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yap-6.3/library/rbtrees.yap

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/*
This code implements Red-Black trees as described in:
"Introduction to Algorithms", Second Edition
Cormen, Leiserson, Rivest, and Stein,
MIT Press
Author: Vitor Santos Costa
*/
:- module(rbtrees,
[rb_new/1,
rb_empty/1,
rb_lookup/3,
rb_update/4,
rb_update/5,
rb_apply/4,
rb_lookupall/3,
rb_insert/4,
rb_delete/3,
rb_delete/4,
rb_visit/2,
rb_visit/3,
rb_keys/2,
rb_keys/3,
rb_map/2,
rb_map/3,
rb_partial_map/4,
rb_clone/3,
rb_clone/4,
rb_min/3,
rb_max/3,
rb_del_min/4,
rb_del_max/4,
rb_next/4,
rb_previous/4,
list_to_rbtree/2,
ord_list_to_rbtree/2,
is_rbtree/1,
rb_size/2,
rb_in/3
]).
:- meta_predicate rb_map(+,:,-), rb_partial_map(+,+,:,-), rb_apply(+,+,:,-).
% create an empty tree.
rb_new(t(Nil,Nil)) :- Nil = black([],[],[],[]).
rb_empty(t(Nil,Nil)) :- Nil = black([],[],[],[]).
rb_new(K,V,t(Nil,black(Nil,K,V,Nil))) :- Nil = black([],[],[],[]).
rb_lookup(Key, Val, t(_,Tree)) :-
lookup(Key, Val, Tree).
lookup(_, _, black([],_,_,[])) :- !, fail.
lookup(Key, Val, Tree) :-
arg(2,Tree,KA),
compare(Cmp,KA,Key),
lookup(Cmp,Key,Val,Tree).
lookup(>, K, V, Tree) :-
arg(1,Tree,NTree),
lookup(K, V, NTree).
lookup(<, K, V, Tree) :-
arg(4,Tree,NTree),
lookup(K, V, NTree).
lookup(=, _, V, Tree) :-
arg(3,Tree,V).
rb_min(t(_,Tree), Key, Val) :-
min(Tree, Key, Val).
min(red(black([],_,_,_),Key,Val,_), Key, Val) :- !.
min(black(black([],_,_,_),Key,Val,_), Key, Val) :- !.
min(red(Right,_,_,_), Key, Val) :-
min(Right,Key,Val).
min(black(Right,_,_,_), Key, Val) :-
min(Right,Key,Val).
rb_max(t(_,Tree), Key, Val) :-
max(Tree, Key, Val).
max(red(_,Key,Val,black([],_,_,_)), Key, Val) :- !.
max(black(_,Key,Val,black([],_,_,_)), Key, Val) :- !.
max(red(_,_,_,Left), Key, Val) :-
max(Left,Key,Val).
max(black(_,_,_,Left), Key, Val) :-
max(Left,Key,Val).
rb_next(t(_,Tree), Key, Next, Val) :-
next(Tree, Key, Next, Val, []).
next(black([],_,_,[]), _, _, _, _) :- !, fail.
next(Tree, Key, Next, Val, Candidate) :-
arg(2,Tree,KA),
arg(3,Tree,VA),
compare(Cmp,KA,Key),
next(Cmp, Key, KA, VA, Next, Val, Tree, Candidate).
next(>, K, KA, VA, NK, V, Tree, _) :-
arg(1,Tree,NTree),
next(NTree,K,NK,V,KA-VA).
next(<, K, _, _, NK, V, Tree, Candidate) :-
arg(4,Tree,NTree),
next(NTree,K,NK,V,Candidate).
next(=, _, _, _, NK, Val, Tree, Candidate) :-
arg(4,Tree,NTree),
(
min(NTree, NK, Val) ->
true
;
Candidate = NK-Val
).
rb_previous(t(_,Tree), Key, Previous, Val) :-
previous(Tree, Key, Previous, Val, []).
previous(black([],_,_,[]), _, _, _, _) :- !, fail.
previous(Tree, Key, Previous, Val, Candidate) :-
arg(2,Tree,KA),
arg(3,Tree,VA),
compare(Cmp,KA,Key),
previous(Cmp, Key, KA, VA, Previous, Val, Tree, Candidate).
previous(>, K, _, _, NK, V, Tree, Candidate) :-
arg(1,Tree,NTree),
previous(NTree,K,NK,V,Candidate).
previous(<, K, KA, VA, NK, V, Tree, _) :-
arg(4,Tree,NTree),
previous(NTree,K,NK,V,KA-VA).
previous(=, _, _, _, K, Val, Tree, Candidate) :-
arg(1,Tree,NTree),
(
max(NTree, K, Val) ->
true
;
Candidate = K-Val
).
