1/*  Part of SWI-Prolog
    2
    3    Author:        Jan Wielemaker
    4    E-mail:        J.Wielemaker@vu.nl
    5    WWW:           http://www.swi-prolog.org
    6    Copyright (c)  2007-2014, University of Amsterdam
    7    All rights reserved.
    8
    9    Redistribution and use in source and binary forms, with or without
   10    modification, are permitted provided that the following conditions
   11    are met:
   12
   13    1. Redistributions of source code must retain the above copyright
   14       notice, this list of conditions and the following disclaimer.
   15
   16    2. Redistributions in binary form must reproduce the above copyright
   17       notice, this list of conditions and the following disclaimer in
   18       the documentation and/or other materials provided with the
   19       distribution.
   20
   21    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   22    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   23    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
   24    FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
   25    COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
   26    INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
   27    BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
   28    LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
   29    CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   30    LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
   31    ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
   32    POSSIBILITY OF SUCH DAMAGE.
   33*/
   34
   35:- module(nb_rbtrees,
   36          [ nb_rb_insert/3,             % !T0, +Key, +Value
   37            nb_rb_get_node/3,           % +Tree, +Key, -Node
   38            nb_rb_node_value/2,         % +Node, -Value
   39            nb_rb_set_node_value/2      % +Node, +Value
   40          ]).

   54                 /*******************************
   55                 *       TREE INSERTION         *
   56                 *******************************/

 nb_rb_insert(!RBTree, +Key, +Value)

Add Key-Value to the tree RBTree using non-backtrackable destructive assignment.

