RB_PREV(3bsd)

1TREE(3bsd)                           LOCAL                          TREE(3bsd)
2

NAME

4     SPLAY_PROTOTYPE, SPLAY_GENERATE, SPLAY_ENTRY, SPLAY_HEAD,
5     SPLAY_INITIALIZER, SPLAY_ROOT, SPLAY_EMPTY, SPLAY_NEXT, SPLAY_MIN,
6     SPLAY_MAX, SPLAY_FIND, SPLAY_LEFT, SPLAY_RIGHT, SPLAY_FOREACH,
7     SPLAY_INIT, SPLAY_INSERT, SPLAY_REMOVE, RB_PROTOTYPE,
8     RB_PROTOTYPE_STATIC, RB_GENERATE, RB_GENERATE_STATIC, RB_ENTRY, RB_HEAD,
9     RB_INITIALIZER, RB_ROOT, RB_EMPTY, RB_NEXT, RB_PREV, RB_MIN, RB_MAX,
10     RB_FIND, RB_NFIND, RB_LEFT, RB_RIGHT, RB_PARENT, RB_FOREACH,
11     RB_FOREACH_REVERSE, RB_INIT, RB_INSERT, RB_REMOVE — implementations of
12     splay and red-black trees
13

SYNOPSIS

15     #include <sys/tree.h>
16     (See libbsd(7) for include usage.)
17
18     SPLAY_PROTOTYPE(NAME, TYPE, FIELD, CMP);
19
20     SPLAY_GENERATE(NAME, TYPE, FIELD, CMP);
21
22     SPLAY_ENTRY(TYPE);
23
24     SPLAY_HEAD(HEADNAME, TYPE);
25
26     struct TYPE *
27     SPLAY_INITIALIZER(SPLAY_HEAD *head);
28
29     SPLAY_ROOT(SPLAY_HEAD *head);
30
31     bool
32     SPLAY_EMPTY(SPLAY_HEAD *head);
33
34     struct TYPE *
35     SPLAY_NEXT(NAME, SPLAY_HEAD *head, struct TYPE *elm);
36
37     struct TYPE *
38     SPLAY_MIN(NAME, SPLAY_HEAD *head);
39
40     struct TYPE *
41     SPLAY_MAX(NAME, SPLAY_HEAD *head);
42
43     struct TYPE *
44     SPLAY_FIND(NAME, SPLAY_HEAD *head, struct TYPE *elm);
45
46     struct TYPE *
47     SPLAY_LEFT(struct TYPE *elm, SPLAY_ENTRY NAME);
48
49     struct TYPE *
50     SPLAY_RIGHT(struct TYPE *elm, SPLAY_ENTRY NAME);
51
52     SPLAY_FOREACH(VARNAME, NAME, SPLAY_HEAD *head);
53
54     void
55     SPLAY_INIT(SPLAY_HEAD *head);
56
57     struct TYPE *
58     SPLAY_INSERT(NAME, SPLAY_HEAD *head, struct TYPE *elm);
59
60     struct TYPE *
61     SPLAY_REMOVE(NAME, SPLAY_HEAD *head, struct TYPE *elm);
62
63     RB_PROTOTYPE(NAME, TYPE, FIELD, CMP);
64
65     RB_PROTOTYPE_STATIC(NAME, TYPE, FIELD, CMP);
66
67     RB_GENERATE(NAME, TYPE, FIELD, CMP);
68
69     RB_GENERATE_STATIC(NAME, TYPE, FIELD, CMP);
70
71     RB_ENTRY(TYPE);
72
73     RB_HEAD(HEADNAME, TYPE);
74
75     RB_INITIALIZER(RB_HEAD *head);
76
77     struct TYPE *
78     RB_ROOT(RB_HEAD *head);
79
80     bool
81     RB_EMPTY(RB_HEAD *head);
82
83     struct TYPE *
84     RB_NEXT(NAME, RB_HEAD *head, struct TYPE *elm);
85
86     struct TYPE *
87     RB_PREV(NAME, RB_HEAD *head, struct TYPE *elm);
88
89     struct TYPE *
90     RB_MIN(NAME, RB_HEAD *head);
91
92     struct TYPE *
93     RB_MAX(NAME, RB_HEAD *head);
94
95     struct TYPE *
96     RB_FIND(NAME, RB_HEAD *head, struct TYPE *elm);
97
98     struct TYPE *
99     RB_NFIND(NAME, RB_HEAD *head, struct TYPE *elm);
100
101     struct TYPE *
102     RB_LEFT(struct TYPE *elm, RB_ENTRY NAME);
103
104     struct TYPE *
105     RB_RIGHT(struct TYPE *elm, RB_ENTRY NAME);
106
107     struct TYPE *
108     RB_PARENT(struct TYPE *elm, RB_ENTRY NAME);
109
110     RB_FOREACH(VARNAME, NAME, RB_HEAD *head);
111
112     RB_FOREACH_REVERSE(VARNAME, NAME, RB_HEAD *head);
113
114     void
115     RB_INIT(RB_HEAD *head);
116
117     struct TYPE *
118     RB_INSERT(NAME, RB_HEAD *head, struct TYPE *elm);
119
120     struct TYPE *
121     RB_REMOVE(NAME, RB_HEAD *head, struct TYPE *elm);
122