rb_update(t(Nil,OldTree), Key, OldVal, Val, t(Nil,NewTree)) :-
update(OldTree, Key, OldVal, Val, NewTree).
rb_update(t(Nil,OldTree), Key, Val, t(Nil,NewTree)) :-
update(OldTree, Key, _, Val, NewTree).
update(black(Left,Key0,Val0,Right), Key, OldVal, Val, NewTree) :-
Left \= [],
compare(Cmp,Key0,Key),
(Cmp == = ->
OldVal = Val0,
NewTree = black(Left,Key0,Val,Right)
;
Cmp == > ->
NewTree = black(NewLeft,Key0,Val0,Right),
update(Left, Key, OldVal, Val, NewLeft)
;
NewTree = black(Left,Key0,Val0,NewRight),
update(Right, Key, OldVal, Val, NewRight)
).
update(red(Left,Key0,Val0,Right), Key, OldVal, Val, NewTree) :-
compare(Cmp,Key0,Key),
(Cmp == = ->
OldVal = Val0,
NewTree = red(Left,Key0,Val,Right)
;
Cmp == > ->
NewTree = red(NewLeft,Key0,Val0,Right),
update(Left, Key, OldVal, Val, NewLeft)
;
NewTree = red(Left,Key0,Val0,NewRight),
update(Right, Key, OldVal, Val, NewRight)
).
rb_apply(t(Nil,OldTree), Key, Goal, t(Nil,NewTree)) :-
apply(OldTree, Key, Goal, NewTree).
%apply(black([],_,_,[]), _, _, _) :- !, fail.
apply(black(Left,Key0,Val0,Right), Key, Goal, black(NewLeft,Key0,Val,NewRight)) :-
Left \= [],
compare(Cmp,Key0,Key),
(Cmp == (=) ->
NewLeft = Left,
NewRight = Right,
call(Goal,Val0,Val)
;
Cmp == (>) ->
NewRight = Right,
Val = Val0,
apply(Left, Key, Goal, NewLeft)
;
NewLeft = Left,
Val = Val0,
apply(Right, Key, Goal, NewRight)
).
apply(red(Left,Key0,Val0,Right), Key, Goal, red(NewLeft,Key0,Val,NewRight)) :-
compare(Cmp,Key0,Key),
(Cmp == (=) ->
NewLeft = Left,
NewRight = Right,
call(Goal,Val0,Val)
;
Cmp == (>) ->
NewRight = Right,
Val = Val0,
apply(Left, Key, Goal, NewLeft)
;
NewLeft = Left,
Val = Val0,
apply(Right, Key, Goal, NewRight)
).
rb_in(Key, Val, t(_,T)) :-
var(Key), !,
enum(Key, Val, T).
rb_in(Key, Val, t(_,T)) :-
lookup(Key, Val, T).
enum(Key, Val, black(L,K,V,R)) :-
L \= [],
enum_cases(Key, Val, L, K, V, R).
enum(Key, Val, red(L,K,V,R)) :-
enum_cases(Key, Val, L, K, V, R).
enum_cases(Key, Val, L, _, _, _) :-
enum(Key, Val, L).
enum_cases(Key, Val, _, Key, Val, _).
enum_cases(Key, Val, _, _, _, R) :-
enum(Key, Val, R).
rb_lookupall(Key, Val, t(_,Tree)) :-
lookupall(Key, Val, Tree).
lookupall(_, _, black([],_,_,[])) :- !, fail.
lookupall(Key, Val, Tree) :-
arg(2,Tree,KA),
compare(Cmp,KA,Key),
lookupall(Cmp,Key,Val,Tree).
lookupall(>, K, V, Tree) :-
arg(4,Tree,NTree),
rb_lookupall(K, V, NTree).
lookupall(=, _, V, Tree) :-
arg(3,Tree,V).
lookupall(=, K, V, Tree) :-
arg(1,Tree,NTree),
lookupall(K, V, NTree).
lookupall(<, K, V, Tree) :-
arg(1,Tree,NTree),
lookupall(K, V, NTree).
%
% Tree insertion
%
% We don't use parent nodes, so we may have to fix the root.
%
rb_insert(t(Nil,Tree0),Key,Val,t(Nil,Tree)) :-
insert(Tree0,Key,Val,Nil,Tree).
insert(Tree0,Key,Val,Nil,Tree) :-
insert2(Tree0,Key,Val,Nil,TreeI,_),
fix_root(TreeI,Tree).
%
% make sure the root is always black.
%
fix_root(black(L,K,V,R),black(L,K,V,R)).
fix_root(red(L,K,V,R),black(L,K,V,R)).
