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tree.h

/*    $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $      */
/*    $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $  */
/* $FreeBSD: src/sys/sys/tree.h,v 1.6.2.1 2008/03/07 22:34:17 jasone Exp $ */

/*-
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

/*
THIS HAS BEEN MODIFIED FROM THE ORIGINAL SOURCE.
I've removed the functions that we don't use.
*/ 

#ifndef     _SYS_TREE_H_
#define     _SYS_TREE_H_

/*#include <sys/cdefs.h>*/

/*
 * This file defines data structures for different types of trees:
 * red-black trees.
 *
 * A red-black tree is a binary search tree with the node color as an
 * extra attribute.  It fulfills a set of conditions:
 *    - every search path from the root to a leaf consists of the
 *      same number of black nodes,
 *    - each red node (except for the root) has a black parent,
 *    - each leaf node is black.
 *
 * Every operation on a red-black tree is bounded as O(lg n).
 * The maximum height of a red-black tree is 2lg (n+1).
 */

/* Macros that define a red-black tree */
#define RB_HEAD(name, type)                                 \
struct name {                                               \
      struct type *rbh_root; /* root of the tree */               \
}

#define RB_INITIALIZER(root)                                \
      { NULL }

#define RB_INIT(root) do {                                  \
      (root)->rbh_root = NULL;                              \
} while (/*CONSTCOND*/ 0)

#define RB_BLACK  0
#define RB_RED          1
#define RB_ENTRY(type)                                      \
struct {                                              \
      struct type *rbe_left;        /* left element */            \
      struct type *rbe_right;       /* right element */           \
      struct type *rbe_parent;      /* parent element */          \
      int rbe_color;                /* node color */        \
}

#define RB_LEFT(elm, field)         (elm)->field.rbe_left
#define RB_RIGHT(elm, field)        (elm)->field.rbe_right
#define RB_PARENT(elm, field)       (elm)->field.rbe_parent
#define RB_COLOR(elm, field)        (elm)->field.rbe_color
#define RB_ROOT(head)               (head)->rbh_root
#define RB_EMPTY(head)              (RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field) do {                           \
      RB_PARENT(elm, field) = parent;                             \
      RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;          \
      RB_COLOR(elm, field) = RB_RED;                              \
} while (/*CONSTCOND*/ 0)

#define RB_SET_BLACKRED(black, red, field) do {                   \
      RB_COLOR(black, field) = RB_BLACK;                    \
      RB_COLOR(red, field) = RB_RED;                              \
} while (/*CONSTCOND*/ 0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x)   do {} while (0)
#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field) do {                \
      (tmp) = RB_RIGHT(elm, field);                         \
      if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \
            RB_PARENT(RB_LEFT(tmp, field), field) = (elm);        \
      }                                               \
      RB_AUGMENT(elm);                                \
      if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {    \
            if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))   \
                  RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
            else                                      \
                  RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
      } else                                                \
            (head)->rbh_root = (tmp);                       \
      RB_LEFT(tmp, field) = (elm);                          \
      RB_PARENT(elm, field) = (tmp);                              \
      RB_AUGMENT(tmp);                                \
      if ((RB_PARENT(tmp, field)))                          \
            RB_AUGMENT(RB_PARENT(tmp, field));              \
} while (/*CONSTCOND*/ 0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {               \
      (tmp) = RB_LEFT(elm, field);                          \
      if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \
            RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);       \
      }                                               \
      RB_AUGMENT(elm);                                \
      if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {    \
            if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))   \
                  RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
            else                                      \
                  RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
      } else                                                \
            (head)->rbh_root = (tmp);                       \
      RB_RIGHT(tmp, field) = (elm);                         \
      RB_PARENT(elm, field) = (tmp);                              \
      RB_AUGMENT(tmp);                                \
      if ((RB_PARENT(tmp, field)))                          \
            RB_AUGMENT(RB_PARENT(tmp, field));              \
} while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */
#define     RB_PROTOTYPE(name, type, field, cmp)                        \
      RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
#define     RB_PROTOTYPE_STATIC(name, type, field, cmp)                 \
      RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)       \
attr void name##_RB_INSERT_COLOR(struct name *, struct type *);         \
attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
attr struct type *name##_RB_REMOVE(struct name *, struct type *); \
attr struct type *name##_RB_INSERT(struct name *, struct type *); \
attr struct type *name##_RB_FIND(struct name *, struct type *);         \
attr struct type *name##_RB_NFIND(struct name *, struct type *);  \
attr struct type *name##_RB_NEXT(struct type *);                  \
attr struct type *name##_RB_PREV(struct type *);                  \
attr struct type *name##_RB_MINMAX(struct name *, int);                 \
                                                      \

