/*

Traffic lights problem in SICStus Prolog.

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.

"""

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

Model created by Hakan Kjellerstrand, hakank@gmail.com

*/

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

:-use_module(library(clpfd)).
:-use_module(library(lists)).

go :-
findall([V,P], traffic_lights(V,P), L),
( foreach([V,P], L) do
( for(I,1,4), param(V,P) do
element(I,V,VI),
element(I,P,PI),
tr(VC,VI),
tr(PC,PI),
format('~w ~w ',[VC,PC])
),
nl
).

traffic_lights(V, P) :-
N  = 4,
length(V, N),
domain(V,1,N),
length(P, N),
domain(P,1,N),

( for(I,1,N),
param(N,V,P) do
( for(J,1,N),
param(N,V,P,I) do
JJ is (1+I) mod N,
J #= JJ ->
element(I,V,VI),
element(I,P,PI),
element(J,V,VJ),
element(J,P,PJ),
check_allowed(VI, PI, VJ, PJ)
% check_allowed_table(VI, PI, VJ, PJ)
;
true
)
),

append(V,P,Vars),
labeling([],Vars).

check_allowed(VI, PI, VJ, PJ) :-
( foreach(El,[VI, PI, VJ, PJ]),
fromto(L,[C|In],In,[]) do
E #= El,
tr(C,E)
),
allowed(L).

% Ah, table/2 needs integers...
% check_allowed_table(VI, PI, VJ, PJ) :-
%        allowed_table(Table),
%        table([VI, PI, VJ, PJ],Table).

tr(r,1).
tr(ry,2).
tr(g,3).
tr(y,4).

allowed([r,r,g,g]).
allowed([ry,r,y,r]).
allowed([g,g,r,r]).
allowed([y,r,ry,r]).

allowed_table([[r,r,g,g],
[ry,r,y,r],
[g,g,r,r],
[y,r,ry,r]]).