%% lists.pl
%%
%% Author(s):
%%
%% CS 60 Hw 8, part 2
%%
%%


% some "nice" prolog settings...  see assignment 
% description for the details on what these do
% -- but it's not crucial to know the details of these Prolog internals
:- set_prolog_flag( prompt_alternatives_on, groundness ).
:- set_prolog_flag(toplevel_print_options, [quoted(true), 
     portray(true), attributes(portray), max_depth(999), priority(699)]).


%% a couple of example predicates that might be helpful...

%
% member( E, L ) should be true if E is a top-level member of the list L
% member should work when E is a variable or bound; L should be bound
%
member( E, [E|_] ).
member( E, [_|R] ) :- member( E, R ).


%
% reverse( L, Rev ) should be true if Rev is the reverse of the list L
% reverse should work when Rev is a variable or bound; L should be bound
%
reverse( [], [] ).   % base case ~ they don't always involve [] in Prolog!
reverse( [F|R], Rev ) :- reverse( R, Tmp ), append( Tmp, [F], Rev ).



%% Here are commented-out placeholders for this week's predicates...

%% Be sure to comment each predicate your write.



%% removeOne( E, L, NewL )


%% count( E, L, N )


%% find( Pattern, Target, Index )


%% depth( E, Tree, N )


% a helper predicate to define a tree
tree1( [ 42, [ 20, [10, [5, [], []], [18, [], []]], [] ],
             [ 100, [67, [50, [], []], []], [150, [], [2009, [], []]] ] ] ).


%% insert( E, Tree, NewTree )



%% path( A, B, Graph, Path )

% a helper predicate to define a graph
graph1(  [ [a,b], [b,c], [c,d], [b,w], [w,x], [x,z], [b,z] ] ).