我在 Udacity 上同样的课程。在从 Wikipedia 阅读 Hierholzer 算法后，我实现了它。这是算法的链接https://en.wikipedia.org/wiki/Eulerian_path
下面是我的代码。毫无疑问，它被评分者接受了（在做了一些 Python3 到 Python2 的更改之后）。 :)
#!/usr/bin/env python3
# Find Eulerian Tour
#
# Write a program that takes in a graph
# represented as a list of tuples
# and return a list of nodes that
# you would follow on an Eulerian Tour
#
# For example, if the input graph was
# [(1, 2), (2, 3), (3, 1)]
# A possible Eulerian tour would be [1, 2, 3, 1]
def get_a_tour():
'''This function returns a possible tour in the current graph and removes the edges included in that tour, from the graph.'''
global graph
nodes_degree = {} # Creating a {node: degree} dictionary for current graph.
for edge in graph:
a, b = edge[0], edge[1]
nodes_degree[a] = nodes_degree.get(a, 0) + 1
nodes_degree[b] = nodes_degree.get(b, 0) + 1
tour =[] # Finding a tour in the current graph.
loop = enumerate(nodes_degree)
while True:
try:
l = loop.__next__()
index = l[0]
node = l[1]
degree = nodes_degree[node]
try:
if (tour[-1], node) in graph or (node, tour[-1]) in graph:
tour.append(node)
try:
graph.remove((tour[-2], tour[-1]))
nodes_degree[tour[-1]] -= 1 # Updating degree of nodes in the graph, not required but for the sake of completeness.
nodes_degree[tour[-2]] -= 1 # Can also be used to check the correctness of program. In the end all degrees must zero.
except ValueError:
graph.remove((tour[-1], tour[-2]))
nodes_degree[tour[-1]] -= 1
nodes_degree[tour[-2]] -= 1
except IndexError:
tour.append(node)
except StopIteration:
loop = enumerate(nodes_degree)
if len(tour) > 2:
if tour[0] == tour[-1]:
return tour
def get_eulerian_tour():
'''This function returns a Eulerian Tour for the input graph.'''
global graph
tour = get_a_tour()
if graph: # If stuck at the beginning, finding additional tour in the graph.
loop = enumerate(tour[: -1])
l = loop.__next__()
i = l[0]
node = l[1]
try:
while True:
if node in list(zip(*graph))[0] or node in list(zip(*graph))[1]:
t = get_a_tour() # Retreivng the additional tour
j = t.index(node)
tour = tour[ : i] + t[j:-1] + t[ :j+1] + tour[i+1: ] # Joining the two tours.
if not graph: # Found Eulerian Tour
return tour # Returning the Eulerian Tour
loop = enumerate(tour[: -1]) # Still stuck? Looping back to search for another tour.
l = loop.__next__()
i = l[0]
node = l[1]
except StopIteration: # Oops! seems like the vertices in the current tour cannot connect to rest of the edges in the graph.
print("Your graph doesn't seem to be connected")
exit()
else: # Found the Eulerian Tour in the very first call. Lucky Enough!
return tour
# Sample inputs
# graph = [(1, 2), (1, 3), (2, 3), (2, 4), (2, 6), (3, 4), (3, 5), (4, 5), (4, 6)]
# graph = [(1, 2), (1, 3), (2, 3)]
# graph = [(1, 2), (1, 3), (2, 3), (2, 4), (2, 6), (3, 4), (3, 5), (4, 5), (4, 6), (9, 10), (10, 11), (11, 9)]
# graph = [(1, 2), (1, 3), (2, 3), (2, 4), (2, 6), (3, 4), (3, 5), (4, 5), (4, 6), (2, 7), (7, 8), (8, 2)]
# graph = [(1, 2), (1, 3), (2, 3), (2, 4), (2, 6), (3, 4), (3, 5), (4, 5), (4, 6), (1, 5), (5, 6), (1, 6)]
# graph = [(1, 2), (2, 3), (3, 1), (3, 4), (4, 3)]
# graph = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]
# graph = [(2, 6), (4, 2), (5, 4), (6, 5), (6, 8), (7, 9), (8, 7), (9, 6)]
# creating a {node: degree} dictionary
nodes_degree = {}
for edge in graph:
a, b = edge[0], edge[1]
nodes_degree[a] = nodes_degree.get(a, 0) + 1
nodes_degree[b] = nodes_degree.get(b, 0) + 1
#checking degree
degrees = nodes_degree.values() # remember it return a view
for degree in degrees:
if degree % 2:
print("Your graph have one or more nodes with odd degrees. Hence an Eulerian Tour is impossible.")
exit()
#finding Eulerian Tour
tour = get_eulerian_tour()
print(tour)
希望这会有所帮助。