PROLOG ASSIGNMENT 3 (SAU).

-
path(A, Z, Graph, Path) :-
          path1(A,[Z],Graph,Path).

path1(A, [A|Path1], Graph, [A|Path1]).
path1(A, [Y|Path1], graph(Nodes, Edges), Path) :-
                (member(e(X,Y), Edges); member(e(Y,X), Edges)),
                not (member(X, Path1)),
                       path1(A, [X,Y|Path1], graph(Nodes, Edges), Path).
member(X, [X|L]).
member(X, [Y|L]) :-
    member(X, L).


eq_set(P, N) :-
    subset(P,N),
    subset(N,P).

subset([],[]).
subset( [X|Set],Subset)  :-            % X not in subset
  subset(Set,Subset).
subset( [X|Set],[X|Subset])  :-      % X included in subset
  subset(Set,Subset).


hpath(graph(Nodes, Edges), Path) :-
                  path(A, Z, graph(Nodes, Edges), Path),
                  eq_set(Path, Nodes).

connected(graph(Nodes,Edges)):-
            hpath(graph(Nodes, Edges), Path).
Run:
sujit@sujit-desktop:~/sunil/prolog$ yap
% Restoring file /usr/lib/Yap/startup
YAP version Yap-5.1.3
   ?- [tr].
 % consulting /home/sujit/sunil/prolog/tr.pl...
 % consulted /home/sujit/sunil/prolog/tr.pl in module user, 0 msec 3592 bytes
yes
   ?-  path(a,d,graph([a,b,c,d],[e(a,b),e(b,d),e(b,c),e(c,d)]),P).
P = [a,b,d] ? ;
P = [a,b,c,d] ? ;
no
   ?-  connected(graph([a,b,c,d],[e(a,b),e(b,d),e(b,c),e(c,d)])).
yes
   ?-  connected(graph([a,b,c,d],[e(a,b),e(b,c),e(c,d)])).
yes
   ?-  connected(graph([a,b,c,d],[e(a,b),e(b,d),e(b,c)])).
no
   ?-  path(graph([a,b,c,d],[e(a,b),e(b,d),e(b,c),e(c,d)]),P).
no
   ?-  hpath(graph([a,b,c,d],[e(a,b),e(b,d),e(b,c),e(c,d)]),P).
P = [a,b,c,d] ? ;
no
   ?-

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