%
% Cormen et al present the algorithm as
% (1) standard tree insertion;
% (2) from the viewpoint of the newly inserted node:
% partially fix the tree;
% move upwards
% until reaching the root.
%
% We do it a little bit different:
%
% (1) standard tree insertion;
% (2) move upwards:
% when reaching a black node;
% if the tree below may be broken, fix it.
% We take advantage of Prolog unification
% to do several operations in a single go.
%
%
% actual insertion
%
insert2(black([],[],[],[]), K, V, Nil, T, Status) :- !,
T = red(Nil,K,V,Nil),
Status = not_done.
insert2(red(L,K0,V0,R), K, V, Nil, red(NL,K0,V0,NR), Flag) :-
( K @< K0 ->
NR = R,
insert2(L, K, V, Nil, NL, Flag)
;
NL = L,
insert2(R, K, V, Nil, NR, Flag)
).
insert2(black(L,K0,V0,R), K, V, Nil, NT, Flag) :-
( K @< K0 ->
insert2(L, K, V, Nil, IL, Flag0),
fix_left(Flag0, black(IL,K0,V0,R), NT, Flag)
;
insert2(R, K, V, Nil, IR, Flag0),
fix_right(Flag0, black(L,K0,V0,IR), NT, Flag)
).
%
% How to fix if we have inserted on the left
%
fix_left(done,T,T,done) :- !.
fix_left(not_done,Tmp,Final,Done) :-
fix_left(Tmp,Final,Done).
%
% case 1 of RB: just need to change colors.
%
fix_left(black(red(Al,AK,AV,red(Be,BK,BV,Ga)),KC,VC,red(De,KD,VD,Ep)),
red(black(Al,AK,AV,red(Be,BK,BV,Ga)),KC,VC,black(De,KD,VD,Ep)),
not_done) :- !.
fix_left(black(red(red(Al,KA,VA,Be),KB,VB,Ga),KC,VC,red(De,KD,VD,Ep)),
red(black(red(Al,KA,VA,Be),KB,VB,Ga),KC,VC,black(De,KD,VD,Ep)),
not_done) :- !.
%
% case 2 of RB: got a knee so need to do rotations
%
fix_left(black(red(Al,KA,VA,red(Be,KB,VB,Ga)),KC,VC,De),
black(red(Al,KA,VA,Be),KB,VB,red(Ga,KC,VC,De)),
done) :- !.
%
% case 3 of RB: got a line
%
fix_left(black(red(red(Al,KA,VA,Be),KB,VB,Ga),KC,VC,De),
black(red(Al,KA,VA,Be),KB,VB,red(Ga,KC,VC,De)),
done) :- !.
%
% case 4 of RB: nothig to do
%
fix_left(T,T,done).
%
% How to fix if we have inserted on the right
%
fix_right(done,T,T,done) :- !.
fix_right(not_done,Tmp,Final,Done) :-
fix_right(Tmp,Final,Done).
%
% case 1 of RB: just need to change colors.
%
fix_right(black(red(Ep,KD,VD,De),KC,VC,red(red(Ga,KB,VB,Be),KA,VA,Al)),
red(black(Ep,KD,VD,De),KC,VC,black(red(Ga,KB,VB,Be),KA,VA,Al)),
not_done) :- !.
fix_right(black(red(Ep,KD,VD,De),KC,VC,red(Ga,Ka,Va,red(Be,KB,VB,Al))),
red(black(Ep,KD,VD,De),KC,VC,black(Ga,Ka,Va,red(Be,KB,VB,Al))),
not_done) :- !.
%
% case 2 of RB: got a knee so need to do rotations
%
fix_right(black(De,KC,VC,red(red(Ga,KB,VB,Be),KA,VA,Al)),
black(red(De,KC,VC,Ga),KB,VB,red(Be,KA,VA,Al)),
done) :- !.
%
% case 3 of RB: got a line
%
fix_right(black(De,KC,VC,red(Ga,KB,VB,red(Be,KA,VA,Al))),
black(red(De,KC,VC,Ga),KB,VB,red(Be,KA,VA,Al)),
done) :- !.
%
% case 4 of RB: nothing to do.
%
fix_right(T,T,done).
%
% simplified processor
%
%
pretty_print(T) :-
pretty_print(T,6).
pretty_print(black([],[],[],[]),_) :- !.
pretty_print(red(L,K,_,R),D) :-
DN is D+6,
pretty_print(L,DN),
format("~t~a:~d~*|~n",[r,K,D]),
pretty_print(R,DN).
pretty_print(black(L,K,_,R),D) :-
DN is D+6,
pretty_print(L,DN),
format("~t~a:~d~*|~n",[b,K,D]),
pretty_print(R,DN).
rb_delete(t(Nil,T), K, t(Nil,NT)) :-
delete(T, K, _, NT, _).
rb_delete(t(Nil,T), K, V, t(Nil,NT)) :-
delete(T, K, V, NT, _).
