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无向图中的访问边，顶点

[英]Visiting edges, vertices in an undirected graph

原文 2013-04-03 03:50:57 0 1 algorithm/ graph/ graph-algorithm/ depth-first-search

Problem: You have an Undirected graph G = (V, E) (V = vertices, E = edges) and you must visit each vertex and pass each edge in both directions. 问题：您有一个无向图G = (V, E) （V =顶点，E =边），您必须访问每个顶点并在两个方向上传递每个边。

The only algorithms I know for graphs are DFS, BFS, and a few MST's (Kruskal, etc.) My friend and I were discussing this problem, if it were directed I would simply DFS, and then DFS the transpose but the graph is unfortunately undirected. 我所知道的关于图形的唯一算法是DFS，BFS和一些MST（例如Kruskal等）。我和我的朋友正在讨论这个问题，如果直接解决，我会简单地选择DFS，然后再转置DFS，但不幸的是，图形无向的。 My friend proposed we perform an MST and DFS the MST and then find the remaining edges by iterating through those that arent in MST. 我的朋友建议我们先执行MST，然后再执行DFS DST，然后通过迭代遍历MST的边找到剩余的边。 I sort of see what he means but I am not sure this is a good approach? 我有点明白他的意思，但是我不确定这是一个好方法吗？ opinions? 意见？ Also, how would I be able to pass by an edge in both directions if it is undirected? 另外，如果它是无向的，我怎么能在两个方向上都经过一条边？

1 个解决方案

It doesn't matter if the graph is directed or undirected. 图形是有向的还是无向的都没有关系。 You could just replace every undirected edge with two directed edges and perform whatever algorithm you have for a directed graph. 您可以只用两个有向边替换每个无向边，然后执行有向图的任何算法。 Both DFS and BFS will traverse the whole vertices and edges. DFS和BFS都将遍历整个顶点和边缘。

I think what you are looking for is called Graph Traversal . 我认为您正在寻找的是图遍历。 BFS and DFS are two graph traversal algorithms and they do not require the graph to be directed. BFS和DFS是两种图形遍历算法，它们不需要对图形进行定向。 MST on the other hand, is not a graph traversal algorithm. 另一方面，MST不是图遍历算法。