Python/graphs/tarjans_scc.py

84 lines
2.6 KiB
Python
Raw Normal View History

2018-10-19 12:48:28 +00:00
from collections import deque
def tarjan(g):
"""
Tarjan's algo for finding strongly connected components in a directed graph
Uses two main attributes of each node to track reachability, the index of that node
within a component(index), and the lowest index reachable from that node(lowlink).
2018-10-19 12:48:28 +00:00
We then perform a dfs of the each component making sure to update these parameters
for each node and saving the nodes we visit on the way.
2018-10-19 12:48:28 +00:00
If ever we find that the lowest reachable node from a current node is equal to the
index of the current node then it must be the root of a strongly connected
component and so we save it and it's equireachable vertices as a strongly
2018-10-19 12:48:28 +00:00
connected component.
Complexity: strong_connect() is called at most once for each node and has a
complexity of O(|E|) as it is DFS.
2018-10-19 12:48:28 +00:00
Therefore this has complexity O(|V| + |E|) for a graph G = (V, E)
"""
n = len(g)
stack = deque()
on_stack = [False for _ in range(n)]
index_of = [-1 for _ in range(n)]
lowlink_of = index_of[:]
def strong_connect(v, index, components):
index_of[v] = index # the number when this node is seen
lowlink_of[v] = index # lowest rank node reachable from here
index += 1
stack.append(v)
on_stack[v] = True
for w in g[v]:
if index_of[w] == -1:
index = strong_connect(w, index, components)
2019-10-05 05:14:13 +00:00
lowlink_of[v] = (
lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
)
2018-10-19 12:48:28 +00:00
elif on_stack[w]:
2019-10-05 05:14:13 +00:00
lowlink_of[v] = (
lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
)
2018-10-19 12:48:28 +00:00
if lowlink_of[v] == index_of[v]:
component = []
w = stack.pop()
on_stack[w] = False
component.append(w)
while w != v:
w = stack.pop()
on_stack[w] = False
component.append(w)
components.append(component)
return index
components = []
for v in range(n):
if index_of[v] == -1:
strong_connect(v, 0, components)
return components
def create_graph(n, edges):
g = [[] for _ in range(n)]
for u, v in edges:
g[u].append(v)
return g
2019-10-05 05:14:13 +00:00
if __name__ == "__main__":
2018-10-19 12:48:28 +00:00
# Test
n_vertices = 7
source = [0, 0, 1, 2, 3, 3, 4, 4, 6]
target = [1, 3, 2, 0, 1, 4, 5, 6, 5]
edges = [(u, v) for u, v in zip(source, target)]
g = create_graph(n_vertices, edges)
assert [[5], [6], [4], [3, 2, 1, 0]] == tarjan(g)