])
                else:
                    low[cur] = min(low[cur], dfn[nei])
            # if low[cur] == dfn[cur] and cur != 0:
            #     res.append([cur,parent])
            
        dfs(0, None)
        res = [] 
        for u,v in connections:
            if dfn[u] < low[v] or dfn[v] < low[u]:
                res.append([u,v])
        return res