def run(self):
"""Executable pseudocode."""
size = self.graph.v()
# Create flow network.
network = self.graph.__class__(size + 2, directed=True)
self.source = size
self.sink = size + 1
network.add_node(self.source)
network.add_node(self.sink)
for node in self.graph.iternodes(): # O(V) time
network.add_node(node)
for node in self.v1: # edges from source to V1
network.add_edge(Edge(self.source, node))
for edge in self.graph.iteredges(): # edges from V1 to V2
if edge.source in self.v1: # weights are 1
network.add_edge(Edge(edge.source, edge.target))
else:
network.add_edge(Edge(edge.target, edge.source))
for node in self.v2: # edges from V2 to sink
network.add_edge(Edge(node, self.sink))
algorithm = FordFulkersonSparse(network)
algorithm.run(self.source, self.sink) # O(V*E) time
for source in self.v1:
for target in self.v2:
if algorithm.flow[source].get(target, 0) == 1:
self.mate[source] = target
self.mate[target] = source
self.cardinality = algorithm.max_flow
def test_ford_fulkerson_sparse(self):
algorithm = FordFulkersonSparse(self.G)
algorithm.run(0, 3)
expected_max_flow = 20
expected_flow = {
0: {
1: 10,
2: 10
},
1: {
0: -10,
2: 0,
3: 10
},
2: {
0: -10,
1: 0,
3: 10
},
3: {
1: -10,
2: -10
}
}
self.assertEqual(algorithm.max_flow, expected_max_flow)
self.assertEqual(algorithm.flow, expected_flow)
def run(self):
"""Executable pseudocode."""
size = self.graph.v()
# Create flow network.
network = self.graph.__class__(size + 2, directed=True)
self.source = size
self.sink = size + 1
network.add_node(self.source)
network.add_node(self.sink)
for node in self.graph.iternodes(): # O(V) time
network.add_node(node)
for node in self.v1: # edges from source to V1
network.add_edge(Edge(self.source, node))
for edge in self.graph.iteredges(): # edges from V1 to V2
if edge.source in self.v1: # weights are 1
network.add_edge(Edge(edge.source, edge.target))
else:
network.add_edge(Edge(edge.target, edge.source))
for node in self.v2: # edges from V2 to sink
network.add_edge(Edge(node, self.sink))
algorithm = FordFulkersonSparse(network)
algorithm.run(self.source, self.sink) # O(V*E) time
for source in self.v1:
for target in self.v2:
if algorithm.flow[source].get(target, 0) == 1:
self.mate[source] = target
self.mate[target] = source
self.cardinality = algorithm.max_flow
def test_ford_fulkerson_sparse(self):
algorithm = FordFulkersonSparse(self.G)
algorithm.run(0, 3)
expected_max_flow = 20
expected_flow = {
0: {1: 10, 2: 10},
1: {0: -10, 2: 0, 3: 10},
2: {0: -10, 1: 0, 3: 10},
3: {1: -10, 2: -10}}
self.assertEqual(algorithm.max_flow, expected_max_flow)
self.assertEqual(algorithm.flow, expected_flow)
def test_ford_fulkerson_sparse(self):
algorithm = FordFulkersonSparse(self.G)
algorithm.run(0, 5)
expected_max_flow = 19
expected_flow = {
0: {1: 10, 2: 9},
1: {0: -10, 2: 0, 3: 4, 4: 6},
2: {0: -9, 1: 0, 4: 9},
3: {1: -4, 4: -5, 5: 9},
4: {1: -6, 2: -9, 3: 5, 5: 10},
5: {3: -9, 4: -10}}
self.assertEqual(algorithm.max_flow, expected_max_flow)
