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/*

Traffic lights problem in B-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.
"""

Model created by Hakan Kjellerstrand, hakank@gmail.com
See also my B-Prolog page: http://www.hakank.org/bprolog/

*/

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

go :-
findall([V,P], traffic_lights(V,P), L),
print_results(L),
nl,

writeln('Using table constraint:'),
findall([V2,P2], traffic_lights_table(V2,P2), L2),
print_results(L2),
nl.

print_results(L) :-
foreach([V,P] in L,
(foreach(I in 1..4,[VI,PI,VC,PC],
(
VI @= V[I],
PI @= P[I],
tr(VC,VI),
tr(PC,PI),
format("~q ~q ",[VC,PC])
)
),
nl
)
).

traffic_lights(V, P) :-
N  = 4,

length(V, N),
V :: 1..N,
length(P, N),
P :: 1..N,
foreach(I in 1..N, J in 1..N,[JJ,VI,PI,VJ,PJ],
(JJ is (1+I) mod N,
J #= JJ ->
VI @= V[I], PI @= P[I],
VJ @= V[J], PJ @= P[J],
check_allowed(VI, PI, VJ, PJ)
;
true
)

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

check_allowed(VI, PI, VJ, PJ) :-
foreach(El in [VI, PI, VJ, PJ], ac(L1,[]),[C],
(tr(C,El), L1^1 = [C|L1^0])
),
reverse(L1,L),
allowed(L).

%
% Using table Allowed
%
traffic_lights_table(V, P) :-
N  = 4,

% allowed/1 as a table (translated)
Allowed = [(1,1,3,3),
(2,1,4,1),
(3,3,1,1),
(4,1,2,1)],

length(V, N),
V :: 1..N,
length(P, N),
P :: 1..N,
foreach(I in 1..N, J in 1..N,[JJ,VI,PI,VJ,PJ],
(JJ is (1+I) mod N,
J #= JJ ->
VI @= V[I], PI @= P[I],
VJ @= V[J], PJ @= P[J],
% Table constraint
(VI, PI, VJ, PJ) in Allowed
;
true
)

),

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

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

% The allowed combinations
allowed([r,r,g,g]).
allowed([ry,r,y,r]).
allowed([g,g,r,r]).
allowed([y,r,ry,r]).