用python解决欧拉七桥问题的代码升级版

欧拉七桥问题是一个经典的数学问题，可以用图论的知识解决。以下是使用Python解决欧拉七桥问题的代码升级版：

from collections import defaultdict

def find_eulerian_tour(graph):
    tour = []
    stack = [list(graph.keys())[0]]
    while stack:
        v = stack[-1]
        if graph[v]:
            stack.append(graph[v].pop())
        else:
            tour.append(stack.pop())
    return tour[::-1]

def upgrade_eulerian_tour(graph):
    degrees = defaultdict(int)
    for v in graph.keys():
        degrees[v] += len(graph[v])
        for u in graph[v]:
            degrees[u] += 1
    odd_vertices = [v for v in degrees if degrees[v] % 2 == 1]
    if odd_vertices:
        graph[odd_vertices[0]].append(odd_vertices[1])
        graph[odd_vertices[1]].append(odd_vertices[0])
    tour = find_eulerian_tour(graph)
    return tour

if __name__ == '__main__':
    graph = {'A': ['B', 'C'],
             'B': ['A', 'D', 'D'],
             'C': ['A', 'D', 'E'],
             'D': ['B', 'C', 'E', 'F'],
             'E': ['C', 'D'],
             'F': ['D']}
    tour = upgrade_eulerian_tour(graph)
    print(tour)

这个升级版的代码加入了一个函数 `upgrade_eulerian_tour`，它先计算所有节点的度数，如果存在奇数度的节点，则将它们连接起来，使得整个图变成了欧拉图。然后调用之前的 `find_eulerian_tour` 函数找到欧拉回路。