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Tarjan's Strongly Connected Components Algorithm
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# Scott Enderle | |
# Originally posted at http://stackoverflow.com/a/6575693/577088 | |
from itertools import chain | |
from collections import defaultdict | |
class Graph(object): | |
def __init__(self, edges, vertices=()): | |
edges = list(list(x) for x in edges) | |
self.edges = edges | |
self.vertices = set(chain(*edges)).union(vertices) | |
self.tails = defaultdict(list) | |
for head, tail in self.edges: | |
self.tails[head].append(tail) | |
@classmethod | |
def from_dict(cls, edge_dict): | |
return cls((k, v) for k, vs in edge_dict.iteritems() for v in vs) | |
class _StrongCC(object): | |
def strong_connect(self, head): | |
lowlink, count, stack = self.lowlink, self.count, self.stack | |
lowlink[head] = count[head] = self.counter = self.counter + 1 | |
stack.append(head) | |
for tail in self.graph.tails[head]: | |
if tail not in count: | |
self.strong_connect(tail) | |
lowlink[head] = min(lowlink[head], lowlink[tail]) | |
elif count[tail] < count[head]: | |
if tail in self.stack: | |
lowlink[head] = min(lowlink[head], count[tail]) | |
if lowlink[head] == count[head]: | |
component = [] | |
while stack and count[stack[-1]] >= count[head]: | |
component.append(stack.pop()) | |
self.connected_components.append(component) | |
def __call__(self, graph): | |
self.graph = graph | |
self.counter = 0 | |
self.count = dict() | |
self.lowlink = dict() | |
self.stack = [] | |
self.connected_components = [] | |
for v in self.graph.vertices: | |
if v not in self.count: | |
self.strong_connect(v) | |
return self.connected_components | |
strongly_connected_components = _StrongCC() | |
if __name__ == '__main__': | |
edges = [('A', 'B'), ('B', 'C'), ('C', 'D'), ('D', 'E'), | |
('E', 'A'), ('A', 'E'), ('C', 'A'), ('C', 'E'), | |
('D', 'F'), ('F', 'B'), ('E', 'F')] | |
print strongly_connected_components(Graph(edges)) | |
edge_dict = {'a':['b', 'c', 'd'], | |
'b':['c', 'a'], | |
'c':['d', 'e'], | |
'd':['e'], | |
'e':['c']} | |
print strongly_connected_components(Graph.from_dict(edge_dict)) |
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