016: Traffic Lights

# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
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"""

  Traffic lights problem in Google CP Solver.

  CSPLib problem 16
  http://www.csplib.org/Problems/prob016
  '''
  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.

  '''

  Note: In this model we use only the constraint solver.AllowedAssignments().


  Compare with these models:
  * MiniZinc: http://www.hakank.org/minizinc/traffic_lights.mzn
  * Comet   : http://www.hakank.org/comet/traffic_lights.co
  * ECLiPSe : http://www.hakank.org/eclipse/traffic_lights.ecl
  * Gecode  : http://hakank.org/gecode/traffic_lights.cpp
  * SICStus : http://hakank.org/sicstus/traffic_lights.pl


  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

"""

import string, sys

from constraint_solver import pywrapcp


def main(base=10, start=1, len1=1, len2=4):

    # Create the solver.
    solver = pywrapcp.Solver('Traffic lights')

    #
    # data
    #
    n = 4
    r, ry, g, y = range(n)
    lights = ["r", "ry", "g", "y"]

    # The allowed combinations
    allowed = pywrapcp.IntTupleSet(4)
    allowed.InsertAll([(r,r,g,g),
                       (ry,r,y,r),
                       (g,g,r,r),
                       (y,r,ry,r)])


    #
    # declare variables
    #
    V = [solver.IntVar(0, n-1, 'V[%i]' % i) for i in range(n)]
    P = [solver.IntVar(0, n-1, 'P[%i]' % i) for i in range(n)]

    #
    # constraints
    #
    for i in range(n):
        for j in range(n):
            if j == (1+i) % n:
                solver.Add(solver.AllowedAssignments((V[i], P[i], V[j], P[j]), allowed))

    #
    # Search and result
    #
    db = solver.Phase(V + P,
                 solver.INT_VAR_SIMPLE,
                 solver.INT_VALUE_DEFAULT)

    solver.NewSearch(db)
    num_solutions = 0
    while solver.NextSolution():
        for i in range(n):
            print "%+2s %+2s" % (lights[V[i].Value()], lights[P[i].Value()]),
        print
        num_solutions += 1

    solver.EndSearch()

    print
    print "num_solutions:", num_solutions
    print "failures:", solver.Failures()
    print "branches:", solver.Branches()
    print "WallTime:", solver.WallTime()
    print


if __name__ == '__main__':
    main()