/* $Id$
Part of SWI-Prolog
Author: Jan Wielemaker
E-mail: wielemak@science.uva.nl
WWW: http://www.swi-prolog.org
Copyright (C): 1985-2007, University of Amsterdam
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
As a special exception, if you link this library with other files,
compiled with a Free Software compiler, to produce an executable, this
library does not by itself cause the resulting executable to be covered
by the GNU General Public License. This exception does not however
invalidate any other reasons why the executable file might be covered by
the GNU General Public License.
*/
:- module(nb_rbtrees,
[ nb_rb_insert/3, % !T0, +Key, +Value
nb_rb_get_node/3, % +Tree, +Key, -Node
nb_rb_node_value/2, % +Node, -Value
nb_rb_set_node_value/2 % +Node, +Value
]).
/** <module> Non-backtrackable operations on red black trees
This library is an extension to rbtrees.pl, implementing Red-black
trees. This library adds non-backtrackable destructive update to RB
trees which allows us to fill RB trees in a failure driven loop.
This module builds on top of the rbtrees.pl and used code copied from
library written by Vitor Santos Costa.
@author Jan Wielemaker
*/
/*******************************
* TREE INSERTION *
*******************************/
%% nb_rb_insert(!RBTree, +Key, +Value)
%
% Add Key-Value to the tree RBTree using non-backtrackable
% destructive assignment.
nb_rb_insert(Tree, Key0, Val0) :-
duplicate_term(Key0, Key),
duplicate_term(Val0, Val),
Tree = t(Nil, T),
insert(T, Key, Val, Nil, NT, Flag),
( Flag == shared
-> true
; nb_linkarg(2, Tree, NT)
).
insert(Tree0,Key,Val,Nil,Tree, Flag) :-
insert2(Tree0,Key,Val,Nil,TreeI,Flag),
( Flag == shared
-> Tree = Tree0
; 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(In, K, V, Nil, NT, Flag) :-
In = red(L,K0,V0,R), !,
( K @< K0
-> insert2(L, K, V, Nil, NL, Flag),
( Flag == shared
-> NT = In
; NT = red(NL,K0,V0,R)
)
; insert2(R, K, V, Nil, NR, Flag),
( Flag == shared
-> NT = In
; NT = red(L,K0,V0,NR)
)
).
insert2(In, K, V, Nil, NT, Flag) :-
In = black(L,K0,V0,R),
( K @< K0
-> insert2(L, K, V, Nil, IL, Flag0),
( Flag0 == shared
-> NT = In
; fix_left(Flag0, black(IL,K0,V0,R), NT0, Flag1),
( Flag1 == share
-> nb_linkarg(1, In, IL),
Flag = shared,
NT = In
; NT = NT0,
Flag = Flag1
)
)
; insert2(R, K, V, Nil, IR, Flag0),
( Flag0 == shared
-> NT = In
; fix_right(Flag0, black(L,K0,V0,IR), NT, Flag1),
( Flag1 == share
-> nb_linkarg(4, In, IR),
Flag = shared,
NT = In
; NT = NT0,
Flag = Flag1
)
)
).
%
% How to fix if we have inserted on the left
%
fix_left(shared,T,T,shared) :- !.
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,share). % shared?
%
% How to fix if we have inserted on the right
%
fix_right(shared,T,T,shared) :- !.
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,share).
/*******************************
* UPDATE *
*******************************/
%% nb_rb_get_node(+RBTree, +Key, -Node) is semidet.
%
% True if Node is the node in RBTree associated to Key. Fails if
% Key is not in RBTree. This predicate is intended to be used
% together with nb_rb_set_node_value/2 to update the associated
% key destructively.
nb_rb_get_node(t(_Nil, Tree), Key, Node) :-
find_node(Key, Tree, Node).
find_node(Key, Tree, Node) :-
arg(2, Tree, K),
compare(Diff, Key, K),
find_node(Diff, Key, Tree, Node).
find_node(=, _, Node, Node).
find_node(<, Key, Tree, Node) :-
arg(1, Tree, Left),
find_node(Key, Left, Node).
find_node(>, Key, Tree, Node) :-
arg(4, Tree, Right),
find_node(Key, Right, Node).
%% nb_rb_node_value(+Node, -Value) is det.
%
% Value is the value associated to Node.
nb_rb_node_value(Node, Value) :-
arg(3, Node, Value).
%% nb_rb_set_node_value(!Node, +Value) is det.
%
% Associate Value with Node.
nb_rb_set_node_value(Node, Value) :-
nb_setarg(3, Node, Value).