Work out the four cases to verify the conservation conditions

the operation augment (f, P) augment(f, P) Input: f, the flow on a network (G Output: returns a new flow f". b:-bottleneck(P, f) for each edge (u, v) P do P, an s-t path without repeat nodes if (u, v) is a forward edge in Gf then else (we have a backward edge) return f' Any s-t path in G is an augmenting path. Computer Algorithms I(CS 401/MCS 401) 23 July 2018 48 emma f' = augment(, P) is a flow. Proof. We verify the capacity and conservation conditions on f. It suffices to consider only the edges on P, as the rest of G was not changed by the operation augment Let b bottleneck(P, f). Consder e an edge on P Either e is a forward edge in G "( e) = f(e) + b