%
% I am afraid our representation is not as nice for delete
%
delete(red(L,K0,V0,R), K, V, NT, Flag) :-
K @< K0, !,
delete(L, K, V, NL, Flag0),
fixup_left(Flag0,red(NL,K0,V0,R),NT, Flag).
delete(red(L,K0,V0,R), K, V, NT, Flag) :-
K @> K0, !,
delete(R, K, V, NR, Flag0),
fixup_right(Flag0,red(L,K0,V0,NR),NT, Flag).
delete(red(L,_,V,R), _, V, OUT, Flag) :-
% K == K0,
delete_red_node(L,R,OUT,Flag).
delete(black(L,K0,V0,R), K, V, NT, Flag) :-
K @< K0, !,
delete(L, K, V, NL, Flag0),
fixup_left(Flag0,black(NL,K0,V0,R),NT, Flag).
delete(black(L,K0,V0,R), K, V, NT, Flag) :-
K @> K0, !,
delete(R, K, V, NR, Flag0),
fixup_right(Flag0,black(L,K0,V0,NR),NT, Flag).
delete(black(L,_,V,R), _, V, OUT, Flag) :-
% K == K0,
delete_black_node(L,R,OUT,Flag).
rb_del_min(t(Nil,T), K, Val, t(Nil,NT)) :-
del_min(T, K, Val, Nil, NT, _).
del_min(red(black([],_,_,_),K,V,R), K, V, Nil, OUT, Flag) :- !,
delete_red_node(Nil,R,OUT,Flag).
del_min(red(L,K0,V0,R), K, V, Nil, NT, Flag) :-
del_min(L, K, V, Nil, NL, Flag0),
fixup_left(Flag0,red(NL,K0,V0,R), NT, Flag).
del_min(black(black([],_,_,_),K,V,R), K, V, Nil, OUT, Flag) :- !,
delete_black_node(Nil,R,OUT,Flag).
del_min(black(L,K0,V0,R), K, V, Nil, NT, Flag) :-
del_min(L, K, V, Nil, NL, Flag0),
fixup_left(Flag0,black(NL,K0,V0,R),NT, Flag).
rb_del_max(t(Nil,T), K, Val, t(Nil,NT)) :-
del_max(T, K, Val, Nil, NT, _).
del_max(red(L,K,V,black([],_,_,_)), K, V, Nil, OUT, Flag) :- !,
delete_red_node(L,Nil,OUT,Flag).
del_max(red(L,K0,V0,R), K, V, Nil, NT, Flag) :-
del_max(R, K, V, Nil, NR, Flag0),
fixup_right(Flag0,red(L,K0,V0,NR),NT, Flag).
del_max(black(L,K,V,black([],_,_,_)), K, V, Nil, OUT, Flag) :- !,
delete_black_node(L,Nil,OUT,Flag).
del_max(black(L,K0,V0,R), K, V, Nil, NT, Flag) :-
del_max(R, K, V, Nil, NR, Flag0),
fixup_right(Flag0,black(L,K0,V0,NR), NT, Flag).
delete_red_node(L1,L2,L1,done) :- L1 == L2, !.
delete_red_node(black([],[],[],[]),R,R,done) :- !.
delete_red_node(L,black([],[],[],[]),L,done) :- !.
delete_red_node(L,R,OUT,Done) :-
delete_next(R,NK,NV,NR,Done0),
fixup_right(Done0,red(L,NK,NV,NR),OUT,Done).
delete_black_node(L1,L2,L1,not_done) :- L1 == L2, !.
delete_black_node(black([],[],[],[]),red(L,K,V,R),black(L,K,V,R),done) :- !.
delete_black_node(black([],[],[],[]),R,R,not_done) :- !.
delete_black_node(red(L,K,V,R),black([],[],[],[]),black(L,K,V,R),done) :- !.
delete_black_node(L,black([],[],[],[]),L,not_done) :- !.
delete_black_node(L,R,OUT,Done) :-
delete_next(R,NK,NV,NR,Done0),
fixup_right(Done0,black(L,NK,NV,NR),OUT,Done).
delete_next(red(black([],[],[],[]),K,V,R),K,V,R,done) :- !.
delete_next(black(black([],[],[],[]),K,V,red(L1,K1,V1,R1)),
K,V,black(L1,K1,V1,R1),done) :- !.
delete_next(black(black([],[],[],[]),K,V,R),K,V,R,not_done) :- !.
delete_next(red(L,K,V,R),K0,V0,OUT,Done) :-
delete_next(L,K0,V0,NL,Done0),
fixup_left(Done0,red(NL,K,V,R),OUT,Done).
delete_next(black(L,K,V,R),K0,V0,OUT,Done) :-
delete_next(L,K0,V0,NL,Done0),
fixup_left(Done0,black(NL,K,V,R),OUT,Done).
fixup_left(done,T,T,done).
fixup_left(not_done,T,NT,Done) :-
fixup2(T,NT,Done).
