The following question is from the book "Introduction to Algorithms" By Cormen and three other authors.
Show how to find a maximum flow in a network $G = (V,E)$ by a sequence of at most $|E|$ augmenting paths. (Hint: Determine the paths after finding the maximum flow.)
I find this question confusing because the hint contradicts the question. Is it asking you to find the maximum flow in a graph? or is it asking you to find a path?
Recall that for a given flow graph $G$ there might be several flows that yield the maximum flow. Is this question asking you to find all the flows that produce a maximum flow? Do you think this question is properly worded?