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% twentyfour.pl -- the 24 problem in prolog
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% Submission site id(s):
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% Comments:


% some "nice" prolog settings...  see assignment 8's
% 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)]).


% here are several predicates that may help with this problem
% (we wrote/looked at these together in class)

% remove an element (which much be present) from a list...
removeOne(X,[X|R],R).
removeOne(X,[F|R],[F|S]) :- removeOne(X,R,S).

% generates permutations of the first input's list
perm([X|Y],Z) :- perm(Y,W), removeOne(X,Z,W).
perm([],[]).

% splits the first argument's list into subsets, i.e.,
% sublists in which the order of elements may vary
split( List, A, B ) :-
   perm( List, L2 ),
   append( A, B, L2 ).  %  note that A and/or B can be [] here!

% this is the eval predicate that evaluates our "24-trees"
% the "nonvar" checks make sure that A and B are both bound to values
% this prevents some prolog implementations of searching for bindings
% for A and B (we only want to search for R).
%
eval(R, R) :- number(R).
eval(['+', A, B], R) :- nonvar(A), nonvar(B),
	eval(A, AR), eval(B, BR), R is AR + BR.
eval(['*', A, B], R) :- nonvar(A), nonvar(B),
	eval(A, AR), eval(B, BR), R is AR * BR.
eval(['-', A, B], R) :- nonvar(A), nonvar(B),
	eval(A, AR), eval(B, BR), R is AR - BR.
eval(['/', A, B], R) :- nonvar(A), nonvar(B),
	eval(A, AR), eval(B, BR), BR\==0, R is AR // BR.


% You will need to write the solve predicate here:
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%   solve(Ops, Values, Result, Tree)
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