def TestDagShortestPathsModified(self):
u = Vertex('u')
v = Vertex('v')
w = Vertex('w')
z = Vertex('z')
u.weight = 1
v.weight = 2
w.weight = 3
z.weight = 4
vertices = [u, v, w, z]
edges = [(u, v), (v, w), (v, z)]
G = Graph(vertices, edges)
self.assertEqual(dag_shortest_paths_modified(G, u), [u, v, z])
def TestDagShortestPathsModified(self):
u = Vertex('u')
v = Vertex('v')
w = Vertex('w')
z = Vertex('z')
u.weight = 1
v.weight = 2
w.weight = 3
z.weight = 4
vertices = [u, v, w, z]
edges = [(u, v), (v, w), (v, z)]
G = Graph(vertices, edges)
self.assertEquals(dag_shortest_paths_modified(G, u), [u, v, z])
def shift(vertex: Vertex, num_vertices: int) -> Vertex:
"""
Returns the Vertex that is the root for this tree
:param vertex: the vertex we want to shift
:param num_vertices: the number of vertices in the graph [invariant]
:return:
"""
# If no neighbour of u has weight > neighbour.weight/2, return u
result = vertex
for neighbour in vertex.neighbours:
if neighbour.weight > num_vertices / 2:
vertex.weight = vertex.weight - neighbour.weight
neighbour.weight = vertex.weight + neighbour.weight
result = shift(neighbour, num_vertices)
return result
def set_weight(root: Vertex, parent: Vertex = None):
"""
Recursively assigns weights to the induced subgraphs starting with the root
:param root: Vertex
:param parent: The parent of the root, because those do not count in the weight of a subgraph
:return:
"""
if root.degree == 1 and root.neighbours[0] == parent:
root.weight = 1
return 1
else:
for neighbour in root.neighbours:
if neighbour != parent:
root.weight += set_weight(root=neighbour, parent=root)
root.weight += 1
return root.weight
