%% clique.lp -- ASP solution to additional exercise for Chapter 6, finding
%% cliques in a graph.
%% Last Modified: 3/26/14
%% A clique is a subset of a graph such that each of its vertices 
%% is connected by an edge to all the other vertices in the clique. 
%% Note that each node of a graph is a clique of size 1 and that the empty
%% set is also a clique.
%% Write an ASP program which finds all cliques in a given undirected graph; 
%% i.e., each answer set will correspond to one clique in the graph.

%% Bonus: Look up the #count aggregate in the manual for your 
%% solver of choice and use it to modify your program to only find
%% cliques of size >= 3.


in_clique(N) | -in_clique(N) :- node(N).

:- in_clique(N1),
   in_clique(N2),
   N1 != N2,
   not edge(N1,N2).
   
%% Bonus:
%% :- #count{N : in_clique(N)} < 3.

%% Graph description (change at will):

node(1..5).

edge(1,2).
edge(2,3).
edge(3,4).
edge(3,5).
edge(4,5).

%% The graph is undirected:
edge(N1,N2) :-
     edge(N2,N1).

%% Output formating of clingo:
%#show in_clique/1.
%% or use -pfilter=in_clique as an inline option with dlv