/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define     RB_GENERATE(name, type, field, cmp)                   \
      RB_GENERATE_INTERNAL(name, type, field, cmp,)
#define     RB_GENERATE_STATIC(name, type, field, cmp)                  \
      RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)        \
attr void                                             \
name##_RB_INSERT_COLOR(struct name *head, struct type *elm)       \
{                                                     \
      struct type *parent, *gparent, *tmp;                        \
      while ((parent = RB_PARENT(elm, field)) != NULL &&          \
          RB_COLOR(parent, field) == RB_RED) {              \
            gparent = RB_PARENT(parent, field);             \
            if (parent == RB_LEFT(gparent, field)) {        \
                  tmp = RB_RIGHT(gparent, field);                 \
                  if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
                        RB_COLOR(tmp, field) = RB_BLACK;    \
                        RB_SET_BLACKRED(parent, gparent, field);\
                        elm = gparent;                      \
                        continue;                     \
                  }                                   \
                  if (RB_RIGHT(parent, field) == elm) {           \
                        RB_ROTATE_LEFT(head, parent, tmp, field);\
                        tmp = parent;                       \
                        parent = elm;                       \
                        elm = tmp;                    \
                  }                                   \
                  RB_SET_BLACKRED(parent, gparent, field);  \
                  RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
            } else {                                  \
                  tmp = RB_LEFT(gparent, field);                  \
                  if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
                        RB_COLOR(tmp, field) = RB_BLACK;    \
                        RB_SET_BLACKRED(parent, gparent, field);\
                        elm = gparent;                      \
                        continue;                     \
                  }                                   \
                  if (RB_LEFT(parent, field) == elm) {            \
                        RB_ROTATE_RIGHT(head, parent, tmp, field);\
                        tmp = parent;                       \
                        parent = elm;                       \
                        elm = tmp;                    \
                  }                                   \
                  RB_SET_BLACKRED(parent, gparent, field);  \
                  RB_ROTATE_LEFT(head, gparent, tmp, field);      \
            }                                         \
      }                                               \
      RB_COLOR(head->rbh_root, field) = RB_BLACK;                 \
}                                                     \
                                                      \
attr void                                             \
name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
{                                                     \
      struct type *tmp;                               \
      while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
          elm != RB_ROOT(head)) {                           \
            if (RB_LEFT(parent, field) == elm) {                  \
                  tmp = RB_RIGHT(parent, field);                  \
                  if (RB_COLOR(tmp, field) == RB_RED) {           \
                        RB_SET_BLACKRED(tmp, parent, field);      \
                        RB_ROTATE_LEFT(head, parent, tmp, field);\
                        tmp = RB_RIGHT(parent, field);            \
                  }                                   \
                  if ((RB_LEFT(tmp, field) == NULL ||       \
                      RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
                      (RB_RIGHT(tmp, field) == NULL ||            \
                      RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
                        RB_COLOR(tmp, field) = RB_RED;            \
                        elm = parent;                       \
                        parent = RB_PARENT(elm, field);           \
                  } else {                            \
                        if (RB_RIGHT(tmp, field) == NULL || \
                            RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
                              struct type *oleft;           \
                              if ((oleft = RB_LEFT(tmp, field)) \
                                  != NULL)                  \
                                    RB_COLOR(oleft, field) = RB_BLACK;\
                              RB_COLOR(tmp, field) = RB_RED;      \
                              RB_ROTATE_RIGHT(head, tmp, oleft, field);\
                              tmp = RB_RIGHT(parent, field);      \
                        }                             \
                        RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
                        RB_COLOR(parent, field) = RB_BLACK; \
                        if (RB_RIGHT(tmp, field))           \
                              RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
                        RB_ROTATE_LEFT(head, parent, tmp, field);\
                        elm = RB_ROOT(head);                \
                        break;                              \
                  }                                   \
            } else {                                  \
                  tmp = RB_LEFT(parent, field);             \
                  if (RB_COLOR(tmp, field) == RB_RED) {           \
                        RB_SET_BLACKRED(tmp, parent, field);      \
                        RB_ROTATE_RIGHT(head, parent, tmp, field);\
                        tmp = RB_LEFT(parent, field);       \
                  }                                   \
                  if ((RB_LEFT(tmp, field) == NULL ||       \
                      RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
                      (RB_RIGHT(tmp, field) == NULL ||            \
                      RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
                        RB_COLOR(tmp, field) = RB_RED;            \
                        elm = parent;                       \
                        parent = RB_PARENT(elm, field);           \
                  } else {                            \
                        if (RB_LEFT(tmp, field) == NULL ||  \
                            RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
                              struct type *oright;          \
                              if ((oright = RB_RIGHT(tmp, field)) \
                                  != NULL)                  \
                                    RB_COLOR(oright, field) = RB_BLACK;\
