def fast_targeted_order(ugraph):
"""
Implementation of algorithm FastTargetedOrder
This function creates a list degree_sets whose kth element is
the set of nodes of degree k. The method then iterates through
the list degree_sets in order of decreasing degree. When it
encounter a non-empty set, the nodes in this set must be of
maximum degree. The method then repeatedly chooses a node from
this set, deletes that node from the graph,
and updates degree_sets appropriately.
Parameters
----------
ugraph: dict
a dictionary represents the undirected graph
Returns
-------
l: list
an ordered list of the nodes in decreasing order of degrees
"""
degree_sets = [set()] * len(ugraph.keys())
new_graph = copy_graph(ugraph)
for node, connected in new_graph.iteritems():
degree_sets[len(connected)].add(node)
l = []
for degree_set in degree_sets[:: -1]:
while len(degree_set) > 0:
u = degree_set.pop()
for v in new_graph[u]:
d = len(new_graph[v])
degree_sets[d].remove(v)
degree_sets[d - 1].add(v)
l.append(u)
# remove u from graph
delete_node(new_graph, u)
return l
def question3_plot():
"""
generate plot for question 3
"""
m = 5
ns = range(10, 1000, 10)
target_time = []
fast_time = []
for n in ns:
upa_graph = upa(n, m)
upa_graph2 = copy_graph(upa_graph)
target_time.append(timeit.timeit(lambda: targeted_order(upa_graph),
number=1))
fast_targeted_order(upa_graph2)
fast_time.append(timeit.timeit(lambda: fast_targeted_order(upa_graph),
number=1))
plt.plot(ns, target_time)
plt.plot(ns, fast_time)
plt.legend(['targeted_order', 'fast_targeted_order'], loc='upper left')
plt.title('Running Time Comparison (Implemented in Desktop Python)')
plt.xlabel('number of nodes')
plt.ylabel('running time')
plt.show()
