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Python

4 weeks ago
# Algorithm from MIT OpenCourseWare (seems correct)
# https://courses.csail.mit.edu/6.006/fall11/rec/rec14.pdf
class DFSResult:
def __init__(self):
self.parent = {}
self.start_time = {}
self.finish_time = {}
self.edges = {} # Edge classification for directed graph.
self.order = []
self.t = 0
def dfs(g):
results = DFSResult()
for vertex in g.vertices():
if vertex not in results.parent:
dfs_visit(g, vertex, results)
return results
def dfs_visit(g, v, results, parent=None):
results.parent[v] = parent
results.t += 1
results.start_time[v] = results.t
if parent is not None:
results.edges[(parent, v)] = 'tree'
for n in g.neighbors(v):
if n not in results.parent: # n is not visited
dfs_visit(g, n, results, v)
elif n not in results.finish_time:
results.edges[(v, n)] = 'back'
elif results.start_time[v] < results.start_time[n]:
results.edges[(v, n)] = 'forward'
else:
results.edges[(v, n)] = 'cross'
results.t += 1
results.finish_time[v] = results.t
results.order.append(v)
def classify_iter(g):
edges = {}
visited = set()
t = 0
start_time = {}
finish_time = {}
for u in g.vertices():
if u in visited:
continue
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continuations = [('node:start', u, None)]
while len(continuations) > 0:
state, u, more = continuations.pop()
if state == 'node:start':
continuations.append(('node:end', u, None))
parent = more
visited.add(u)
t += 1
start_time[u] = t
if parent is not None:
edges[(parent, u)] = 'tree'
continuations.append(('node:neighbors', u, 0))
elif state == 'node:neighbors':
i = more
neighbors = g.neighbors(u)[i:]
for i in range(len(neighbors)):
v = neighbors[i]
if v not in visited:
continuations.append(('node:neighbors', u, i + 1))
continuations.append(('node:start', v, u))
break
elif v not in finish_time:
edges[(u, v)] = 'back'
elif start_time[u] < start_time[v]:
edges[(u, v)] = 'forward'
else:
edges[(u, v)] = 'cross'
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elif state == 'node:end':
t += 1
finish_time[u] = t
return edges
# Graph structure
class Graph:
def __init__(self):
self.adjacency_list = {}
def add_edge(self, u, v):
if u not in self.adjacency_list:
self.adjacency_list[u] = []
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self.adjacency_list[u].append(v)
def vertices(self):
return self.adjacency_list.keys()
def neighbors(self, v):
return self.adjacency_list.get(v, [])
# Example usage:
g = Graph()
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# g.add_edge(0, 1)
# g.add_edge(1, 2)
# g.add_edge(2, 3)
# g.add_edge(3, 0)
# g.add_edge(3, 4)
# g.add_edge(4, 5)
# g.add_edge(5, 0)
# g.add_edge(4, 2)
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# g.add_edge(0, 1)
# g.add_edge(1, 2)
# g.add_edge(0, 2)
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g.add_edge("u", "v")
g.add_edge("u", "x")
g.add_edge("v", "y")
g.add_edge("y", "x")
g.add_edge("x", "v")
g.add_edge("w", "y")
g.add_edge("w", "z")
# Running DFS
# results = dfs(g)
# print("Parent Map:", results.parent)
# print("Start Times:", results.start_time)
# print("Finish Times:", results.finish_time)
# print("Edge Classifications:", results.edges)
# print("DFS Order:", results.order)
# Running Iterative DFS
edges = classify_iter(g)
print("Edge Classifications:", edges)