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Find an aficient algorithm that computes the shortest paths from a source node s to all the other nodes, that contain AT MOST ONE negative

Find an aficient algorithm that computes the shortest paths from a source node s to all the other nodes, that contain AT MOST ONE negative edge. The graph is directed and connected and of course negative weights are allowed. We want to compute the d_neg[v] for each vertex. This represents the weight of the sortest path from s to v that contains at most one negative edge. In general the graph can have many negative edges. Our goal is to use at most one negative edge at every path

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