%
% case 1: x moves down, so we have to try to fix it again.
% case 1 -> 2,3,4 -> done
%
fixup2(black(black(Al,KA,VA,Be),KB,VB,red(black(Ga,KC,VC,De),KD,VD,black(Ep,KE,VE,Fi))),
black(T1,KD,VD,black(Ep,KE,VE,Fi)),done) :- !,
fixup2(red(black(Al,KA,VA,Be),KB,VB,black(Ga,KC,VC,De)),
T1,
_).
%
% case 2: x moves up, change one to red
%
fixup2(red(black(Al,KA,VA,Be),KB,VB,black(black(Ga,KC,VC,De),KD,VD,black(Ep,KE,VE,Fi))),
black(black(Al,KA,VA,Be),KB,VB,red(black(Ga,KC,VC,De),KD,VD,black(Ep,KE,VE,Fi))),done) :- !.
fixup2(black(black(Al,KA,VA,Be),KB,VB,black(black(Ga,KC,VC,De),KD,VD,black(Ep,KE,VE,Fi))),
black(black(Al,KA,VA,Be),KB,VB,red(black(Ga,KC,VC,De),KD,VD,black(Ep,KE,VE,Fi))),not_done) :- !.
%
% case 3: x stays put, shift left and do a 4
%
fixup2(red(black(Al,KA,VA,Be),KB,VB,black(red(Ga,KC,VC,De),KD,VD,black(Ep,KE,VE,Fi))),
red(black(black(Al,KA,VA,Be),KB,VB,Ga),KC,VC,black(De,KD,VD,black(Ep,KE,VE,Fi))),
done) :- !.
fixup2(black(black(Al,KA,VA,Be),KB,VB,black(red(Ga,KC,VC,De),KD,VD,black(Ep,KE,VE,Fi))),
black(black(black(Al,KA,VA,Be),KB,VB,Ga),KC,VC,black(De,KD,VD,black(Ep,KE,VE,Fi))),
done) :- !.
%
% case 4: rotate left, get rid of red
%
fixup2(red(black(Al,KA,VA,Be),KB,VB,black(C,KD,VD,red(Ep,KE,VE,Fi))),
red(black(black(Al,KA,VA,Be),KB,VB,C),KD,VD,black(Ep,KE,VE,Fi)),
done).
fixup2(black(black(Al,KA,VA,Be),KB,VB,black(C,KD,VD,red(Ep,KE,VE,Fi))),
black(black(black(Al,KA,VA,Be),KB,VB,C),KD,VD,black(Ep,KE,VE,Fi)),
done).
fixup_right(done,T,T,done).
fixup_right(not_done,T,NT,Done) :-
fixup3(T,NT,Done).
%
% case 1: x moves down, so we have to try to fix it again.
% case 1 -> 2,3,4 -> done
%
fixup3(black(red(black(Fi,KE,VE,Ep),KD,VD,black(De,KC,VC,Ga)),KB,VB,black(Be,KA,VA,Al)),
black(black(Fi,KE,VE,Ep),KD,VD,T1),done) :- !,
fixup3(red(black(De,KC,VC,Ga),KB,VB,black(Be,KA,VA,Al)),T1,_).
%
% case 2: x moves up, change one to red
%
fixup3(red(black(black(Fi,KE,VE,Ep),KD,VD,black(De,KC,VC,Ga)),KB,VB,black(Be,KA,VA,Al)),
black(red(black(Fi,KE,VE,Ep),KD,VD,black(De,KC,VC,Ga)),KB,VB,black(Be,KA,VA,Al)),
done) :- !.
fixup3(black(black(black(Fi,KE,VE,Ep),KD,VD,black(De,KC,VC,Ga)),KB,VB,black(Be,KA,VA,Al)),
black(red(black(Fi,KE,VE,Ep),KD,VD,black(De,KC,VC,Ga)),KB,VB,black(Be,KA,VA,Al)),
not_done):- !.
