mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-24 12:10:16 +00:00
9316e7c014
* flake8 --max-line-length=88
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
84 lines
2.6 KiB
Python
84 lines
2.6 KiB
Python
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).
|
|
|
|
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.
|
|
|
|
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
|
|
connected component.
|
|
|
|
Complexity: strong_connect() is called at most once for each node and has a
|
|
complexity of O(|E|) as it is DFS.
|
|
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)
|
|
lowlink_of[v] = (
|
|
lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
|
|
)
|
|
elif on_stack[w]:
|
|
lowlink_of[v] = (
|
|
lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
|
|
)
|
|
|
|
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
|
|
|
|
|
|
if __name__ == "__main__":
|
|
# 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)
|