def find_path_with_capacity_dfs(graph: DirectedGraph, current_node, end_node,
visited, flows: Dict):
"""
Finds a path with available capacity from current node to end node
Returns none if no such paths exist
"""
visited.add(current_node)
for edge in graph.get_edges(current_node):
origin, destination = (edge.a,
edge.b) if edge.a == current_node else (edge.b,
edge.a)
if (edge.weight > flows[edge]
and edge.a == current_node) or (0 < flows[edge]
and edge.b == current_node):
if destination in visited:
continue
if destination == end_node:
return [edge]
result = find_path_with_capacity_dfs(graph, destination, end_node,
visited, flows)
if result:
return [edge] + result
visited.remove(current_node)
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
def find_path_with_capacity_dfs(graph: DirectedGraph, current_node, end_node, visited, flows: Dict):
"""
Finds a path with available capacity from current node to end node
Returns none if no such paths exist
"""
visited.add(current_node)
for edge in graph.get_edges(current_node):
origin, destination = (edge.a, edge.b) if edge.a == current_node else (edge.b, edge.a)
if (edge.weight > flows[edge] and edge.a == current_node) or (0 < flows[edge] and edge.b == current_node):
if destination in visited:
continue
if destination == end_node:
return [edge]
result = find_path_with_capacity_dfs(graph, destination, end_node, visited, flows)
if result:
return [edge] + result
visited.remove(current_node)
