def _find_augmenting_path (graph, capacities, flows, source, sink, path):
"""Helper method to find an augmenting path in the graph. An augmenting path is a path whose
flow can be increased (none of the edges in the path has a maximized flow). This is used in
the Ford-Fulkerson algorithm.
@param graph - A graph object.
@param capacities - A dictionary of tuples (source, target) representing edges, to their capacities
@param flows - A dictionary of tuples (source, target) representing edges, to their current flows
@param source - The source node.
@param sink - The sink node.
@param path - The current path (recursively builds it).
@return res - The augmenting path.
"""
if source == sink:
return path
for b in graph.adjNodes[source]:
residual = capacities[(source, b)] - flows[(source, b)]
if residual > 0 and (source, b) not in util.get_edge_list_from_path(path):
res = _find_augmenting_path(graph, capacities, flows, b, sink, path + [b])
if res != None:
return res
def test_multiNodePath(self):
path = ['a', 'b', 'c', 'd', 'e']
edgeList = [('a', 'b'), ('b', 'c'), ('c', 'd'), ('d', 'e')]
self.assertEqual(util.get_edge_list_from_path(path), edgeList)
def test_singleNodePath(self):
path = ['a']
self.assertEqual(util.get_edge_list_from_path(path), [])
