016: Traffic Lights

/*

  Traffic lights problem in Comet.

  
  CSPLib problem 16
  http://www.cs.st-andrews.ac.uk/~ianm/CSPLib/prob/prob016/index.html
  """
  Specification:
  Consider a four way traffic junction with eight traffic lights. Four of the traffic 
  lights are for the vehicles and can be represented by the variables V1 to V4 with domains 
  {r,ry,g,y} (for red, red-yellow, green and yellow). The other four traffic lights are 
  for the pedestrians and can be represented by the variables P1 to P4 with domains {r,g}.
  
  The constraints on these variables can be modelled by quaternary constraints on 
  (Vi, Pi, Vj, Pj ) for 1<=i<=4, j=(1+i)mod 4 which allow just the tuples 
  {(r,r,g,g), (ry,r,y,r), (g,g,r,r), (y,r,ry,r)}.
 
  It would be interesting to consider other types of junction (e.g. five roads 
  intersecting) as well as modelling the evolution over time of the traffic light sequence. 
  ...
 
  Results
  Only 2^2 out of the 2^12 possible assignments are solutions.
  
  (V1,P1,V2,P2,V3,P3,V4,P4) = 
     {(r,r,g,g,r,r,g,g), (ry,r,y,r,ry,r,y,r), (g,g,r,r,g,g,r,r), (y,r,ry,r,y,r,ry,r)}
     [(1,1,3,3,1,1,3,3), ( 2,1,4,1, 2,1,4,1), (3,3,1,1,3,3,1,1), (4,1, 2,1,4,1, 2,1)}
 
 
  The problem has relative few constraints, but each is very tight. Local propagation 
  appears to be rather ineffective on this problem.
    
  """
  
  Compare with the MiniZinc model http://www.hakank.org/minizinc/traffic_lights.mzn


  This Comet model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also, see my Comet page: http://www.hakank.org/comet 

 */

// Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/

import cotfd;

int t0 = System.getCPUTime();

int n  = 4;
int r  = 1; // red
int ry = 2; // red-yellow
int g  = 3; // green
int y  = 4; // yellow

int allowed[1..n, 1..n] = 
  [
   [r,r,g,g], 
   [ry,r,y,r], 
   [g,g,r,r], 
   [y,r,ry,r]
   ];


Solver<CP> m();
var<CP>{int} V[1..n](m, 1..n);
var<CP>{int} P[1..n](m, 1..n);

Integer num_solutions(0);
// explore<m> {
exploreall<m> {

  // TODO: * using table/FunctionTable?
  forall(i in 1..n, j in 1..n : j == (1+i) % n) {
    var<CP>{int} a(m, 1..n);
    m.post(V[i] == allowed[a,1]);
    m.post(P[i] == allowed[a,2]);
    m.post(V[j] == allowed[a,3]);
    m.post(P[j] == allowed[a,4]);
  }


} using {
      
  labelFF(m);
  num_solutions := num_solutions + 1;

  forall(i in 1..4)
    cout << V[i] << " " << P[i] << " ";
  cout << endl;
}


cout << "\nnum_solutions: " << num_solutions << endl;
    
int t1 = System.getCPUTime();
cout << "time:      " << (t1-t0) << endl;
cout << "#choices = " << m.getNChoice() << endl;
cout << "#fail    = " << m.getNFail() << endl;
cout << "#propag  = " << m.getNPropag() << endl;