使用Dijkstra在循环图中找到最短路径

Question

我有一个周期性的有向图。下面是图表作为python dict的表示

graph = {
          'A': {'B': 5, 'D': 5, 'E': 7 },
          'B': {'C': 4},
          'C': {'D': 8, 'E': 2},
          'D': {'C': 8, 'E':  6},
          'E': {'B': 3}
        }

我写了一个Dijkstra最短路径的简单实现。这似乎适用于两点。以下是我的实施。

def shortestpath(self, start, end, visited=[],distances={},predecessors={}):
        # initialize a big number
        maxint = 10000 

        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 self.graph[start]:
            if neighbor not in visited:
                neighbordist = distances.get(neighbor,maxint)
                tentativedist = distances[start] + self.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,maxint)) for k in self.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 self.shortestpath(closestnode,end,visited,distances,predecessors)

现在这个简单的实现似乎有效。例如，如果我做这样的事情

shortestpath('A', 'C')

它会给我路径和最短的重量

  

（9，['A'，'B'，'C']）

在这种情况下。 但是，每当我shortestpath('B', 'B')程序中断时。 现在有B to B的最短路径，因为它是一个循环图，路径是B-C-E-B。我只是不知道如何检查并相应地修改Dijktra的算法，以检查像这样的循环情况。任何建议都非常感谢。谢谢:)）