/* 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).