无法为 bellman-ford 算法生成正确的图

Question

I have an implementation of the algorithm of Bellman - Ford. The input program supplied a list of edges. Without optimization it looks like this:

int i, j;
        for (i = 0; i < number_of_vertices; i++) {
            distances[i] = MAX;
        }
        distances[source] = 0;
        for (i = 1; i < number_of_vertices - 1; ++i) {

            for (j = 0; j < e; ++j) { //here i am calculating the shortest path
                if (distances[edges.get(j).source] + edges.get(j).weight < distances[edges.get(j).destination]) {
                    distances[edges.get(j).destination] = distances[edges.get(j).source] + edges.get(j).weight;
                }
            }
        }

it has the complexity of O(V * E) But with optimization his works very fast. it looks like

while (true) {

            boolean any = false;
            for (j = 0; j < e; ++j) { //here i am calculating the shortest path
                if (distances[edges.get(j).source] + edges.get(j).weight < distances[edges.get(j).destination]) {
                    distances[edges.get(j).destination] = distances[edges.get(j).source] + edges.get(j).weight;
                    any = true;
                }
            }
            if (!any) break;
        }

In practice, if the number of vertices , for example ten thousand , in the outer loop had only 10-12 passes iterations instead of 10 thousand, and the algorithm completes its work .

This is my generate code:

//q - vertices

for (int q = 100; q <= 20000; q += 100) {
          List<Edge> edges = new ArrayList();
                for (int i = 0; i < q; i++) {
                    for (int j = 0; j < q; j++) {
                        if (i == j) {
                            continue;
                        }

                        double random = Math.random();
                        if (random < 0.005) {
                            int x = ThreadLocalRandom.current().nextInt(1, 100000);
                           edges.add(new Edge(i, j, x));
                            edges++;
                        }
                    }

                }
              //write edges to file edges
            }

But I need to generate a graph on which it will not be so fast to finish his work. That can be changed in the generator?

Answer 1

The complexity of Bellman Ford algorithm like you said is O(|E|*|V|). In your generator, the probability of adding an edge is negligible (0.005) which is why according to me the code works fast.

Increase the probability, there shall be more edges and consequently the Bellman Ford shall then take longer time.