# An AMPL implementation of the reaching algorithm as described 
# in "Network Flows: Theory, Algorithms, and Applications" by
# Ahuja, Magnanti, and Orlin.

# Requires: mcnfp_model.txt.
# Assumes that the nodes have already been
# labeled according to a topological ordering

param d {NODES} default Infinity;
param pred {NODES} default 0;


let d[1] := 0;
for {i in 1 .. card(NODES)} {
  for {j in NODES: (i,j) in ARCS} {
    if d[j] > d[i] + c[i,j] then {
      let d[j] := d[i] + c[i,j];
      let pred[j] := i;
    } # end if d[j] > d[i] + c[i,j] then
  }# end for {j in NODES: (i,j) in ARCS} 
} # end for {i in 1 .. card(NODES)}

display d;
display pred;