graph - Dijkstra for The Single-Source Longest Path

Question

Ok, I posted this question because of this exercise:

Can we modify Dijkstra’s algorithm to solve the single-source longest path problem by changing mi

Answer 1

Yes, we can. And your answer is almost correct. Except one thing.

You assume no negative weights. In this case Dijkstra's algorithm cannot find longest path.

But if you assume only negative weights, you can easily find the longest path. To prove correctness, just take absolute values of all weights and you get exactly the usual Dijkstra's algorithm with positive weights.