# Finding Articulation Points in Undirected Graph
def computeAP(l):
n = len(l)
outEdgeCount = 0
low = [0] * n
visited = [False] * n
isArt = [False] * n
def dfs(root, at, parent, outEdgeCount):
if parent == root:
outEdgeCount += 1
visited[at] = True
low[at] = at
for to in l[at]:
if to == parent:
pass
elif not visited[to]:
outEdgeCount = dfs(root, to, at, outEdgeCount)
low[at] = min(low[at], low[to])
# AP found via bridge
if at < low[to]:
isArt[at] = True
# AP found via cycle
if at == low[to]:
isArt[at] = True
else:
low[at] = min(low[at], to)
return outEdgeCount
for i in range(n):
if not visited[i]:
outEdgeCount = 0
outEdgeCount = dfs(i, i, -1, outEdgeCount)
isArt[i] = (outEdgeCount > 1)
for x in range(len(isArt)):
if isArt[x] == True:
print(x)
# Adjacency list of graph
l = {0:[1,2], 1:[0,2], 2:[0,1,3,5], 3:[2,4], 4:[3], 5:[2,6,8], 6:[5,7], 7:[6,8], 8:[5,7]}
computeAP(l)