Python/graphs/articulation_points.py

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# Finding Articulation Points in Undirected Graph
def compute_ap(graph):
n = len(graph)
out_edge_count = 0
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low = [0] * n
visited = [False] * n
is_art = [False] * n
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def dfs(root, at, parent, out_edge_count):
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if parent == root:
out_edge_count += 1
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visited[at] = True
low[at] = at
for to in graph[at]:
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if to == parent:
pass
elif not visited[to]:
out_edge_count = dfs(root, to, at, out_edge_count)
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low[at] = min(low[at], low[to])
# AP found via bridge
if at < low[to]:
is_art[at] = True
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# AP found via cycle
if at == low[to]:
is_art[at] = True
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else:
low[at] = min(low[at], to)
return out_edge_count
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for i in range(n):
if not visited[i]:
out_edge_count = 0
out_edge_count = dfs(i, i, -1, out_edge_count)
is_art[i] = out_edge_count > 1
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for x in range(len(is_art)):
if is_art[x] is True:
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print(x)
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# Adjacency list of graph
graph = {
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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],
}
compute_ap(graph)