Bellman ford queue based approach from Sedgewick and Wayne - Algorithms, 4th edition

Question

I was studying queue-based approach for Bellman-Ford algorithmfor single source shortest path from Robert Sedgewick and Kevin Wayne - Algorit

Answer 1

Very happy to see the answers by Miljen Mikic. It really helps to understand the algorithm. However, I still have another question. In the text, it says "To complete the implementation, we need to ensure that the algorithm terminates after V passes. One way to achieve this end is to explicitly keep track of the passes." Here, I believe the variable "cost" is the count of the passes, but shouldn't the lines

if (cost++ % G.V() == 0)
    findNegativeCycle();

be at least outside of the for loop? Like

private void relax(EdgeWeightedDigraph G, int v)
    {
        for (DirectedEdge e : G.adj(v)
             {
                  int w = e.to();
                  if (distTo[w] > distTo[v] + e.weight())
                       {
                           distTo[w] = distTo[v] + e.weight();
                           edgeTo[w] = e;
                           if (!onQ[w])
                                 {
                                      q.enqueue(w);
                                      onQ[w] = true;
                                 }
                        }
              }
         if (cost++ % G.V() == 0)
              findNegativeCycle();
      }

Actually even it's outside of the for loop, it's not the best solution, as during each pass, there could be multiple vertices to be relaxed. So it could be designed better in the constructor of BellmanFordSP by remembering how many vertices to be relaxed during each pass. Am I correct? Thanks!