def find_shortest_path(cls, net, depart_time, start, end=None):
if end != None and start == end:
return {end.id: (None, 0.0, depart_time)}
# creater a FIFO queue for searching
queue = deque()
# create containers with default values
cost = defaultdict(constant_factory(float('+inf')))
time = defaultdict(constant_factory(float('+inf')))
prev = defaultdict(None)
# set values for the start node
cost[start.id] = 0.0
time[start.id] = depart_time
queue.appendleft(start.id)
# continue until the queue is empty
while len(queue) > 0:
# pop out the first object in the queue
qtop = queue.pop()
node = net.nodes[qtop]
# relax each adjacent edges
for edge in node.adj_edges:
# get the traffic flow on the edge
if Time.lessthan_maxtick(time[node.id]):
edge_flow = net.flows[edge.id][time[node.id]]
else:
edge_flow = 0.0
# if the relaxation makes a shorter path
travel_time = edge.calc_travel_time(edge_flow)
travel_cost = edge.calc_travel_cost(travel_time)
if cost[edge.tail.id] > cost[node.id] + travel_cost:
# then update cost and time labels
cost[edge.tail.id] = cost[node.id] + travel_cost
time[edge.tail.id] = time[node.id] + travel_time
# and save the edge on the shortest path
prev[edge.tail.id] = edge
# and append the expanded node to the queue
queue.appendleft(edge.tail.id)
# if end node is given, extract the shortest path to end node recursively
if end != None:
# if the end node is reached, there is at least one path
# if the end node is not reached, the start and end nodes are not connected
path = cls.create_shortest_path(start, end, prev, time) if end.id in prev else None
return {end.id: (path, cost[end.id], time[end.id])}
else:
# if end node is not given, extract the shortest paths from start to all the other nodes
paths = cls.create_all_shortest_paths(start, prev, time)
# no path is defined for a ring and the travel time/cost is zero
tuples = {start.id: (None, 0.0, depart_time)}
for id_ in paths:
# wrap the path, cost and time in a tuple
# note that time[id_] is the arrival time at node[id_]
# that is, time[id_] = depart_time + travel_time
tuples[id_] = (paths[id_], cost[id_], time[id_])
return tuples
