In a particular network G = (V,E) whose edges have integer capicites Ce, we have already found the maximum s-t flow. However, we made a mistake in the capacity values of edge (u, v): we used Cuv but the capacity is only Cuv -1.
Moreover, the max flow f uses edge (u,v) at full capacity. Can you find a new optimal flow faster than by recomputing max flow in G?