linux 中的rbtree算法

rbtree.h

 

#ifndef    _LINUX_RBTREE_H
#define    _LINUX_RBTREE_H

#include <linux/kernel.h>
#include <linux/stddef.h>

struct rb_node
{
    unsigned long  rb_parent_color;
#define    RB_RED        0
#define    RB_BLACK    1
    struct rb_node *rb_right;
    struct rb_node *rb_left;
} __attribute__((aligned(sizeof(long))));
    /* The alignment might seem pointless, but allegedly CRIS needs it */

struct rb_root
{
    struct rb_node *rb_node;
};


#define rb_parent(r)   ((struct rb_node *)((r)->rb_parent_color & ~3))
#define rb_color(r)   ((r)->rb_parent_color & 1)
#define rb_is_red(r)   (!rb_color(r))
#define rb_is_black(r) rb_color(r)
#define rb_set_red(r)  do { (r)->rb_parent_color &= ~1; } while (0)
#define rb_set_black(r)  do { (r)->rb_parent_color |= 1; } while (0)

static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
{
    rb->rb_parent_color = (rb->rb_parent_color & 3) | (unsigned long)p;
}
static inline void rb_set_color(struct rb_node *rb, int color)
{
    rb->rb_parent_color = (rb->rb_parent_color & ~1) | color;
}

#define RB_ROOT    (struct rb_root) { NULL, }
#define    rb_entry(ptr, type, member) container_of(ptr, type, member)

#define RB_EMPTY_ROOT(root)    ((root)->rb_node == NULL)
#define RB_EMPTY_NODE(node)    (rb_parent(node) == node)
#define RB_CLEAR_NODE(node)    (rb_set_parent(node, node))

extern void rb_insert_color(struct rb_node *, struct rb_root *);
extern void rb_erase(struct rb_node *, struct rb_root *);

/* Find logical next and previous nodes in a tree */
extern struct rb_node *rb_next(const struct rb_node *);
extern struct rb_node *rb_prev(const struct rb_node *);
extern struct rb_node *rb_first(const struct rb_root *);
extern struct rb_node *rb_last(const struct rb_root *);

/* Fast replacement of a single node without remove/rebalance/add/rebalance */
extern void rb_replace_node(struct rb_node *victim, struct rb_node *new,
                struct rb_root *root);

static inline void rb_link_node(struct rb_node * node, struct rb_node * parent,
                struct rb_node ** rb_link)
{
    node->rb_parent_color = (unsigned long )parent;
    node->rb_left = node->rb_right = NULL;

    *rb_link = node;
}

#endif    /* _LINUX_RBTREE_H */

==============================================================

rbtree.c

 

/*
  Red Black Trees
  (C) 1999  Andrea Arcangeli <[e-mail]>
  (C) 2002  David Woodhouse <[e-mail]>
 
  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 program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

  linux/lib/rbtree.c
*/

#include <linux/rbtree.h>
#include <linux/module.h>

static void __rb_rotate_left(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *right = node->rb_right;
    struct rb_node *parent = rb_parent(node);

    if ((node->rb_right = right->rb_left))
        rb_set_parent(right->rb_left, node);
    right->rb_left = node;

    rb_set_parent(right, parent);

    if (parent)
    {
        if (node == parent->rb_left)
            parent->rb_left = right;
        else
            parent->rb_right = right;
    }
    else
        root->rb_node = right;
    rb_set_parent(node, right);
}

static void __rb_rotate_right(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *left = node->rb_left;
    struct rb_node *parent = rb_parent(node);

    if ((node->rb_left = left->rb_right))
        rb_set_parent(left->rb_right, node);
    left->rb_right = node;

    rb_set_parent(left, parent);

    if (parent)
    {
        if (node == parent->rb_right)
            parent->rb_right = left;
        else
            parent->rb_left = left;
    }
    else
        root->rb_node = left;
    rb_set_parent(node, left);
}

void rb_insert_color(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *parent, *gparent;

    while ((parent = rb_parent(node)) && rb_is_red(parent))
    {
        gparent = rb_parent(parent);

        if (parent == gparent->rb_left)
        {
            {
                register struct rb_node *uncle = gparent->rb_right;
                if (uncle && rb_is_red(uncle))
                {
                    rb_set_black(uncle);
                    rb_set_black(parent);
                    rb_set_red(gparent);
                    node = gparent;
                    continue;
                }
            }