%
% case 3: x stays put, shift left and do a 4
%
fixup3(red(black(black(Fi,KE,VE,Ep),KD,VD,red(De,KC,VC,Ga)),KB,VB,black(Be,KA,VA,Al)),
red(black(black(Fi,KE,VE,Ep),KD,VD,De),KC,VC,black(Ga,KB,VB,black(Be,KA,VA,Al))),
done) :- !.
fixup3(black(black(black(Fi,KE,VE,Ep),KD,VD,red(De,KC,VC,Ga)),KB,VB,black(Be,KA,VA,Al)),
black(black(black(Fi,KE,VE,Ep),KD,VD,De),KC,VC,black(Ga,KB,VB,black(Be,KA,VA,Al))),
done) :- !.
%
% case 4: rotate right, get rid of red
%
fixup3(red(black(red(Fi,KE,VE,Ep),KD,VD,C),KB,VB,black(Be,KA,VA,Al)),
red(black(Fi,KE,VE,Ep),KD,VD,black(C,KB,VB,black(Be,KA,VA,Al))),
done).
fixup3(black(black(red(Fi,KE,VE,Ep),KD,VD,C),KB,VB,black(Be,KA,VA,Al)),
black(black(Fi,KE,VE,Ep),KD,VD,black(C,KB,VB,black(Be,KA,VA,Al))),
done).
%
% whole list
%
rb_visit(t(_,T),Lf) :-
visit(T,[],Lf).
rb_visit(t(_,T),L0,Lf) :-
visit(T,L0,Lf).
visit(black([],_,_,_),L,L) :- !.
visit(red(L,K,V,R),L0,Lf) :-
visit(L,[K-V|L1],Lf),
visit(R,L0,L1).
visit(black(L,K,V,R),L0,Lf) :-
visit(L,[K-V|L1],Lf),
visit(R,L0,L1).
rb_map(t(Nil,Tree),Goal,t(Nil,NewTree)) :-
map(Tree,Goal,NewTree).
map(black([],[],[],[]),_,black([],[],[],[])) :- !.
map(red(L,K,V,R),Goal,red(NL,K,NV,NR)) :-
call(Goal,V,NV), !,
map(L,Goal,NL),
map(R,Goal,NR).
map(black(L,K,V,R),Goal,black(NL,K,NV,NR)) :-
call(Goal,V,NV), !,
map(L,Goal,NL),
map(R,Goal,NR).
rb_map(t(_,Tree),Goal) :-
map(Tree,Goal).
map(black([],[],[],[]),_) :- !.
map(red(L,_,V,R),Goal) :-
call(Goal,V), !,
map(L,Goal),
map(R,Goal).
map(black(L,_,V,R),Goal) :-
call(Goal,V), !,
map(L,Goal),
map(R,Goal).
rb_clone(t(Nil,T),t(Nil,NT),Ns) :-
clone(T,NT,Ns,[]).
clone(black([],[],[],[]),black([],[],[],[]),Ns,Ns) :- !.
clone(red(L,K,_,R),red(NL,K,NV,NR),NsF,Ns0) :-
clone(L,NL,NsF,[K-NV|Ns1]),
clone(R,NR,Ns1,Ns0).
clone(black(L,K,_,R),black(NL,K,NV,NR),NsF,Ns0) :-
clone(L,NL,NsF,[K-NV|Ns1]),
clone(R,NR,Ns1,Ns0).
rb_clone(t(Nil,T),ONs,t(Nil,NT),Ns) :-
clone(T,ONs,[],NT,Ns,[]).
clone(black([],[],[],[]),ONs,ONs,black([],[],[],[]),Ns,Ns) :- !.
clone(red(L,K,V,R),ONsF,ONs0,red(NL,K,NV,NR),NsF,Ns0) :-
clone(L,ONsF,[K-V|ONs1],NL,NsF,[K-NV|Ns1]),
clone(R,ONs1,ONs0,NR,Ns1,Ns0).
clone(black(L,K,V,R),ONsF,ONs0,black(NL,K,NV,NR),NsF,Ns0) :-
clone(L,ONsF,[K-V|ONs1],NL,NsF,[K-NV|Ns1]),
clone(R,ONs1,ONs0,NR,Ns1,Ns0).
rb_partial_map(t(Nil,T0), Map, Goal, t(Nil,TF)) :-
partial_map(T0, Map, [], Nil, Goal, TF).
rb_partial_map(t(Nil,T0), Map, Map0, Goal, t(Nil,TF)) :-
rb_partial_map(T0, Map, Map0, Nil, Goal, TF).
partial_map(T,[],[],_,_,T) :- !.
partial_map(black([],_,_,_),Map,Map,Nil,_,Nil) :- !.
