Articulation points tarjan algorithm

'''
The idea is to use DFS (Depth First Search). In DFS, we follow vertices in tree form called DFS tree. In DFS tree, a vertex u is parent of another vertex v, if v is discovered by u (obviously v is an adjacent of u in graph).
In DFS tree, a vertex u is articulation point if one of the following two conditions is true.
1.u is root of DFS tree and it has at least two children.
2.u is not root of DFS tree and it has a child v such that no vertex in subtree rooted with v has a back edge to one of the ancestors (in DFS tree) of u.
'''
class Solution:
    #Function to return Breadth First Traversal of given graph.
    def articulationPoints(self, n, adj):
        #ap:articulation point
        parent,disc,low,time,ap,vis=[-1]*n,[1e9]*n,[1e9]*n,0,[False]*n,[False]*n
        def dfs(u):
            nonlocal time
            vis[u]=True
            disc[u]=low[u]=time
            time+=1
            children=0
            for v in adj[u]:
                if vis[v]==False:
                    children+=1
                    parent[v]=u
                    dfs(v)
                    low[u]=min(low[v],low[u])
                    #condition for root of dfs tree
                    if parent[u]==-1 and children>=2:
                        ap[u]=True
                    #condition for non root disc[u]<=low[v]----->VVIMP
                    elif parent[u]!=-1 and disc[u]<=low[v]:
                        ap[u]=True
                #already vertices which are not main parent. We need to update low time there
                #low[u]=min(disc[v],low[u]) -------->vvvimp
                elif v!=parent[u]:
                    low[u]=min(disc[v],low[u])
        for i in range(n):
            if vis[i]==False:
                dfs(i)
        t=[i for i,j in enumerate(ap) if j==True]
        return t if t else [-1]

#alternatively we can remove vis array and use disc array as vis array combiningly

import sys
sys.setrecursionlimit(10**6)

class Solution:

    #Function to return Breadth First Traversal of given graph.
    def articulationPoints(self, n, adj):
        parent,disc,low,time,ap=[-1]*n,[-1]*n,[1e9]*n,0,[False]*n
        def dfs(u):
            nonlocal time
            disc[u]=low[u]=time
            time+=1
            children=0
            for v in adj[u]:
                if disc[v]==-1:
                    children+=1
                    parent[v]=u
                    dfs(v)
                    low[u]=min(low[v],low[u])
                    if parent[u]==-1 and children>=2:
                        ap[u]=True
                    elif parent[u]!=-1 and disc[u]<=low[v]:
                        ap[u]=True
                elif v!=parent[u]:
                    low[u]=min(disc[v],low[u])
        for i in range(n):
            if disc[i]==-1:
                dfs(i)
        t=[i for i,j in enumerate(ap) if j==True]
        return t if t else [-1]