016: Traffic Lights

% 
% Traffic lights problem in MiniZinc.
% 
% 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: This is the same as http://www.hakank.org/minizinc/taffic_lights.mzn
% except that it use the global constraint table.

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

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

include "globals.mzn";

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

set of int: Cars = {r,ry,g,y};
set of int: Pedestrians = {r,g};

array[1..4, 1..4] of Cars: allowed;

array[1..n] of var Cars: V;
array[1..n] of var Pedestrians: P;


solve satisfy;

constraint
 forall(i in 1..n, j in 1..n where j = (1+i) mod 4)  (
   table([V[i], P[i], V[j], P[j]], allowed)
 )
;


allowed = array2d(1..4, 1..4, 
[
 r,r,g,g, 
 ry,r,y,r, 
 g,g,r,r, 
 y,r,ry,r
]);


% output [
%  "V: ", show(V), "\nP: ", show(P), "\n"
% ];
output [
 show(V[i]) ++ " " ++ show(P[i]) ++ " "
  | i in 1..n
] ++ ["\n"];