/* 

  Critical path in Picat.

  Problem and model from 
  Winston "Introduction to Operations Research", page 441.

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


% import util.
import cp.


main => go.


go =>

  NumNodes = 6,  
  % Nodes = 1..NumNodes,  
  
  % the arcs (dependencies between projects)
  Arcs = [
           [1,2], 
           [1,3],
           [2,3], 
           [3,4], 
           [3,5], 
           [4,5], 
           [5,6]],

  NumArcs = Arcs.length,

  % durations (of the dependency arcs)
  Dur = [9,6,0,7,8,10,12],
  SumDur = sum(Dur),

  % decision variables
  Time = new_list(NumNodes),
  Time :: 0..SumDur,

  Z #= Time[NumNodes] - Time[1],

  
  % calculate the start times
  foreach(I in 1..NumArcs)
      Time[Arcs[I,2]] #>= Time[Arcs[I,1]] + Dur[I]
  end,

  solve($[min(Z)], Time),

  println(z=Z),
  println(time=Time),

  nl.