            if (parent->rb_right == node)
            {
                register struct rb_node *tmp;
                __rb_rotate_left(parent, root);
                tmp = parent;
                parent = node;
                node = tmp;
            }

            rb_set_black(parent);
            rb_set_red(gparent);
            __rb_rotate_right(gparent, root);
        } else {
            {
                register struct rb_node *uncle = gparent->rb_left;
                if (uncle && rb_is_red(uncle))
                {
                    rb_set_black(uncle);
                    rb_set_black(parent);
                    rb_set_red(gparent);
                    node = gparent;
                    continue;
                }
            }

            if (parent->rb_left == node)
            {
                register struct rb_node *tmp;
                __rb_rotate_right(parent, root);
                tmp = parent;
                parent = node;
                node = tmp;
            }

            rb_set_black(parent);
            rb_set_red(gparent);
            __rb_rotate_left(gparent, root);
        }
    }

    rb_set_black(root->rb_node);
}
EXPORT_SYMBOL(rb_insert_color);

static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
                 struct rb_root *root)
{
    struct rb_node *other;

    while ((!node || rb_is_black(node)) && node != root->rb_node)
    {
        if (parent->rb_left == node)
        {
            other = parent->rb_right;
            if (rb_is_red(other))
            {
                rb_set_black(other);
                rb_set_red(parent);
                __rb_rotate_left(parent, root);
                other = parent->rb_right;
            }
            if ((!other->rb_left || rb_is_black(other->rb_left)) &&
                (!other->rb_right || rb_is_black(other->rb_right)))
            {
                rb_set_red(other);
                node = parent;
                parent = rb_parent(node);
            }
            else
            {
                if (!other->rb_right || rb_is_black(other->rb_right))
                {
                    rb_set_black(other->rb_left);
                    rb_set_red(other);
                    __rb_rotate_right(other, root);
                    other = parent->rb_right;
                }
                rb_set_color(other, rb_color(parent));
                rb_set_black(parent);
                rb_set_black(other->rb_right);
                __rb_rotate_left(parent, root);
                node = root->rb_node;
                break;
            }
        }
        else
        {
            other = parent->rb_left;
            if (rb_is_red(other))
            {
                rb_set_black(other);
                rb_set_red(parent);
                __rb_rotate_right(parent, root);
                other = parent->rb_left;
            }
            if ((!other->rb_left || rb_is_black(other->rb_left)) &&
                (!other->rb_right || rb_is_black(other->rb_right)))
            {
                rb_set_red(other);
                node = parent;
                parent = rb_parent(node);
            }
            else
            {
                if (!other->rb_left || rb_is_black(other->rb_left))
                {
                    rb_set_black(other->rb_right);
                    rb_set_red(other);
                    __rb_rotate_left(other, root);
                    other = parent->rb_left;
                }
                rb_set_color(other, rb_color(parent));
                rb_set_black(parent);
                rb_set_black(other->rb_left);
                __rb_rotate_right(parent, root);
                node = root->rb_node;
                break;
            }
        }
    }
    if (node)
        rb_set_black(node);
}

void rb_erase(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *child, *parent;
    int color;

    if (!node->rb_left)
        child = node->rb_right;
    else if (!node->rb_right)
        child = node->rb_left;
    else
    {
        struct rb_node *old = node, *left;

        node = node->rb_right;
        while ((left = node->rb_left) != NULL)
            node = left;
        child = node->rb_right;
        parent = rb_parent(node);
        color = rb_color(node);

        if (child)
            rb_set_parent(child, parent);
        if (parent == old) {
            parent->rb_right = child;
            parent = node;
        } else
            parent->rb_left = child;

        node->rb_parent_color = old->rb_parent_color;
        node->rb_right = old->rb_right;
        node->rb_left = old->rb_left;

        if (rb_parent(old))
        {
            if (rb_parent(old)->rb_left == old)
                rb_parent(old)->rb_left = node;
            else
                rb_parent(old)->rb_right = node;
        } else
            root->rb_node = node;

        rb_set_parent(old->rb_left, node);
        if (old->rb_right)
            rb_set_parent(old->rb_right, node);
        goto color;
    }

    parent = rb_parent(node);
    color = rb_color(node);

    if (child)
        rb_set_parent(child, parent);
    if (parent)
    {
        if (parent->rb_left == node)
            parent->rb_left = child;
        else
            parent->rb_right = child;
    }
    else
        root->rb_node = child;

 color:
    if (color == RB_BLACK)
        __rb_erase_color(child, parent, root);
}
EXPORT_SYMBOL(rb_erase);

