/*

Traffic lights problem in Picat.

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

*/

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

import cp.

main => go.

go =>
L = findall([V,P], $traffic_lights(V,P)), writeln(L), print_results(L), nl, writef("Using table constraint:\n"), L2 = findall([V2,P2],$traffic_lights_table(V2,P2)),
print_results(L2),
nl.

print_results(L) =>
foreach([V,P] in L)
foreach(I in 1..4)
tr(VC,V[I]),
tr(PC,P[I]),
writef("%w %w ",VC,PC)
end,
nl
end.

traffic_lights(V, P) =>
N  = 4,

V = new_list(N),
V :: 1..N,
P = new_list(N),
P :: 1..N,
Allowed = [[r,r,g,g],
[ry,r,y,r],
[g,g,r,r],
[y,r,ry,r]],

foreach(I in 1..N, J in 1..N)
JJ = (1+I) mod N,
if J == JJ then
check_allowed(V[I], P[I], V[J], P[J])
% check_allowed2(V[I], P[I], V[J], P[J], Allowed)
end
end,

Vars = V ++ P,
solve(Vars),
writeln(vars=Vars).

check_allowed(VI, PI, VJ, PJ) ?=>
L1 = [],
foreach(El in [VI, PI, VJ, PJ])
if tr(C,El) then
L1 := L1 ++ [C]
end
end,
L = L1,

allowed(L).

check_allowed2(VI, PI, VJ, PJ, Allowed) ?=>
L1 = [],
foreach(El in [VI, PI, VJ, PJ])
writeln(el=El),
if tr(C,El) then
L1 := L1 ++ [C]
end
end,
L = L1,
writeln(l=L),
writef("before element\n"),
element(C,Allowed,L),
writef("after element\n"),
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)],

V = new_list(N),
V :: 1..N,
P = new_list(N),
P :: 1..N,
foreach(I in 1..N, J in 1..N)
JJ = (1+I) mod N,
if J #= JJ then
VI = V[I], PI = P[I],
VJ = V[J], PJ = P[J],
% Table constraint
table_in((VI, PI, VJ, PJ), Allowed)
end
end,

Vars = V ++ P,
solve(Vars).

% Note: I'm not sure this is the best
%       representation...
tr(L,A) ?=> L=r,  A=1.
tr(L,A) ?=> L=ry, A=2.
tr(L,A) ?=> L=g,  A=3.
tr(L,A)  => L=y,  A=4.

% The allowed combinations
allowed(A) ?=> A = [r,r,g,g].
allowed(A) ?=> A = [ry,r,y,r].
allowed(A) ?=> A = [g,g,r,r].
allowed(A)  => A = [y,r,ry,r].