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 both negative and positive weights are allowed on the edges.

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.

Here is an example: