title: Find the maximum flow f, in which f(e) is the maximum flow possible in a given edge e
body: <blockquote>
    <p>Given a flow network, G(V,E), a source s, a sink t and a capacity function c: E --> R U {0}. Also, given an edge e=(u,v) in E. I need to find an efficient algorithm to find among all the maximum flows from s to t, a maximum flow f in the network, in which f(e) is the maximum flow possible in the edge e.</p>
  </blockquote>
  
  <p>Please solve the problem and explain why the algorithm works correctly.</p>