                              RB_COLOR(tmp, field) = RB_RED;      \
                              RB_ROTATE_LEFT(head, tmp, oright, field);\
                              tmp = RB_LEFT(parent, field); \
                        }                             \
                        RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
                        RB_COLOR(parent, field) = RB_BLACK; \
                        if (RB_LEFT(tmp, field))            \
                              RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
                        RB_ROTATE_RIGHT(head, parent, tmp, field);\
                        elm = RB_ROOT(head);                \
                        break;                              \
                  }                                   \
            }                                         \
      }                                               \
      if (elm)                                        \
            RB_COLOR(elm, field) = RB_BLACK;                \
}                                                     \
                                                      \
attr struct type *                                          \
name##_RB_REMOVE(struct name *head, struct type *elm)             \
{                                                     \
      struct type *child, *parent, *old = elm;              \
      int color;                                      \
      if (RB_LEFT(elm, field) == NULL)                      \
            child = RB_RIGHT(elm, field);                   \
      else if (RB_RIGHT(elm, field) == NULL)                      \
            child = RB_LEFT(elm, field);                    \
      else {                                                \
            struct type *left;                              \
            elm = RB_RIGHT(elm, field);                     \
            while ((left = RB_LEFT(elm, field)) != NULL)          \
                  elm = left;                         \
            child = RB_RIGHT(elm, field);                   \
            parent = RB_PARENT(elm, field);                       \
            color = RB_COLOR(elm, field);                   \
            if (child)                                \
                  RB_PARENT(child, field) = parent;         \
            if (parent) {                                   \
                  if (RB_LEFT(parent, field) == elm)        \
                        RB_LEFT(parent, field) = child;           \
                  else                                \
                        RB_RIGHT(parent, field) = child;    \
                  RB_AUGMENT(parent);                       \
            } else                                          \
                  RB_ROOT(head) = child;                    \
            if (RB_PARENT(elm, field) == old)               \
                  parent = elm;                             \
            (elm)->field = (old)->field;                    \
            if (RB_PARENT(old, field)) {                    \
                  if (RB_LEFT(RB_PARENT(old, field), field) == old)\
                        RB_LEFT(RB_PARENT(old, field), field) = elm;\
                  else                                \
                        RB_RIGHT(RB_PARENT(old, field), field) = elm;\
                  RB_AUGMENT(RB_PARENT(old, field));        \
            } else                                          \
                  RB_ROOT(head) = elm;                      \
            RB_PARENT(RB_LEFT(old, field), field) = elm;          \
            if (RB_RIGHT(old, field))                       \
                  RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
            if (parent) {                                   \
                  left = parent;                            \
                  do {                                \
                        RB_AUGMENT(left);             \
                  } while ((left = RB_PARENT(left, field)) != NULL); \
            }                                         \
            goto color;                               \
      }                                               \
      parent = RB_PARENT(elm, field);                             \
      color = RB_COLOR(elm, field);                         \
      if (child)                                      \
            RB_PARENT(child, field) = parent;               \
      if (parent) {                                         \
            if (RB_LEFT(parent, field) == elm)              \
                  RB_LEFT(parent, field) = child;                 \
            else                                      \
                  RB_RIGHT(parent, field) = child;          \
            RB_AUGMENT(parent);                             \
      } else                                                \
            RB_ROOT(head) = child;                          \
color:                                                      \
      if (color == RB_BLACK)                                \
            name##_RB_REMOVE_COLOR(head, parent, child);          \
      return (old);                                         \
}                                                     \
                                                      \
/* Inserts a node into the RB tree */                             \
attr struct type *                                          \
name##_RB_INSERT(struct name *head, struct type *elm)             \
{                                                     \
      struct type *tmp;                               \
      struct type *parent = NULL;                           \
      int comp = 0;                                         \
      tmp = RB_ROOT(head);                                  \
      while (tmp) {                                         \
            parent = tmp;                                   \
            comp = (cmp)(elm, parent);                      \
            if (comp < 0)                                   \
                  tmp = RB_LEFT(tmp, field);                \
            else if (comp > 0)                              \
                  tmp = RB_RIGHT(tmp, field);               \
            else                                      \
                  return (tmp);                             \
      }                                               \
      RB_SET(elm, parent, field);                           \
      if (parent != NULL) {                                 \
            if (comp < 0)                                   \
                  RB_LEFT(parent, field) = elm;             \
            else                                      \
                  RB_RIGHT(parent, field) = elm;                  \
            RB_AUGMENT(parent);                             \
      } else                                                \
            RB_ROOT(head) = elm;                            \