/*
 * This function returns the first node (in sort order) of the tree.
 */
struct rb_node *rb_first(const struct rb_root *root)
{
    struct rb_node    *n;

    n = root->rb_node;
    if (!n)
        return NULL;
    while (n->rb_left)
        n = n->rb_left;
    return n;
}
EXPORT_SYMBOL(rb_first);

struct rb_node *rb_last(const struct rb_root *root)
{
    struct rb_node    *n;

    n = root->rb_node;
    if (!n)
        return NULL;
    while (n->rb_right)
        n = n->rb_right;
    return n;
}
EXPORT_SYMBOL(rb_last);

struct rb_node *rb_next(const struct rb_node *node)
{
    struct rb_node *parent;

    if (rb_parent(node) == node)
        return NULL;

    /* If we have a right-hand child, go down and then left as far
       as we can. */
    if (node->rb_right) {
        node = node->rb_right;
        while (node->rb_left)
            node=node->rb_left;
        return (struct rb_node *)node;
    }

    /* No right-hand children.  Everything down and left is
       smaller than us, so any 'next' node must be in the general
       direction of our parent. Go up the tree; any time the
       ancestor is a right-hand child of its parent, keep going
       up. First time it's a left-hand child of its parent, said
       parent is our 'next' node. */
    while ((parent = rb_parent(node)) && node == parent->rb_right)
        node = parent;

    return parent;
}
EXPORT_SYMBOL(rb_next);

struct rb_node *rb_prev(const struct rb_node *node)
{
    struct rb_node *parent;

    if (rb_parent(node) == node)
        return NULL;

    /* If we have a left-hand child, go down and then right as far
       as we can. */
    if (node->rb_left) {
        node = node->rb_left;
        while (node->rb_right)
            node=node->rb_right;
        return (struct rb_node *)node;
    }

    /* No left-hand children. Go up till we find an ancestor which
       is a right-hand child of its parent */
    while ((parent = rb_parent(node)) && node == parent->rb_left)
        node = parent;

    return parent;
}
EXPORT_SYMBOL(rb_prev);

void rb_replace_node(struct rb_node *victim, struct rb_node *new,
             struct rb_root *root)
{
    struct rb_node *parent = rb_parent(victim);

    /* Set the surrounding nodes to point to the replacement */
    if (parent) {
        if (victim == parent->rb_left)
            parent->rb_left = new;
        else
            parent->rb_right = new;
    } else {
        root->rb_node = new;
    }
    if (victim->rb_left)
        rb_set_parent(victim->rb_left, new);
    if (victim->rb_right)
        rb_set_parent(victim->rb_right, new);

    /* Copy the pointers/colour from the victim to the replacement */
    *new = *victim;
}
EXPORT_SYMBOL(rb_replace_node);

 

===================================================

rbtree.txt

 

 

