## Programming Challenge – LeetCode: Bellman Ford C # Network Delay Time

https://leetcode.com/problems/network-delay-time/

There are N network nodes labeled 1 through N.

Given times, a list of travel times as directed edge times (i) = (u,
v, w), where u is the source node, v is the destination node and w is the
Time it takes a signal to get from the source to the destination.

Now we send a signal from a certain node K. How long will it take
all nodes to receive the signal? If this is not possible, return -1.

Note:

1. N is in the range (1, 100).
2. K is in the range (1, N). The
3. The time period is in the range (1, 6000).
4. All edge times (i) = (u, v, w) have 1 <= u, v <= N and 0 <= w <= 100.

``````   (TestClass)
public class NetworkDelayTimeTest
{
(TestMethod)
public void ExampleTestBellmanFord()
{
int N = 4;
int K = 2;
int()() times = { new() { 2, 1, 1 }, new() { 2, 3, 1 }, new() { 3, 4, 1 } };
NetworkDelayTimeBellmanFord bellmanFord = new NetworkDelayTimeBellmanFord();
Assert.AreEqual(2, bellmanFord.NetworkDelayTime(times, N, K));
}
}

public class NetworkDelayTimeBellmanFord
{
public int NetworkDelayTime(int()() times, int N, int K)
{
var dist = Enumerable.Repeat(int.MaxValue, N + 1).ToList();
dist(K) = 0;
for (int i = 0; i < N; i++)
{
foreach (var e in times)
{
int u = e(0);
int v = e(1);
int w = e(2);
if (dist(u) != int.MaxValue && dist(v) > dist(u) + w)
{
dist(v) = dist(u) + w;
}
}
}

int maxWait = 0;
for (int i = 1; i <= N; i++)
{
maxWait = Math.Max(maxWait, dist(i));
}

if (maxWait == int.MaxValue)
{
return -1;
}

return maxWait;
}
}
``````

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## Algorithms – Bellman Ford – negative cycle

This is my code for detecting a negative cycle in a graph using the Bellman-Ford algorithm, but I can not figure out why it returns an incorrect answer

``````public static final int INF = Integer.MAX_VALUE;
private static int negativeCycle(ArrayList() adj, ArrayList() cost) {
for(int i=0; i dep(j) + cost(j).get(v_index)) {
dep(v) = dep(j) + cost(j).get(v_index);

}
}
}
}

for (int j = 0; j < adj.length; j++) {
for (int v : adj(j)) {
if (dep(v) > dep(j) + cost(j).get(v_index)) {
return 1;
}
}
}

return 0;
}
``````

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BlackHatKings.com – Web, Internet Marketing and SEO Forums

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,

## ford fulkerson – Maxflow of the graph equal to the flow value plus maxflow of the residual graph

I check the max flow min cut for an upcoming exam, and one of the proofs is based on the fact that it is used for each flow $$f$$ in the graphic $$G$$ and rest graph $$G_f$$,
$$maxflow (G) = value (f) + maxflow (G_f)$$, That seems intuitively true, but I can not prove it. Any help would be appreciated!

## Algorithms – why not use Dijkstra Algo + Bellman Ford's last line instead of Bellman Ford

correct me if wrong
1. For a given chart, use dijkstra on it.
2. Now after v-1 iterations or after finding all possible minimum distances for each node.
3.check for each edge (u, v) in the graph
if (vd> u + w (u, v))
then you return wrong
Here the temporal complexity is lower than with bellman ford and also negative cycles are considered

## Graph Theory – Is there a Ford Fulkerson run for each flownet in which all extension paths consist of forward edges only?

Is there a Ford Fulkerson algorithm for each flownet in which all extension paths consist of forward edges only?

I've seen this claim for a flow network where all edges have c (e) = 1, and I tried to find a counter example for networks with different capacities, but could not.

Is this statement always correct? and if so, do we need reverse edges just because we can not know which paths have only forward edges while we are executing the FF algorithm?

Many Thanks!