%

%--------------------------------------%
%         Example network plans        %
%--------------------------------------%


% first network plan; 6 solutions for N = 3
%                     no solution for N < 3
ac1(a, b).
ac1(a, c).
ac1(a, d).
ac1(a, e).
ac1(a, f).
ac1(a, g).
ac1(b, c).
ac1(c, d).
ac1(d, e).
ac1(e, f).
ac1(f, g).
ac1(g, b).
ac1(g, h).
ac1(h, b).


% second network plan; 6 solutions for N = 3
%                      no solution for N < 3
ac2(a, b).
ac2(b, c).
ac2(c, d).
ac2(d, a).
ac2(g, a).
ac2(g, b).
ac2(g, c).
ac2(g, d).


% third network plan; 18 solutions for N = 3
%                      2 solutions for N = 2
%                     no solutions for N < 2
ac3(a, b).
ac3(b, c).
ac3(c, d).
ac3(d, a).

%--------------------------------------%
%           Helper functions           %
%--------------------------------------%

% counts the number of solutions for given N
% and a selected network plan in `acOverlap`
countSolutions(N, Count) :-
    findall(_X, channelise(N, _XS), Res),
    length(Res, Count).

% makes access point overlapping symmetric
% replace _ with the index of a target network plan
acOverlap(X, Y) :- ac1(X, Y).
acOverlap(X, Y) :- ac1(Y, X).


% unifies all access points to ACS
accessPoints(ACS) :- setof(X, Y^acOverlap(X, Y), ACS).

%--------------------------------------%
%             Your solution            %
%--------------------------------------%

% implement channelise(?N, -CS).
channelise(_N, []).