dijkstra算法的步数条件

Question

我目前是一名学生，正在开展一个小型项目。我的目标是能够确定两个给定城市之间的最短路径，但条件是需要经过指定数量的其他城市（或者您可能已经了解，我工作时会有一定数量的节点）用图表）。我已经按照dijkstra算法的基本标题编写了大部分程序（这是我唯一可以使用的算法），但发现自己无法指定需要经过的节点数量，你们其中一个人有没有我怎么想的呢？

import sys
def shortestpath(graph,start,end,visited=[],distances={},predecessors={}):
"""Find the shortest path between start and end nodes in a graph"""
# we've found our end node, now find the path to it, and return
if start==end:
    path=[]
    while end != None:
        path.append(end)
        end=predecessors.get(end,None)
    return distances[start], path[::-1]
# detect if it's the first time through, set current distance to zero
if not visited: distances[start]=0
# process neighbors as per algorithm, keep track of predecessors
for neighbor in graph[start]:
    if neighbor not in visited:
        neighbordist = distances.get(neighbor,sys.maxsize)
        tentativedist = distances[start] + graph[start][neighbor]
        if tentativedist < neighbordist:
            distances[neighbor] = tentativedist
            predecessors[neighbor]=start
# neighbors processed, now mark the current node as visited
visited.append(start)
# finds the closest unvisited node to the start
unvisiteds = dict((k, distances.get(k,sys.maxsize)) for k in graph if k not in visited)
closestnode = min(unvisiteds, key=unvisiteds.get)
# now we can take the closest node and recurse, making it current
return shortestpath(graph,closestnode,end,visited,distances,predecessors)

if __name__ == "__main__":
graph = {'Paris':       {               'Marseille': 773,   'Lyon': 464,    'Toulouse': 677,    'Nice': 930,    'Nantes': 383,  'Angers': 294,      'Strasbourg': 492},
        'Marseille':    {'Paris': 773,                      'Lyon': 314,    'Toulouse': 403,    'Nice': 207,    'Nantes': 985,  'Angers': 905,      'Strasbourg': 802},
        'Lyon':         {'Paris': 464,  'Marseille': 314,                   'Toulouse': 537,    'Nice': 471,    'Nantes': 685,  'Angers': 596,      'Strasbourg': 493},
        'Toulouse':     {'Paris': 677,  'Marseille': 403,   'Lyon': 537,                        'Nice': 561,    'Nantes': 585,  'Angers': 642,      'Strasbourg': 969},
        'Nice':         {'Paris': 930,  'Marseille': 207,   'Lyon': 471,    'Toulouse': 561,                    'Nantes': 1143, 'Angers': 1063,     'Strasbourg': 785},
        'Nantes':       {'Paris': 383,  'Marseille': 985,   'Lyon': 685,    'Toulouse': 585,    'Nice': 1143,                   'Angers': 91,       'Strasbourg': 866},
        'Angers':       {'Paris': 294,  'Marseille': 905,   'Lyon': 596,    'Toulouse': 642,    'Nice': 1063,   'Nantes': 91,                       'Strasbourg': 777},
        'Strasbourg':   {'Paris': 492,  'Marseille': 802,   'Lyon': 493,    'Toulouse': 969,    'Nice': 785,    'Nantes': 866,  'Angers': 777}}