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) {
    int dep() = new int(adj.length);
    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)) {
            int v_index = adj(j).indexOf(v);
            if (dep(v) > dep(j) + cost(j).get(v_index)) {
                return 1;
            }
        }
    }

    return 0;
}

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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!

1997 Ford F-150 RWD, transmission truck does not move on. Please help!?

1997 Ford F-150 RWD, transmission truck does not move on. Please help!?

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All four presidents who died during my life are Republicans (Nixon, Reagan, Ford, Bush Sr.). What does that say about something?

We recently had a number of Republican presidents.

List of the last ten presidents of the USA.

Donald Trump (2017-)
Barack Obama (2009-2017)
George W. Bush (2001-2009)
Bill Clinton (1993-2001)
George H.W. Bush (1989-1993) R – died at the age of 94
Ronald Reagan (1981-1989) R – died at the age of 93
Jimmy Carter (1977-1981)
Gerald Ford (August 9, 1974-1977) R – died at the age of 94 years
Richard Nixon (1969 – August 9, 1974) R – died at the age of 81 years
Lyndon Johnson (22nd November 1963-1969) D – died at the age of 63
John Kennedy (1961-22 November 1963) D – died at 46 years old

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