// -*- coding: utf-8; indent-tabs-mode: nil -*-
\ALGORITHM{Ford–Fulkerson} \WITH
  \INPUTS{Given a network \expr{G = (V, E)} with flow capacity \expr{c}, a source node \expr{s}, and a sink node \expr{t}}
  \OUTPUT{Compute a flow \expr{f} from \expr{s} to \expr{t} of maximum value}
\IS
  \TEXT{1. \expr{f(u, v) <- 0} for all edges \expr{(u, v)}

  2. While there is a path \expr{p} from \expr{s} to \expr{t} in \expr{G_f},
     such that \expr{c_f(u, v) > 0} for all edges \expr{(u, v) ∈ p}:

     1. Find \expr{c_f(p) = min{c_f(u, v): (u, v) ∈ p\}}

     2. For each edge \expr{(u, v) ∈ p}

        1. \expr{f(u, v) <- f(u, v) + c_f(p)}   \expr{\rem Send flow along the path

}	2. \expr{f(v, u) <- f(v, u) - c_f(p)}   \expr{\rem The flow might be "returned" later
}}
\END ALGORITHM {Ford–Fulkerson}