DESCRIPTION

124     These macros define data structures for different types of trees: splay
125     trees and red-black trees.
126
127     In the macro definitions, TYPE is the name tag of a user defined struc‐
128     ture that must contain a field of type SPLAY_ENTRY, or RB_ENTRY, named
129     ENTRYNAME.  The argument HEADNAME is the name tag of a user defined
130     structure that must be declared using the macros SPLAY_HEAD(), or
131     RB_HEAD().  The argument NAME has to be a unique name prefix for every
132     tree that is defined.
133
134     The function prototypes are declared with SPLAY_PROTOTYPE(),
135     RB_PROTOTYPE(), or RB_PROTOTYPE_STATIC().  The function bodies are gener‐
136     ated with SPLAY_GENERATE(), RB_GENERATE(), or RB_GENERATE_STATIC().  See
137     the examples below for further explanation of how these macros are used.
138

SPLAY TREES

140     A splay tree is a self-organizing data structure.  Every operation on the
141     tree causes a splay to happen.  The splay moves the requested node to the
142     root of the tree and partly rebalances it.
143
144     This has the benefit that request locality causes faster lookups as the
145     requested nodes move to the top of the tree.  On the other hand, every
146     lookup causes memory writes.
147
148     The Balance Theorem bounds the total access time for m operations and n
149     inserts on an initially empty tree as O((m + n)lg n).  The amortized cost
150     for a sequence of m accesses to a splay tree is O(lg n).
151
152     A splay tree is headed by a structure defined by the SPLAY_HEAD() macro.
153     A structure is declared as follows:
154
155           SPLAY_HEAD(HEADNAME, TYPE) head;
156
157     where HEADNAME is the name of the structure to be defined, and struct
158     TYPE is the type of the elements to be inserted into the tree.
159
160     The SPLAY_ENTRY() macro declares a structure that allows elements to be
161     connected in the tree.
162
163     In order to use the functions that manipulate the tree structure, their
164     prototypes need to be declared with the SPLAY_PROTOTYPE() macro, where
165     NAME is a unique identifier for this particular tree.  The TYPE argument
166     is the type of the structure that is being managed by the tree.  The
167     FIELD argument is the name of the element defined by SPLAY_ENTRY().
168
169     The function bodies are generated with the SPLAY_GENERATE() macro.  It
170     takes the same arguments as the SPLAY_PROTOTYPE() macro, but should be
171     used only once.
172
173     Finally, the CMP argument is the name of a function used to compare tree
174     nodes with each other.  The function takes two arguments of type struct
175     TYPE *.  If the first argument is smaller than the second, the function
176     returns a value smaller than zero.  If they are equal, the function
177     returns zero.  Otherwise, it should return a value greater than zero.
178     The compare function defines the order of the tree elements.
179
180     The SPLAY_INIT() macro initializes the tree referenced by head.
181
182     The splay tree can also be initialized statically by using the
183     SPLAY_INITIALIZER() macro like this:
184
185           SPLAY_HEAD(HEADNAME, TYPE) head = SPLAY_INITIALIZER(&head);
186
187     The SPLAY_INSERT() macro inserts the new element elm into the tree.
188
189     The SPLAY_REMOVE() macro removes the element elm from the tree pointed by
190     head.
191
192     The SPLAY_FIND() macro can be used to find a particular element in the
193     tree.
194
195           struct TYPE find, *res;
196           find.key = 30;
197           res = SPLAY_FIND(NAME, head, &find);
198
199     The SPLAY_ROOT(), SPLAY_MIN(), SPLAY_MAX(), and SPLAY_NEXT() macros can
200     be used to traverse the tree:
201
202           for (np = SPLAY_MIN(NAME, &head); np != NULL; np = SPLAY_NEXT(NAME, &head, np))
203
204     Or, for simplicity, one can use the SPLAY_FOREACH() macro:
205
206           SPLAY_FOREACH(np, NAME, head)
207
208     The SPLAY_EMPTY() macro should be used to check whether a splay tree is
209     empty.
210

