def run(self):
"""Finding all shortest paths."""
# graph copy
size = self.graph.v()
self._new_graph = self.graph.__class__(size + 1, directed=True)
for node in self.graph.iternodes(): # O(V) time
self._new_graph.add_node(node)
for edge in self.graph.iteredges(): # O(E) time
self._new_graph.add_edge(edge)
self._new_node = size
self._new_graph.add_node(self._new_node)
for node in self.graph.iternodes(): # O(V) time
self._new_graph.add_edge(Edge(self._new_node, node, 0))
self._bf = BellmanFord(self._new_graph)
# If this step detects a negative cycle, the algorithm is terminated.
self._bf.run(self._new_node) # O(V*E) time
# Edges are reweighted.
for edge in list(self._new_graph.iteredges()): # O(E) time
edge.weight = (edge.weight + self._bf.distance[edge.source] -
self._bf.distance[edge.target])
self._new_graph.del_edge(edge)
self._new_graph.add_edge(edge)
# Remove _new_node with edges.
self._new_graph.del_node(self._new_node)
# Weights are modified!
self.distance = dict()
for source in self.graph.iternodes():
self.distance[source] = dict()
algorithm = Dijkstra(self._new_graph) # O(V*E*log(V)) total time
algorithm.run(source)
for target in self.graph.iternodes(): # O(V^2) total time
self.distance[source][target] = (algorithm.distance[target] -
self._bf.distance[source] +
self._bf.distance[target])
def test_shortest_path_cormen(self):
source = 0
target = 4
algorithm = BellmanFord(self.G)
algorithm.run(source)
distance_expected = {3: 7, 2: 4, 0: 0, 4: -2, 1: 2}
self.assertEqual(algorithm.distance, distance_expected)
parent_expected = {3: 0, 2: 3, 0: None, 4: 1, 1: 2}
self.assertEqual(algorithm.parent, parent_expected)
path_expected = [0, 3, 2, 1, 4]
self.assertEqual(algorithm.path(target), path_expected)
def test_shortest_path(self):
source = 0
target = 3
algorithm = BellmanFord(self.G)
algorithm.run(source)
distance_expected = {0: 0, 2: 2, 1: 1, 3: 3}
self.assertEqual(algorithm.distance, distance_expected)
parent_expected = {0: None, 2: 1, 1: 0, 3: 2}
self.assertEqual(algorithm.parent, parent_expected)
path_expected = [0, 1, 2, 3]
self.assertEqual(algorithm.path(target), path_expected)