self.assertEqual(algorithm.flow, expected_flow)
def test_ford_fulkerson_sparse(self):
algorithm = FordFulkersonSparse(self.G)
algorithm.run(0, 6)
expected_max_flow = 5
expected_flow = {
0: {1: 2, 2: 0, 3: 3},
1: {0: -2, 2: 2, 4: 0},
2: {0: 0, 1: -2, 3: 1, 4: 1},
3: {0: -3, 2: -1, 4: 0, 5: 4},
4: {1: 0, 2: -1, 3: 0, 6: 1},
5: {3: -4, 6: 4},
6: {4: -1, 5: -4}}
self.assertEqual(algorithm.max_flow, expected_max_flow)
self.assertEqual(algorithm.flow, expected_flow)
def test_ford_fulkerson_sparse(self):
algorithm = FordFulkersonSparse(self.G)
algorithm.run(0, 6)
expected_max_flow = 5
expected_flow = {
0: {
1: 2,
2: 0,
3: 3
},
1: {
0: -2,
2: 2,
4: 0
},
2: {
0: 0,
1: -2,
3: 1,
4: 1
},
3: {
0: -3,
2: -1,
4: 0,
5: 4
},
4: {
1: 0,
2: -1,
3: 0,
6: 1
},
5: {
3: -4,
6: 4
},
6: {
4: -1,
5: -4
}
}
self.assertEqual(algorithm.max_flow, expected_max_flow)
self.assertEqual(algorithm.flow, expected_flow)
def test_ford_fulkerson_sparse(self):
algorithm = FordFulkersonSparse(self.G)
algorithm.run(0, 5)
expected_max_flow = 19
expected_flow = {
0: {
1: 10,
2: 9
},
1: {
0: -10,
2: 0,
3: 4,
4: 6
},
2: {
0: -9,
1: 0,
4: 9
},
3: {
1: -4,
4: -5,
5: 9
},
4: {
1: -6,
2: -9,
3: 5,
5: 10
},
5: {
3: -9,
4: -10
}
}
self.assertEqual(algorithm.max_flow, expected_max_flow)
self.assertEqual(algorithm.flow, expected_flow)
def test_exceptions(self):
self.assertRaises(ValueError, FordFulkerson, Graph())
self.assertRaises(ValueError, FordFulkersonSparse, Graph())
self.assertRaises(ValueError, FordFulkersonWithEdges, Graph())
self.assertRaises(ValueError, FordFulkersonRecursive, Graph())
self.assertRaises(ValueError, lambda: FordFulkerson(self.G).run(0, 0))
self.assertRaises(ValueError,
lambda: FordFulkersonSparse(self.G).run(0, 0))
self.assertRaises(ValueError,
lambda: FordFulkersonWithEdges(self.G).run(0, 0))
self.assertRaises(ValueError,
lambda: FordFulkersonRecursive(self.G).run(0, 0))
self.assertRaises(
ValueError,
lambda: FordFulkersonRecursiveWithEdges(self.G).run(0, 0))
graph_factory = GraphFactory(Graph) G = graph_factory.make_flow_network(V) E = G.e() #G.show() print "Calculate parameters ..." print "Nodes:", G.v(), V print "Edges:", G.e(), E print "Directed:", G.is_directed() print "Testing FordFulkerson ..." t1 = timeit.Timer(lambda: FordFulkerson(G).run(0, V - 1)) print V, E, t1.timeit(1) # single run print "Testing FordFulkersonSparse ..." t1 = timeit.Timer(lambda: FordFulkersonSparse(G).run(0, V - 1)) print V, E, t1.timeit(1) # single run print "Testing FordFulkersonWithEdges ..." t1 = timeit.Timer(lambda: FordFulkersonWithEdges(G).run(0, V - 1)) print V, E, t1.timeit(1) # single run print "Testing FordFulkersonRecursive ..." t1 = timeit.Timer(lambda: FordFulkersonRecursive(G).run(0, V - 1)) print V, E, t1.timeit(1) # single run print "Testing EdmondsKarp ..." t1 = timeit.Timer(lambda: EdmondsKarp(G).run(0, V - 1)) print V, E, t1.timeit(1) # single run print "Testing EdmondsKarpSparse ..."