      name##_RB_INSERT_COLOR(head, elm);                    \
      return (NULL);                                        \
}                                                     \
                                                      \
/* Finds the node with the same key as elm */                     \
attr struct type *                                          \
name##_RB_FIND(struct name *head, struct type *elm)               \
{                                                     \
      struct type *tmp = RB_ROOT(head);                     \
      int comp;                                       \
      while (tmp) {                                         \
            comp = cmp(elm, tmp);                           \
            if (comp < 0)                                   \
                  tmp = RB_LEFT(tmp, field);                \
            else if (comp > 0)                              \
                  tmp = RB_RIGHT(tmp, field);               \
            else                                      \
                  return (tmp);                             \
      }                                               \
      return (NULL);                                        \
}                                                     \
                                                      \
/* Finds the first node greater than or equal to the search key */      \
attr struct type *                                          \
name##_RB_NFIND(struct name *head, struct type *elm)              \
{                                                     \
      struct type *tmp = RB_ROOT(head);                     \
      struct type *res = NULL;                              \
      int comp;                                       \
      while (tmp) {                                         \
            comp = cmp(elm, tmp);                           \
            if (comp < 0) {                                 \
                  res = tmp;                          \
                  tmp = RB_LEFT(tmp, field);                \
            }                                         \
            else if (comp > 0)                              \
                  tmp = RB_RIGHT(tmp, field);               \
            else                                      \
                  return (tmp);                             \
      }                                               \
      return (res);                                         \
}                                                     \
                                                      \
/* ARGSUSED */                                              \
attr struct type *                                          \
name##_RB_NEXT(struct type *elm)                            \
{                                                     \
      if (RB_RIGHT(elm, field)) {                           \
            elm = RB_RIGHT(elm, field);                     \
            while (RB_LEFT(elm, field))                     \
                  elm = RB_LEFT(elm, field);                \
      } else {                                        \
            if (RB_PARENT(elm, field) &&                    \
                (elm == RB_LEFT(RB_PARENT(elm, field), field)))   \
                  elm = RB_PARENT(elm, field);              \
            else {                                          \
                  while (RB_PARENT(elm, field) &&                 \
                      (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
                        elm = RB_PARENT(elm, field);        \
                  elm = RB_PARENT(elm, field);              \
            }                                         \
      }                                               \
      return (elm);                                         \
}                                                     \
                                                      \
/* ARGSUSED */                                              \
attr struct type *                                          \
name##_RB_PREV(struct type *elm)                            \
{                                                     \
      if (RB_LEFT(elm, field)) {                            \
            elm = RB_LEFT(elm, field);                      \
            while (RB_RIGHT(elm, field))                    \
                  elm = RB_RIGHT(elm, field);               \
      } else {                                        \
            if (RB_PARENT(elm, field) &&                    \
                (elm == RB_RIGHT(RB_PARENT(elm, field), field)))  \
                  elm = RB_PARENT(elm, field);              \
            else {                                          \
                  while (RB_PARENT(elm, field) &&                 \
                      (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
                        elm = RB_PARENT(elm, field);        \
                  elm = RB_PARENT(elm, field);              \
            }                                         \
      }                                               \
      return (elm);                                         \
}                                                     \
                                                      \
attr struct type *                                          \
name##_RB_MINMAX(struct name *head, int val)                      \
{                                                     \
      struct type *tmp = RB_ROOT(head);                     \
      struct type *parent = NULL;                           \
      while (tmp) {                                         \
            parent = tmp;                                   \
            if (val < 0)                                    \
                  tmp = RB_LEFT(tmp, field);                \
            else                                      \
                  tmp = RB_RIGHT(tmp, field);               \
      }                                               \
      return (parent);                                \
}

#define RB_NEGINF -1
#define RB_INF    1

#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y)   name##_RB_FIND(x, y)
#define RB_NFIND(name, x, y)  name##_RB_NFIND(x, y)
#define RB_NEXT(name, x, y)   name##_RB_NEXT(y)
#define RB_PREV(name, x, y)   name##_RB_PREV(y)
#define RB_MIN(name, x)       name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x)       name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head)                           \
      for ((x) = RB_MIN(name, head);                              \
           (x) != NULL;                               \
           (x) = name##_RB_NEXT(x))

#define RB_FOREACH_REVERSE(x, name, head)                   \
      for ((x) = RB_MAX(name, head);                              \
           (x) != NULL;                               \
           (x) = name##_RB_PREV(x))

#endif      /* _SYS_TREE_H_ */

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