def topological_sort(graph: DirectedGraph) -> List:
"""
Called Kahns algorithm
Sorts the vertices of a graph in a topological order
or raises an exception when the graph is cyclical
:param graph: The graph to be sorted toplogically
"""
graph = copy.deepcopy(graph)
sorted_nodes = []
nodes = Queue()
# Add the nodes without incoming edges to the starting nodes
for vertex in graph.get_vertices():
if not graph.has_incoming_edge(vertex):
nodes.enqueue(vertex)
# Keep removing nodes and edges while nodes with no incoming edges exist
while not nodes.is_empty():
node = nodes.dequeue()
sorted_nodes.append(node)
for edge in graph.get_edges(node)[:]:
graph.delete_edge(edge.a, edge.b)
if not graph.has_incoming_edge(edge.b):
nodes.enqueue(edge.b)
if len(list(graph.get_all_edges())):
raise RuntimeError('Graph is cyclical')
return sorted_nodes
class TestQueue(unittest.TestCase):
def setUp(self):
self.queue = Queue()
self.queue.enqueue(1)
self.queue.enqueue(2)
self.queue.enqueue(3)
self.empty_queue = Queue()
def test_dequeue(self):
assert self.queue.dequeue() == 1
assert self.queue.dequeue() == 2
assert self.queue.dequeue() == 3
assert_raises(IndexError, self.queue.dequeue)
def test_enqueue(self):
self.queue.enqueue(7)
assert len(self.queue) == 4
def test_is_empty(self):
assert self.empty_queue.is_empty()
def test_peek(self):
assert self.queue.peek() == self.queue.peek()
assert self.queue.peek() == 1
assert len(self.queue) == 3
assert_raises(IndexError, self.empty_queue.peek)
def breadth_first_traversal(self) -> Iterator['BinaryNode']:
"""
Returns an iterator which traverses this subtree breadth first
"""
q = Queue([self])
while not q.is_empty():
node = q.dequeue()
yield node
if node.lnode: q.enqueue(node.lnode)
if node.rnode: q.enqueue(node.rnode)
def contains_cycle(graph: UndirectedGraph) -> bool:
"""
Simple breadth first cycle detection for Undirected graphs
"""
graph = copy.deepcopy(graph) # type: Graph
visited_nodes = set()
queue = Queue()
queue.enqueue(graph.get_vertices()[0])
while not queue.is_empty():
vertex = queue.dequeue()
for neighbour in graph.get_successive_vertices(vertex):
if neighbour in visited_nodes:
return True
visited_nodes.add(neighbour)
queue.enqueue(neighbour)
graph.delete_edge(vertex, neighbour)
return False
def contains_cycle(graph: UndirectedGraph) -> bool:
"""
Simple breadth first cycle detection for Undirected graphs
"""
graph = copy.deepcopy(graph) # type: Graph
visited_nodes = set()
queue = Queue()
queue.enqueue(graph.get_vertices()[0])
while not queue.is_empty():
vertex = queue.dequeue()
for neighbour in graph.get_successive_vertices(vertex):
if neighbour in visited_nodes:
return True
visited_nodes.add(neighbour)
queue.enqueue(neighbour)
graph.delete_edge(vertex, neighbour)
return False
