I'm trying to implement the depth-first search (DFS) algorithm for directed graphs as described in Cormen et al., Introduction to Algorithms (3rd ed.). Here is my implementation so far:
import pytest
from collections import OrderedDict
import copy
class Node(object):
def __init__(self, color='white', parent=None, d=None, f=None):
self.color = color
self.parent = parent
self.d = d # Discovery time
self.f = f # Finishing time
class Graph(object):
def __init__(self, edges, node_indices=None):
self.edges = edges
self.nodes = self.initialize_nodes(node_indices )
self.adj = self.initialize_adjacency_list()
def initialize_nodes(self, node_indices=None):
if node_indices is None:
node_indices = sorted(list(set(node for edge in self.edges for node in edge)))
return OrderedDict([(node_index, Node()) for node_index in node_indices])
def initialize_adjacency_list(self):
A = {node: [] for node in self.nodes}
for edge in self.edges:
u, v = edge
A[u].append(v)
return A
def dfs(self):
self.time = 0
for u, node in self.nodes.items():
if node.color == 'white':
self.dfs_visit(u)
def dfs_visit(self, u):
self.time += 1
self.nodes[u].d = self.time
self.nodes[u].color = 'gray'
for v in self.adj[u]:
if self.nodes[v].color == 'white':
self.nodes[v].parent = u
self.dfs_visit(v)
self.nodes[u].color = 'black'
self.time += 1
self.nodes[u].f = self.time
@staticmethod
def transpose(edges):
return [(v,u) for (u,v) in edges]
def strongly_connected_components(self):
self.dfs()
finishing_times = {u: node.f for u, node in self.nodes.items()}
self.__init__(self.transpose(self.edges))
node_indices = sorted(finishing_times, key=finishing_times.get, reverse=True)
self.nodes = self.initialize_nodes(node_indices)
self.dfs()
return self.trees()
def trees(self):
_trees = []
nodes = copy.deepcopy(self.nodes)
while nodes:
for u, node in nodes.items():
if node.parent is None:
_trees.append([u])
nodes.pop(u)
else:
for tree in _trees:
if node.parent in tree:
tree.append(u)
nodes.pop(u)
return _trees
To test that it works, I've taken an example from Figure 22.9 of the book:
After renaming the nodes a to h 1 to 8, respectively, I ran the following test:
def test_strongly_connected_components():
edges = [(1,2), (5,1), (2,5), (5,6), (2,6), (6,7), (7,6), (2,3), (3,7), (3,4), (4,3), (4,8), (7,8), (8,8)]
graph = Graph(edges)
assert graph.strongly_connected_components() == [[1, 5, 2], [3, 4], [6, 7], [8]]
if __name__ == "__main__":
pytest.main([__file__+"::test_strongly_connected_components", "-s"])
This test passes, confirming the gray-shaded SCCs in the figure.
For the 'real' exercise, however, I need to use an input file, SCC.txt, which contains 875,714 lines representing edges (as a head-tail pair of integers), and output the size of the five largest SCCs. To this end I tried the following test:
@pytest.fixture
def edges():
with open('SCC.txt') as f:
return [tuple(map(int, line.split())) for line in f.read().splitlines()]
def test_SCC_on_full_graph(edges):
graph = Graph(edges)
SCCs = graph.strongly_connected_components()
print([map(len, SCCs)].sort(reverse=True)) # Read off the size of the largest SCCs
if __name__ == "__main__":
pytest.main([__file__+"::test_SCC_on_full_graph", "-s"])
However, I run into a RuntimeError: maximum recursion depth exceeded in cmp:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
self = <scc.Graph object at 0x103253690>, u = 209099
def dfs_visit(self, u):
self.time += 1
self.nodes[u].d = self.time
self.nodes[u].color = 'gray'
for v in self.adj[u]:
> if self.nodes[v].color == 'white':
E RuntimeError: maximum recursion depth exceeded in cmp
scc.py:53: RuntimeError
========================== 1 failed in 21.79 seconds ===========================
I've read about increasing sys.setrecursionlimit, but this doesn't seem to be a recommended practice. Other than than I'm not sure how I could improve the code as it fairly literally implements the pseudocode given in the book. Any ideas on how I can overcome this error?
