可以使用Bellman-Ford算法在只有正边的图形上找到最短路径吗？

Question

I know that Dijkstra's algorithm can be used only on positive lengths of edges, and Bellman-Ford can be used when the graph also has negative ones.

Suppose we have a graph with only positive edges, though. Will Bellman-Ford give the same results as Dijkstra?

Answer 1

Yes, it will give the same results. It will run slower, though, as it could also have been used for graphs with negative edges (subject to the absence of negative cycles). If you look at the proof of BF's correctness, there is no assumption there that some of the edges are negative.

Answer 2

I want to add something to Ami Tavory's answer. Bellman-ford's algorithm can be made a little bit faster if you can detect that on any pass, there is no node value update, then return from there. If there is no node update then it proves that every node traversal is complete.