Red-black Trees (rbtree) in Linux January 18, 2007 Rob Landley <[e-mail]> =============================
What are red-black trees, and what are they for?
------------------------------------------------
Red-black trees are a type of self-balancing binary search tree, used for storing sortable key/value data pairs.  This differs from radix trees (which are used to efficiently store sparse arrays and thus use long integer indexes to insert/access/delete nodes) and hash tables (which are not kept sorted to be easily traversed in order, and must be tuned for a specific size and hash function where rbtrees scale gracefully storing arbitrary keys).
Red-black trees are similar to AVL trees, but provide faster real-time bounded worst case performance for insertion and deletion (at most two rotations and three rotations, respectively, to balance the tree), with slightly slower (but still O(log n)) lookup time.
To quote Linux Weekly News:
    There are a number of red-black trees in use in the kernel.
    The anticipatory, deadline, and CFQ I/O schedulers all employ rbtrees to track requests; the packet CD/DVD driver does the same.
    The high-resolution timer code uses an rbtree to organize outstanding timer requests.  The ext3 filesystem tracks directory entries in a
    red-black tree.  Virtual memory areas (VMAs) are tracked with red-black trees, as are epoll file descriptors, cryptographic keys, and network packets in the "hierarchical token bucket" scheduler.
This document covers use of the Linux rbtree implementation.  For more information on the nature and implementation of Red Black Trees,  see:
  Linux Weekly News article on red-black trees http://lwn.net/Articles/184495/
  Wikipedia entry on red-black trees http://en.wikipedia.org/wiki/Red-black_tree
Linux implementation of red-black trees
---------------------------------------
Linux's rbtree implementation lives in the file "lib/rbtree.c".  To use it, "#include <linux/rbtree.h>".
The Linux rbtree implementation is optimized for speed, and thus has one less layer of indirection (and better cache locality) than more traditional tree implementations.  Instead of using pointers to separate rb_node and data structures, each instance of struct rb_node is embedded in the data structure it organizes.  And instead of using a comparison callback function pointer, users are expected to write their own tree search and insert functions which call the provided rbtree functions.  Locking is also left up to the user of the rbtree code.
Creating a new rbtree
---------------------
Data nodes in an rbtree tree are structures containing a struct rb_node member:
  struct mytype { struct rb_node node;
      char *keystring; };
When dealing with a pointer to the embedded struct rb_node, the containing data structure may be accessed with the standard container_of() macro.  In addition, individual members may be accessed directly via rb_entry(node, type, member).
At the root of each rbtree is an rb_root structure, which is initialized to be empty via:
  struct rb_root mytree = RB_ROOT;
Searching for a value in an rbtree
----------------------------------
Writing a search function for your tree is fairly straightforward: start at the root, compare each value, and follow the left or right branch as necessary.
Example:
  struct mytype *my_search(struct rb_root *root, char *string)
  { struct rb_node *node = root->rb_node;
      while (node) { struct mytype *data = container_of(node, struct mytype, node); int result;
        result = strcmp(string, data->keystring);
        if (result < 0) node = node->rb_left; else if (result > 0) node = node->rb_right; else return data; }
    return NULL; }
Inserting data into an rbtree
-----------------------------
Inserting data in the tree involves first searching for the place to insert the new node, then inserting the node and rebalancing ("recoloring") the tree.
The search for insertion differs from the previous search by finding the location of the pointer on which to graft the new node.  The new node also needs a link to its parent node for rebalancing purposes.
Example:
  int my_insert(struct rb_root *root, struct mytype *data)
  { struct rb_node **new = &(root->rb_node), *parent = NULL;
      /* Figure out where to put new node */
      while (*new) { struct mytype *this = container_of(*new, struct mytype, node);
          int result = strcmp(data->keystring, this->keystring);
        parent = *new; if (result < 0) new = &((*new)->rb_left); else if (result > 0) new = &((*new)->rb_right); else return FALSE; }
      /* Add new node and rebalance tree. */
      rb_link_node(data->node, parent, new);
      rb_insert_color(data->node, root);
    return TRUE; }
Removing or replacing existing data in an rbtree
------------------------------------------------
To remove an existing node from a tree, call:
  void rb_erase(struct rb_node *victim, struct rb_root *tree);
Example:
  struct mytype *data = mysearch(mytree, "walrus");
  if (data) { rb_erase(data->node, mytree);
      myfree(data); }
To replace an existing node in a tree with a new one with the same key, call:
  void rb_replace_node(struct rb_node *old, struct rb_node *new, struct rb_root *tree);
Replacing a node this way does not re-sort the tree: If the new node doesn't have the same key as the old node, the rbtree will probably become corrupted.
Iterating through the elements stored in an rbtree (in sort order)
------------------------------------------------------------------
Four functions are provided for iterating through an rbtree's contents in sorted order.  These work on arbitrary trees, and should not need to be modified or wrapped (except for locking purposes):
  struct rb_node *rb_first(struct rb_root *tree);
  struct rb_node *rb_last(struct rb_root *tree);
  struct rb_node *rb_next(struct rb_node *node);
  struct rb_node *rb_prev(struct rb_node *node);
To start iterating, call rb_first() or rb_last() with a pointer to the root of the tree, which will return a pointer to the node structure contained in the first or last element in the tree.  To continue, fetch the next or previous node by calling rb_next() or rb_prev() on the current node.  This will return NULL when there are no more nodes left.
The iterator functions return a pointer to the embedded struct rb_node, from which the containing data structure may be accessed with the container_of() macro, and individual members may be accessed directly via rb_entry(node, type, member).
Example:
  struct rb_node *node;
  for (node = rb_first(&mytree); node; node = rb_next(node)) printk("key=%s/n", rb_entry(node, int, keystring));