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 TestGraph(unittest.TestCase):
def setUp(self):
self.undirected = UndirectedGraph()
self.undirected.add_edge(1, 2, 2)
self.undirected.add_edge(1, 3, 6)
self.undirected.add_edge(2, 3, 3)
self.undirected.add_edge(2, 4, 1)
self.undirected.add_edge(3, 4, 1)
self.undirected.add_edge(3, 5, 4)
self.undirected.add_edge(4, 5, 6)
self.directed = DirectedGraph()
self.directed.add_edge(1, 2, 2)
self.directed.add_edge(1, 3, 6)
self.directed.add_edge(2, 3, 3)
self.directed.add_edge(2, 4, 1)
self.directed.add_edge(3, 4, 1)
self.directed.add_edge(3, 5, 4)
self.directed.add_edge(4, 5, 6)
def test_get_edges(self):
assert self.undirected.get_all_edges() == self.directed.get_all_edges()
assert self.undirected.get_vertices() == self.directed.get_vertices()
def test_directed_graph(self):
assert len(self.directed.get_successive_vertices(4)) == 1
assert len(self.undirected.get_successive_vertices(4)) == 3
assert self.undirected.edge_exists(4, 3)
assert not self.directed.edge_exists(4, 3)
self.directed.delete_edge(4, 3)
self.undirected.delete_edge(4, 3)
assert len(self.directed.get_all_edges()) == len(self.undirected.get_all_edges()) + 1
def test_undirected_graph(self):
g = UndirectedGraph()
class TestGraph(unittest.TestCase):
def setUp(self):
self.undirected = UndirectedGraph()
self.undirected.add_edge(1, 2, 2)
self.undirected.add_edge(1, 3, 6)
self.undirected.add_edge(2, 3, 3)
self.undirected.add_edge(2, 4, 1)
self.undirected.add_edge(3, 4, 1)
self.undirected.add_edge(3, 5, 4)
self.undirected.add_edge(4, 5, 6)
self.directed = DirectedGraph()
self.directed.add_edge(1, 2, 2)
self.directed.add_edge(1, 3, 6)
self.directed.add_edge(2, 3, 3)
self.directed.add_edge(2, 4, 1)
self.directed.add_edge(3, 4, 1)
self.directed.add_edge(3, 5, 4)
self.directed.add_edge(4, 5, 6)
def test_get_edges(self):
assert self.undirected.get_all_edges() == self.directed.get_all_edges()
assert self.undirected.get_vertices() == self.directed.get_vertices()
def test_directed_graph(self):
assert len(self.directed.get_successive_vertices(4)) == 1
assert len(self.undirected.get_successive_vertices(4)) == 3
assert self.undirected.edge_exists(4, 3)
assert not self.directed.edge_exists(4, 3)
self.directed.delete_edge(4, 3)
self.undirected.delete_edge(4, 3)
assert len(self.directed.get_all_edges()) == len(
self.undirected.get_all_edges()) + 1
def test_undirected_graph(self):
g = UndirectedGraph()
def ford_fulkerson(graph: DirectedGraph, source,
sink) -> Tuple[Dict[Any, int], int]:
"""
In optimization theory, maximum flow problems involve finding a feasible flow through a
single-source, single-sink flow network that is maximum.
:param graph: Directed graph with the capacity of each edge as the weight
:param source: Source node (from which the flow originates)
:param sink: Sink node (where the flow leaves the system
"""
# Store the current flows in a dict
flows = {edge: 0 for edge in graph.get_all_edges()}
max_flow = 0
while True:
# Find a path with capacity from source to sink and stop is none is available
next_path = find_path_with_capacity_dfs(graph, source, sink, set(),
flows)
if next_path is None:
break
# Calculate the max flow for the current path
current_max_flow = sys.maxsize
start = source
for edge in next_path:
if edge.a == start:
current_max_flow = min(current_max_flow,
edge.weight - flows[edge])
start = edge.b
else:
current_max_flow = min(current_max_flow, flows[edge])
start = edge.a
# Add this flow to the found path
start = source
for edge in next_path:
if edge.a == start:
flows[edge] += current_max_flow
start = edge.b
else:
flows[edge] -= current_max_flow
start = edge.a
max_flow += current_max_flow
# Return the optimal flows per edge and the total max flow
return flows, max_flow
def ford_fulkerson(graph: DirectedGraph, source, sink) -> Tuple[Dict[Any, int], int]:
"""
In optimization theory, maximum flow problems involve finding a feasible flow through a
single-source, single-sink flow network that is maximum.
:param graph: Directed graph with the capacity of each edge as the weight
:param source: Source node (from which the flow originates)
:param sink: Sink node (where the flow leaves the system
"""
# Store the current flows in a dict
flows = {edge: 0 for edge in graph.get_all_edges()}
max_flow = 0
while True:
# Find a path with capacity from source to sink and stop is none is available
next_path = find_path_with_capacity_dfs(graph, source, sink, set(), flows)
if next_path is None:
break
# Calculate the max flow for the current path
current_max_flow = sys.maxsize
start = source
for edge in next_path:
if edge.a == start:
current_max_flow = min(current_max_flow, edge.weight - flows[edge])
start = edge.b
else:
current_max_flow = min(current_max_flow, flows[edge])
start = edge.a
# Add this flow to the found path
start = source
for edge in next_path:
if edge.a == start:
flows[edge] += current_max_flow
start = edge.b
else:
flows[edge] -= current_max_flow
start = edge.a
max_flow += current_max_flow
# Return the optimal flows per edge and the total max flow
return flows, max_flow
