So I'm watching Stanford's algorithm lectures and I'm on Kosaraju's algorithm. In the lecture, the algorthm was given in 3 steps: calculate the graph with all arcs reversed, run dfs on reversed graph, run dfs on original graph. Then an optimization was given, which was to instead of using the naive implementation of remaking the entire graph with the arcs reversed, you can instead run dfs on the original graph but going backwards along the arc instead of forward, which simulates running dfs on the reversed graph.
The lecturer made it seems so simple to do this and gave no further explanation. I'm completely stumped on how you can achieve this. Can someone give me some help or point me in the right direction?