def Bicomponent(G,S):
'''Construct an auxiliary graph that shows biconnected component'''
Auxiliary = Graph() # initially empty auxiliary graph
Auxiliary.Set_directed(True)
Auxiliary.Set_weighted(False)
explored_v, explored_e, back_edges = DFS(G,S, sort = True) # run DFS once
discovery_edges = [p for p in explored_e if p not in back_edges]
examined_backedges = []
print("---------------------------------------------------")
print("Above is DFS information")
# add all discovery edges as vertices
for u,v in discovery_edges:
Auxiliary.Add_vertice(tuple((u,v)))
print(Auxiliary.vertices)
# for every node, DFS reach order, process back edges that link to it
for v in explored_v:
for be in back_edges:
if v in be and be not in examined_backedges:
print("Back Edge", be, "connect to vertice", v)
examined_backedges.append(be)
Auxiliary.Add_vertice(be)
u = G.GetDestination(be,v)
while (u != v):
p = G.FindParent(discovery_edges, u)
f = tuple((p,u))
Auxiliary.Add_edge(be,f)
print("Added", be, "link to", f)
u = p
return Auxiliary
G1.Set_weighted(False)
G1.Set_directed(True)
V1 = ['A', 'B', 'C', 'D', 'E']
E1 = [
('A', 'B'),
('B', 'C'),
('C', 'A'),
('E', 'A'),
('B', 'D'),
('C', 'D'),
('D', 'E'),
]
for u, v in E1:
G1.Add_edge(u, v)
print("G1", TestStrongConnectivity(G1, 'A'))
G2 = Graph()
G2.Set_weighted(False)
G2.Set_directed(True)
V2 = ['A', 'B', 'C', 'D', 'E']
E2 = [
('A', 'B'),
('B', 'C'),
('C', 'A'),
('A', 'E'),
('B', 'D'),
('C', 'D'),
return Auxiliary
if __name__ == "__main__":
image = Image.open('images\AuxiliaryGraph.PNG').show()
V = ['A','B','C','D','E','F','H','J','K','L','M','P','N','Q']
E = [('A','B'),('A','C'),('B','C'),('C','D'),('D','E'),('E','F'),
('F','H'),('H','J'),('J','D'),('H','D'),('C','K'),('K','L'),
('L','M'),('M','P'),('P','Q'),('P','N'),('C','Q'),('L','Q'),
('C','P')]
G = Graph()
G.Set_directed(False)
G.Set_weighted(False)
for v,u in E:
G.Add_edge(u,v)
AuxiliaryGraph = Bicomponent(G, 'A')
if (new_cost < result[v][0]):
result[v][0] = new_cost
result[v][1] = u
visited_vertices.append(vertex_smallest_cost)
return result
if __name__ == "__main__":
image = Image.open('images\dijkstra_example.PNG').show()
V = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J']
E = [('A', 'B', 12), ('A', 'C', 3), ('A', 'D', 7), ('B', 'C', 8),
('C', 'D', 6), ('B', 'E', 15), ('C', 'F', 2), ('D', 'G', 1),
('C', 'E', 5), ('C', 'G', 4), ('E', 'F', 5), ('F', 'G', 6),
('E', 'I', 10), ('G', 'J', 9), ('F', 'H', 10), ('E', 'H', 9),
('G', 'H', 6), ('H', 'I', 2), ('H', 'J', 5), ('I', 'J', 12)]
G = Graph()
G.Set_directed(False)
G.Set_weighted(True)
for u, v, w in E:
G.Add_edge(u, v, w)
result = Dijkstra(G, 'A')
for i in sorted(result):
print(i, result[i])