partial_map(red(L,K,V,R),Map,MapF,Nil,Goal,red(NL,K,NV,NR)) :-
partial_map(L,Map,MapI,Nil,Goal,NL),
(
MapI == [] ->
NR = R, NV = V, MapF = []
;
MapI = [K1|MapR],
(
K == K1
->
( call(Goal,V,NV) -> true ; NV = V ),
MapN = MapR
;
NV = V,
MapN = MapI
),
partial_map(R,MapN,MapF,Nil,Goal,NR)
).
partial_map(black(L,K,V,R),Map,MapF,Nil,Goal,black(NL,K,NV,NR)) :-
partial_map(L,Map,MapI,Nil,Goal,NL),
(
MapI == [] ->
NR = R, NV = V, MapF = []
;
MapI = [K1|MapR],
(
K == K1
->
( call(Goal,V,NV) -> true ; NV = V ),
MapN = MapR
;
NV = V,
MapN = MapI
),
partial_map(R,MapN,MapF,Nil,Goal,NR)
).
%
% whole keys
%
rb_keys(t(_,T),Lf) :-
keys(T,[],Lf).
rb_keys(t(_,T),L0,Lf) :-
keys(T,L0,Lf).
keys(black([],[],[],[]),L,L) :- !.
keys(red(L,K,_,R),L0,Lf) :-
keys(L,[K|L1],Lf),
keys(R,L0,L1).
keys(black(L,K,_,R),L0,Lf) :-
keys(L,[K|L1],Lf),
keys(R,L0,L1).
ord_list_to_rbtree(List,Tree) :-
list_to_rbtree(List,Tree).
list_to_rbtree(List,Tree) :-
rb_new(T0),
list_to_rbtree(List,T0,Tree).
list_to_rbtree([],Tree,Tree).
list_to_rbtree([K-V|List],T0,Tree) :-
rb_insert(T0, K, V, T1),
list_to_rbtree(List,T1,Tree).
/*
list_to_rbtree(List,t(Nil,Tree)) :-
Nil = black([], [], [], []),
sort(List,Sorted),
Ar =.. [seq|Sorted],
functor(Ar,_,L),
construct_rbtree(1, L, Ar, black, Nil, Tree).
ord_list_to_rbtree(List,t(Nil,Tree)) :-
Nil = black([], [], [], []),
Ar =.. [seq|List],
functor(Ar,_,L),
construct_rbtree(1, L, Ar, black, Nil, Tree).
*/
construct_rbtree(L, M, _, _, Nil, Nil) :- M < L, !.
construct_rbtree(L, L, Ar, Color, Nil, Node) :- !,
arg(L, Ar, K-Val),
build_node(Color, Nil, K, Val, Nil, Node, _).
construct_rbtree(I0, Max, Ar, Color, Nil, Node) :-
I is (I0+Max)//2,
arg(I, Ar, K-Val),
build_node(Color, Left, K, Val, Right, Node, NewColor),
I1 is I-1,
construct_rbtree(I0, I1, Ar, NewColor, Nil, Left),
I2 is I+1,
construct_rbtree(I2, Max, Ar, NewColor, Nil, Right).
build_node(black, Left, K, Val, Right, black(Left, K, Val, Right), red).
build_node(red, Left, K, Val, Right, red(Left, K, Val, Right), black).
rb_size(t(_,T),Size) :-
size(T,0,Size).
size(black([],_,_,_),Sz,Sz) :- !.
size(red(L,_,_,R),Sz0,Szf) :-
Sz1 is Sz0+1,
size(L,Sz1,Sz2),
size(R,Sz2,Szf).
size(black(L,_,_,R),Sz0,Szf) :-
Sz1 is Sz0+1,
size(L,Sz1,Sz2),
size(R,Sz2,Szf).
is_rbtree(t(Nil,Nil)) :- !.
is_rbtree(t(_,T)) :-
catch(rbtree1(T), msg(_,_), fail).
%
% This code checks if a tree is ordered and a rbtree
%
%
rbtree(black([],[],[],[])) :- !.
rbtree(T) :-
catch(rbtree1(T),msg(S,Args),format(S,Args)).
rbtree1(black(L,K,_,R)) :-
find_path_blacks(L, 0, Bls),
check_rbtree(L,-inf,K,Bls),
check_rbtree(R,K,+inf,Bls).
rbtree1(red(_,_,_,_)) :-
throw(msg("root should be black",[])).
find_path_blacks(black([],[],[],[]), Bls, Bls) :- !.
find_path_blacks(black(L,_,_,_), Bls0, Bls) :-
Bls1 is Bls0+1,
find_path_blacks(L, Bls1, Bls).
find_path_blacks(red(L,_,_,_), Bls0, Bls) :-
find_path_blacks(L, Bls0, Bls).
check_rbtree(black([],[],[],[]),Min,Max,Bls0) :- !,
check_height(Bls0,Min,Max).