RED-BLACK TREES

212     A red-black tree is a binary search tree with the node color as an extra
213     attribute.  It fulfills a set of conditions:
214
215           1.   Every search path from the root to a leaf consists of the same
216                number of black nodes.
217
218           2.   Each red node (except for the root) has a black parent.
219
220           3.   Each leaf node is black.
221
222     Every operation on a red-black tree is bounded as O(lg n).  The maximum
223     height of a red-black tree is 2lg(n + 1).
224
225     A red-black tree is headed by a structure defined by the RB_HEAD() macro.
226     A structure is declared as follows:
227
228           RB_HEAD(HEADNAME, TYPE) head;
229
230     where HEADNAME is the name of the structure to be defined, and struct
231     TYPE is the type of the elements to be inserted into the tree.
232
233     The RB_ENTRY() macro declares a structure that allows elements to be con‐
234     nected in the tree.
235
236     In order to use the functions that manipulate the tree structure, their
237     prototypes need to be declared with the RB_PROTOTYPE() or
238     RB_PROTOTYPE_STATIC() macro, where NAME is a unique identifier for this
239     particular tree.  The TYPE argument is the type of the structure that is
240     being managed by the tree.  The FIELD argument is the name of the element
241     defined by RB_ENTRY().
242
243     The function bodies are generated with the RB_GENERATE() or
244     RB_GENERATE_STATIC() macro.  These macros take the same arguments as the
245     RB_PROTOTYPE() and RB_PROTOTYPE_STATIC() macros, but should be used only
246     once.
247
248     Finally, the CMP argument is the name of a function used to compare tree
249     nodes with each other.  The function takes two arguments of type struct
250     TYPE *.  If the first argument is smaller than the second, the function
251     returns a value smaller than zero.  If they are equal, the function
252     returns zero.  Otherwise, it should return a value greater than zero.
253     The compare function defines the order of the tree elements.
254
255     The RB_INIT() macro initializes the tree referenced by head.
256
257     The red-black tree can also be initialized statically by using the
258     RB_INITIALIZER() macro like this:
259
260           RB_HEAD(HEADNAME, TYPE) head = RB_INITIALIZER(&head);
261
262     The RB_INSERT() macro inserts the new element elm into the tree.
263
264     The RB_REMOVE() macro removes the element elm from the tree pointed by
265     head.
266
267     The RB_FIND() and RB_NFIND() macros can be used to find a particular ele‐
268     ment in the tree.
269
270           struct TYPE find, *res;
271           find.key = 30;
272           res = RB_FIND(NAME, head, &find);
273
274     The RB_ROOT(), RB_MIN(), RB_MAX(), RB_NEXT(), and RB_PREV() macros can be
275     used to traverse the tree:
276
277           for (np = RB_MIN(NAME, &head); np != NULL; np = RB_NEXT(NAME,
278           &head, np))
279
280     Or, for simplicity, one can use the RB_FOREACH() or RB_FOREACH_REVERSE()
281     macro:
282
283           RB_FOREACH(np, NAME, head)
284
285     The RB_EMPTY() macro should be used to check whether a red-black tree is
286     empty.
287

NOTES

289     Trying to free a tree in the following way is a common error:
290
291           SPLAY_FOREACH(var, NAME, head) {
292                   SPLAY_REMOVE(NAME, head, var);
293                   free(var);
294           }
295           free(head);
296
297     Since var is freed, the FOREACH() macro refers to a pointer that may have
298     been reallocated already.  Proper code needs a second variable.
299
300           for (var = SPLAY_MIN(NAME, head); var != NULL; var = nxt) {
301                   nxt = SPLAY_NEXT(NAME, head, var);
302                   SPLAY_REMOVE(NAME, head, var);
303                   free(var);
304           }
305
306     Both RB_INSERT() and SPLAY_INSERT() return NULL if the element was
307     inserted in the tree successfully, otherwise they return a pointer to the
308     element with the colliding key.
309
310     Accordingly, RB_REMOVE() and SPLAY_REMOVE() return the pointer to the
311     removed element otherwise they return NULL to indicate an error.
312

AUTHORS

317     The author of the tree macros is Niels Provos.
318
319BSD                            December 27, 2007                           BSD