def add_edge(self, edge):
"""
Anade una arista dirigida al grafo conectando dos nodos.
Una arista es un par de nodos de la forma (nodo1, nodo2).
@type edge: tuple
@param edge: Arista.
@raise Exception: Si la arista a anadir produce un ciclo, no sera anadida y se lanzara una excepcion.
"""
super().add_edge(edge)
cycle = find_cycle(self)
if cycle:
raise Exception("La arista " + str(edge) + " produciria el ciclo " + str(cycle))
def transitive_edges(graph):
"""
Return a list of transitive edges.
Example of transitivity within graphs: A -> B, B -> C, A -> C
in this case the transitive edge is: A -> C
@attention: This function is only meaningful for directed acyclic graphs.
@type graph: digraph
@param graph: Digraph
@rtype: List
@return: List containing tuples with transitive edges (or an empty array if the digraph
contains a cycle)
"""
#if the graph contains a cycle we return an empty array
if not len(find_cycle(graph)) == 0:
return []
tranz_edges = [] # create an empty array that will contain all the tuples
#run trough all the nodes in the graph
for start in topological_sorting(graph):
#find all the successors on the path for the current node
successors = []
for a in traversal(graph,start,'pre'):
successors.append(a)
del successors[0] #we need all the nodes in it's path except the start node itself
for next in successors:
#look for an intersection between all the neighbors of the
#given node and all the neighbors from the given successor
intersect_array = _intersection(graph.neighbors(next), graph.neighbors(start) )
for a in intersect_array:
if graph.has_edge((start, a)):
##check for the detected edge and append it to the returned array
tranz_edges.append( (start,a) )
return tranz_edges # return the final array
def critical_path(graph):
"""
Compute and return the critical path in an acyclic directed weighted graph.
@attention: This function is only meaningful for directed weighted acyclic graphs
@type graph: digraph
@param graph: Digraph
@rtype: List
@return: List containing all the nodes in the path (or an empty array if the graph
contains a cycle)
"""
#if the graph contains a cycle we return an empty array
if not len(find_cycle(graph)) == 0:
return []
#this empty dictionary will contain a tuple for every single node
#the tuple contains the information about the most costly predecessor
#of the given node and the cost of the path to this node
#(predecessor, cost)
node_tuples = {}
topological_nodes = topological_sorting(graph)
#all the tuples must be set to a default value for every node in the graph
for node in topological_nodes:
node_tuples.update( {node :(None, 0)} )
#run trough all the nodes in a topological order
for node in topological_nodes:
predecessors =[]
#we must check all the predecessors
for pre in graph.incidents(node):
max_pre = node_tuples[pre][1]
predecessors.append( (pre, graph.edge_weight( (pre, node) ) + max_pre ) )
max = 0; max_tuple = (None, 0)
for i in predecessors:#look for the most costly predecessor
if i[1] >= max:
max = i[1]
max_tuple = i
#assign the maximum value to the given node in the node_tuples dictionary
node_tuples[node] = max_tuple
#find the critical node
max = 0; critical_node = None
for k,v in list(node_tuples.items()):
if v[1] >= max:
max= v[1]
critical_node = k
path = []
#find the critical path with backtracking trought the dictionary
def mid_critical_path(end):
if node_tuples[end][0] != None:
path.append(end)
mid_critical_path(node_tuples[end][0])
else:
path.append(end)
#call the recursive function
mid_critical_path(critical_node)
path.reverse()
return path #return the array containing the critical path