check_rbtree(red(L,K,_,R),Min,Max,Bls) :-
check_val(K,Min,Max),
check_red_child(L),
check_red_child(R),
check_rbtree(L,Min,K,Bls),
check_rbtree(R,K,Max,Bls).
check_rbtree(black(L,K,_,R),Min,Max,Bls0) :-
check_val(K,Min,Max),
Bls is Bls0-1,
check_rbtree(L,Min,K,Bls),
check_rbtree(R,K,Max,Bls).
check_height(0,_,_) :- !.
check_height(Bls0,Min,Max) :-
throw(msg("Unbalance ~d between ~w and ~w~n",[Bls0,Min,Max])).
check_val(K, Min, Max) :- ( K @> Min ; Min == -inf), (K @< Max ; Max == +inf), !.
check_val(K, Min, Max) :-
throw(msg("not ordered: ~w not between ~w and ~w~n",[K,Min,Max])).
check_red_child(black(_,_,_,_)).
check_red_child(red(_,K,_,_)) :-
throw(msg("must be red: ~w~n",[K])).
%count(1,16,X), format("deleting ~d~n",[X]), new(1,a,T0), insert(T0,2,b,T1), insert(T1,3,c,T2), insert(T2,4,c,T3), insert(T3,5,c,T4), insert(T4,6,c,T5), insert(T5,7,c,T6), insert(T6,8,c,T7), insert(T7,9,c,T8), insert(T8,10,c,T9),insert(T9,11,c,T10), insert(T10,12,c,T11),insert(T11,13,c,T12),insert(T12,14,c,T13),insert(T13,15,c,T14), insert(T14,16,c,T15),delete(T15,X,T16),pretty_print(T16),rbtree(T16),fail.
% count(1,16,X0), X is -X0, format("deleting ~d~n",[X]), new(-1,a,T0), insert(T0,-2,b,T1), insert(T1,-3,c,T2), insert(T2,-4,c,T3), insert(T3,-5,c,T4), insert(T4,-6,c,T5), insert(T5,-7,c,T6), insert(T6,-8,c,T7), insert(T7,-9,c,T8), insert(T8,-10,c,T9),insert(T9,-11,c,T10), insert(T10,-12,c,T11),insert(T11,-13,c,T12),insert(T12,-14,c,T13),insert(T13,-15,c,T14), insert(T14,-16,c,T15),delete(T15,X,T16),pretty_print(T16),rbtree(T16),fail.
count(I,_,I).
count(I,M,L) :-
I < M, I1 is I+1, count(I1,M,L).
test_pos :-
new(1,a,T0),
N = 10000,
build_ptree(2,N,T0,T),
% pretty_print(T),
rbtree(T),
clean_tree(1,N,T,_),
bclean_tree(N,1,T,_),
count(1,N,X), ( delete(T,X,TF) -> true ; abort ),
% pretty_print(TF),
rbtree(TF),
format("done ~d~n",[X]),
fail.
test_pos.
build_ptree(X,X,T0,TF) :- !,
insert(T0,X,X,TF).
build_ptree(X1,X,T0,TF) :-
insert(T0,X1,X1,TI),
X2 is X1+1,
build_ptree(X2,X,TI,TF).
clean_tree(X,X,T0,TF) :- !,
delete(T0,X,TF),
( rbtree(TF) -> true ; abort).
clean_tree(X1,X,T0,TF) :-
delete(T0,X1,TI),
X2 is X1+1,
( rbtree(TI) -> true ; abort),
clean_tree(X2,X,TI,TF).
bclean_tree(X,X,T0,TF) :- !,
format("cleaning ~d~n", [X]),
delete(T0,X,TF),
( rbtree(TF) -> true ; abort).
bclean_tree(X1,X,T0,TF) :-
format("cleaning ~d~n", [X1]),
delete(T0,X1,TI),
X2 is X1-1,
( rbtree(TI) -> true ; abort),
bclean_tree(X2,X,TI,TF).
test_neg :-
Size = 10000,
new(-1,a,T0),
build_ntree(2,Size,T0,T),
% pretty_print(T),
rbtree(T),
MSize is -Size,
clean_tree(MSize,-1,T,_),
bclean_tree(-1,MSize,T,_),
count(1,Size,X), NX is -X, ( delete(T,NX,TF) -> true ; abort ),
% pretty_print(TF),
rbtree(TF),
format("done ~d~n",[X]),
fail.
test_neg.
build_ntree(X,X,T0,TF) :- !,
X1 is -X,
insert(T0,X1,X1,TF).
build_ntree(X1,X,T0,TF) :-
NX1 is -X1,
insert(T0,NX1,NX1,TI),
X2 is X1+1,
build_ntree(X2,X,TI,TF).