/*
 * @(#) ari_lib.txt - Sample library in Prolog.
 * (c) 1997 Ivan Maidanski <ivmai@chat.ru> http://ivmai.chat.ru
 * Freeware program source. All rights reserved.
 **
 * Language: Prolog
 * Tested with: Arity Prolog v1.0
 * Last modified: 1997-04-11 16:30:00 GMT+04:00
 */

max(X,Y,X):-X>=Y,!.
max(X,Y,Y).

min(X,Y,X):-X=<Y,!.
min(X,Y,Y).

even(0).
even(X):-X>0,XX is X-2,even(XX).

is_list([_]).

list_len([],0).
list_len([_|V],L):-list_len(V,LL),inc(LL,L).

get_elem([X|V],1,X).
get_elem([X|V],N,Y):-dec(N,NN),get_elem(V,NN,Y).

sub_list(U,[],[]).
sub_list(U,[N|V],[X|W]):-sub_list(U,V,W),get_elem(U,N,X).

del_elem([X|V],1,V).
del_elem([X|U],N,[X|V]):-dec(N,NN),del_elem(U,NN,V).

del_all_matches([],X,[]).
del_all_matches([X|U],X,V):-!,del_all_matches(U,X,V).
del_all_matches([Y|U],X,[Y|V]):-del_all_matches(U,X,V).

del_all_elems_reps([],[]).
del_all_elems_reps([X|U],[X|V]):-del_all_matches(U,X,W),
                                 del_all_elems_reps(W,V).

get_elem_count([],X,0).
get_elem_count([X|V],X,C):-!,get_elem_count(V,X,CC),inc(CC,C).
get_elem_count([_|V],X,C):-get_elem_count(V,X,C).

list_elem_sum([],0).
list_elem_sum([X|V],S):-list_elem_sum(V,SS),S is SS+X.

get_list_all_even_elem([],[]).
get_list_all_even_elem([X|U],[X|V]):-even(X),!,get_list_all_even_elem(U,V).
get_list_all_even_elem([X|U],V):-get_list_all_even_elem(U,V).

get_list_all_even_pos_elem([],[]).
get_list_all_even_pos_elem([X],[]).
get_list_all_even_pos_elem([X,Y|U],[Y|V]):-get_list_all_even_pos_elem(U,V).

max_elem([X],X).
max_elem([X|V],Y):-max_elem(V,Z),max(X,Z,Y).

min_elem([X],X).
min_elem([X|V],Y):-min_elem(V,Z),min(X,Z,Y).

reverse_list(U,V):-reverse_list_temp(U,V,[]).
reverse_list_temp([],V,V).
reverse_list_temp([X|U],V,W):-reverse_list_temp(U,V,[X|W]).

concat_list([],V,V).
concat_list([X|U],V,[X|W]):-concat_list(U,V,W).

sort_list([],[]).
sort_list([X|U],V):-sort_list(U,W),sort_list_temp(X,W,V).
sort_list_temp(X,[],[X]).
sort_list_temp(X,[Y|U],[X,Y|U]):-X<Y,!.
sort_list_temp(X,[Y|U],[Y|V]):-sort_list_temp(X,U,V).

all_list_exchanges([],[]).
all_list_exchanges([X|U],V):-all_list_exchanges(U,W),
                             all_list_exchanges_temp(X,W,V).
all_list_exchanges_temp(X,V,[X|V]).
all_list_exchanges_temp(X,[Y|U],[Y|V]):-all_list_exchanges_temp(X,U,V).

all_list_sublists([],[]).
all_list_sublists([X|U],V):-all_list_sublists(U,V).
all_list_sublists([X|U],[X|V]):-all_list_sublists(U,V).

is_set(V):-del_all_elems_reps(V,V).

list_to_set(U,V):-del_all_elems_reps(U,W),sort_list(W,V).

is_in_set(X,V):-get_elem_count(V,X,C),C>0.

is_subset(U,V):-cross_set(U,V,U).

all_subsets(U,V):-all_list_sublists(U,V).

set_range(H,L,[]):-H>L,!.
set_range(L,H,[L|V]):-inc(L,LL),set_range(LL,H,V).

join_set(U,V,W):-concat_list(U,V,WW),del_all_elems_reps(WW,W).

cross_set(U,V,W):-substract_set(U,V,WW),substract_set(U,WW,W).

substract_set(U,[],U).
substract_set(U,[X|V],W):-del_all_matches(U,X,WW),substract_set(WW,V,W).

mul_set([],U,[]).
mul_set([X],[],[]):-!.
mul_set([X],[Y|V],[[X,Y]|W]):-mul_set([X],V,W),!.
mul_set([X|U],V,W):-mul_set([X],V,S),mul_set(U,V,T),join_set(S,T,W).