   63nb_rb_insert(Tree, Key0, Val0) :-
   64    duplicate_term(Key0, Key),
   65    duplicate_term(Val0, Val),
   66    Tree = t(Nil, T),
   67    insert(T, Key, Val, Nil, NT, Flag),
   68    (   Flag == shared
   69    ->  true
   70    ;   nb_linkarg(2, Tree, NT)
   71    ).
   72
   73insert(Tree0,Key,Val,Nil,Tree, Flag) :-
   74    insert2(Tree0,Key,Val,Nil,TreeI,Flag),
   75    (   Flag == shared
   76    ->  Tree = Tree0
   77    ;   fix_root(TreeI,Tree)
   78    ).
   79
   80%
   81% make sure the root is always black.
   82%
   83fix_root(black(L,K,V,R),black(L,K,V,R)).
   84fix_root(red(L,K,V,R),black(L,K,V,R)).
   85
   86
   87%
   88% Cormen et al present the algorithm as
   89% (1) standard tree insertion;
   90% (2) from the viewpoint of the newly inserted node:
   91%     partially fix the tree;
   92%     move upwards
   93% until reaching the root.
   94%
   95% We do it a little bit different:
   96%
   97% (1) standard tree insertion;
   98% (2) move upwards:
   99%      when reaching a black node;
  100%        if the tree below may be broken, fix it.
  101% We take advantage of Prolog unification
  102% to do several operations in a single go.
  103%
  104
  105
  106
  107%
  108% actual insertion
  109%
  110insert2(black('',_,_,''), K, V, Nil, T, Status) :-
  111    !,
  112    T = red(Nil,K,V,Nil),
  113    Status = not_done.
  114insert2(In, K, V, Nil, NT, Flag) :-
  115    In = red(L,K0,V0,R),
  116    !,
  117    (   K @< K0
  118    ->  insert2(L, K, V, Nil, NL, Flag),
  119        (   Flag == shared
  120        ->  NT = In
  121        ;   NT = red(NL,K0,V0,R)
  122        )
  123    ;   insert2(R, K, V, Nil, NR, Flag),
  124        (   Flag == shared
  125        ->  NT = In
  126        ;   NT = red(L,K0,V0,NR)
  127        )
  128    ).
  129insert2(In, K, V, Nil, NT, Flag) :-
  130    In = black(L,K0,V0,R),
  131    (   K @< K0
  132    ->  insert2(L, K, V, Nil, IL, Flag0),
  133        (   Flag0 == shared
  134        ->  NT = In
  135        ;   fix_left(Flag0, black(IL,K0,V0,R), NT0, Flag1),
  136            (   Flag1 == share
  137            ->  nb_linkarg(1, In, IL),
  138                Flag = shared,
  139                NT = In
  140            ;   NT = NT0,
  141                Flag = Flag1
  142            )
  143        )
  144    ;   insert2(R, K, V, Nil, IR, Flag0),
  145        (   Flag0 == shared
  146        ->  NT = In
  147        ;   fix_right(Flag0, black(L,K0,V0,IR), NT0, Flag1),
  148            (   Flag1 == share
  149            ->  nb_linkarg(4, In, IR),
  150                Flag = shared,
  151                NT = In
  152            ;   NT = NT0,
  153                Flag = Flag1
  154            )
  155        )
  156    ).
  157
  158%
  159% How to fix if we have inserted on the left
  160%
  161fix_left(shared,T,T,shared) :- !.
  162fix_left(done,T,T,done) :- !.
  163fix_left(not_done,Tmp,Final,Done) :-
  164    fix_left(Tmp,Final,Done).
  165
  166%
  167% case 1 of RB: just need to change colors.
  168%
  169fix_left(black(red(Al,AK,AV,red(Be,BK,BV,Ga)),KC,VC,red(De,KD,VD,Ep)),
  170        red(black(Al,AK,AV,red(Be,BK,BV,Ga)),KC,VC,black(De,KD,VD,Ep)),
  171        not_done) :- !.
  172fix_left(black(red(red(Al,KA,VA,Be),KB,VB,Ga),KC,VC,red(De,KD,VD,Ep)),
  173        red(black(red(Al,KA,VA,Be),KB,VB,Ga),KC,VC,black(De,KD,VD,Ep)),
  174        not_done) :- !.
  175%
  176% case 2 of RB: got a knee so need to do rotations
  177%
  178fix_left(black(red(Al,KA,VA,red(Be,KB,VB,Ga)),KC,VC,De),
  179        black(red(Al,KA,VA,Be),KB,VB,red(Ga,KC,VC,De)),
  180        done) :- !.
  181%
  182% case 3 of RB: got a line
  183%
  184fix_left(black(red(red(Al,KA,VA,Be),KB,VB,Ga),KC,VC,De),
  185        black(red(Al,KA,VA,Be),KB,VB,red(Ga,KC,VC,De)),
  186        done) :- !.
  187%
  188% case 4 of RB: nothig to do
  189%
  190fix_left(T,T,share).                    % shared?
  191
  192%
  193% How to fix if we have inserted on the right
  194%
  195fix_right(shared,T,T,shared) :- !.
  196fix_right(done,T,T,done) :- !.
  197fix_right(not_done,Tmp,Final,Done) :-
  198    fix_right(Tmp,Final,Done).
  199
  200%
  201% case 1 of RB: just need to change colors.
  202%
  203fix_right(black(red(Ep,KD,VD,De),KC,VC,red(red(Ga,KB,VB,Be),KA,VA,Al)),
  204        red(black(Ep,KD,VD,De),KC,VC,black(red(Ga,KB,VB,Be),KA,VA,Al)),
  205        not_done) :- !.
  206fix_right(black(red(Ep,KD,VD,De),KC,VC,red(Ga,Ka,Va,red(Be,KB,VB,Al))),
  207        red(black(Ep,KD,VD,De),KC,VC,black(Ga,Ka,Va,red(Be,KB,VB,Al))),
  208        not_done) :- !.
  209%
  210% case 2 of RB: got a knee so need to do rotations
  211%
  212fix_right(black(De,KC,VC,red(red(Ga,KB,VB,Be),KA,VA,Al)),
  213        black(red(De,KC,VC,Ga),KB,VB,red(Be,KA,VA,Al)),
  214        done) :- !.
  215%
  216% case 3 of RB: got a line
  217%
  218fix_right(black(De,KC,VC,red(Ga,KB,VB,red(Be,KA,VA,Al))),
  219        black(red(De,KC,VC,Ga),KB,VB,red(Be,KA,VA,Al)),
  220        done) :- !.
  221%
  222% case 4 of RB: nothing to do.
  223%
  224fix_right(T,T,share).
  225
  226
  227                 /*******************************
  228                 *            UPDATE            *
  229                 *******************************/

 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.

  238nb_rb_get_node(t(_Nil, Tree), Key, Node) :-
  239    find_node(Key, Tree, Node).
  240
  241find_node(Key, Tree, Node) :-
  242    Tree \== '',
  243    arg(2, Tree, K),
  244    compare(Diff, Key, K),
  245    find_node(Diff, Key, Tree, Node).
  246
  247find_node(=, _, Node, Node).
  248find_node(<, Key, Tree, Node) :-
  249    arg(1, Tree, Left),
  250    find_node(Key, Left, Node).
  251find_node(>, Key, Tree, Node) :-
  252    arg(4, Tree, Right),
  253    find_node(Key, Right, Node).

 nb_rb_node_value(+Node, -Value) is det

Value is the value associated to Node.

  259nb_rb_node_value(Node, Value) :-
  260    arg(3, Node, Value).

 nb_rb_set_node_value(!Node, +Value) is det

Associate Value with Node.

  266nb_rb_set_node_value(Node, Value) :-
  267    nb_setarg(3, Node, Value)