Those are network flow questions, any idea will help, thanks.

2. We are given a flow network G = (V, E) and labels f : E R+. (4 points) Give an algorithm that verifies whether f is a maximum flow. Your algorithm needs to run in linear time, ie, in time 0(M + EI). (6 points) Suppose we have verified that f is indeed a maximum flow. Further assume that all capacities in G are integers, and f is integer-valued as well. Also, there is no cycle in G such that f is positive on each edge of the cycle. Now take an edge e from E with c >0, and reduce its capacity by one unit. Give a linear-time algorithm that finds a maximum flow in the resulting network