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NAME

rbtree — red-black tree

LIBRARY

library “libc”

SYNOPSIS

#include <sys/rbtree.h>

void
rb_tree_init(rb_tree_t *rbt, const rb_tree_ops_t *ops);

void *
rb_tree_insert_node(rb_tree_t *rbt, void *rb);

void
rb_tree_remove_node(rb_tree_t *rbt, void *rb);

void *
rb_tree_find_node(rb_tree_t *rbt, const void *key);

void *
rb_tree_find_node_geq(rb_tree_t *rbt, const void *key);

void *
rb_tree_find_node_leq(rb_tree_t *rbt, const void *key);

void *
rb_tree_iterate(rb_tree_t *rbt, void *rb, unsigned int direction);

void *
RB_TREE_MIN(rb_tree_t *rbt);

void *
RB_TREE_MAX(rb_tree_t *rbt);

RB_TREE_NEXT(rb_tree_t *rbt, void *rb);

RB_TREE_PREV(rb_tree_t *rbt, void *rb);

RB_TREE_FOREACH(void *rb, rb_tree_t *rbt);

RB_TREE_FOREACH_SAFE(void *rb, rb_tree_t *rbt, void *tmp);

RB_TREE_FOREACH_REVERSE(void *rb, rb_tree_t *rbt);

RB_TREE_FOREACH_REVERSE_SAFE(void *rb, rb_tree_t *rbt, void *tmp);

DESCRIPTION

rbtree provides 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:

1. Every search path from the root to a leaf consists of the same number of black nodes.
2. Each red node (except for the root) has a black parent.
3. 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).

TYPES

rb_tree_t

A red-black tree.

typedef signed int (* rbto_compare_nodes_fn)(void *context, const void *node1, const void *node2);

The node-comparison function. Defines an ordering on nodes. Returns a negative value if the first node node1 precedes the second node node2. Returns a positive value if the first node node1 follows the second node node2. Returns 0 if the first node node1 and the second node node2 are identical according to the ordering.

typedef signed int (* rbto_compare_key_fn)(void *context, const void *node, const void *key);

The node-key comparison function. Defines the order of nodes and keys. Returns a negative value if the node node precedes the key key. Returns a positive value if the node node follows the key key. Returns 0 if the node node is identical to the key key according to the ordering.

rb_tree_ops_t

Defines the function for comparing two nodes in the same tree, the function for comparing a node in the tree with a key, the offset of member rb_node_t within the node type, and the opaque context pointer passed to the comparison functions. Members of rb_tree_ops_t are

        rbto_compare_nodes_fn rbto_compare_nodes;
        rbto_compare_key_fn rbto_compare_key;
        size_t rbto_node_offset;
        void *rbto_context;

rb_node_t

A node in a red-black tree has this structure as a member. The offset of the rb_node_t member in the caller's node structure should be provided as rbto_node_offset. (None of the functions in the rbtree interface are meant to take pointers directly to the rb_node_t member.)

FUNCTIONS

rb_tree_init(rbt, ops)

Initialize the red-black tree rbt. Let the comparison functions given by ops define the order of nodes in the tree for the purposes of insertion, search, and iteration. rb_tree_init() always succeeds.

rb_tree_insert_node(rbt, rb)

Insert the node rb into the tree rbt. Return inserted node on success, already existing node on failure.

rb_tree_remove_node(rbt, rb)

Remove the node rb from the tree rbt.

rb_tree_find_node(rbt, key)

Search the tree rbt for a node exactly matching key. If no such node is in the tree, return NULL. Otherwise, return the matching node.

rb_tree_find_node_geq(rbt, key)

Search the tree rbt for a node that exactly matches key and return it. If no such node is present, return the first node following key or, if no such node is in the tree, return NULL.

rb_tree_find_node_leq(rbt, key)

Search the tree rbt for a node that exactly matches key and return it. If no such node is present, return the first node preceding key or, if no such node is in the tree, return NULL.

rb_tree_iterate(rbt, rb, direction)

If direction is RB_DIR_LEFT, return the node in the tree rbt immediately preceding the node rb or, if rb is NULL, return the first node in rbt or, if the tree is empty, return NULL.

If direction is RB_DIR_RIGHT, return the node in the tree rbt immediately following the node rb or, if rb is NULL, return the last node in rbt or, if the tree is empty, return NULL.

RB_TREE_MIN(rbt)

Return the first node in rbt, i.e. the node with the least key, or NULL if rbt is empty.

RB_TREE_MAX(rbt)

Return the last node in rbt, i.e. the node with the greatest key, or NULL if rbt is empty.

RB_TREE_NEXT(rbt, rb)

Return the next node in rbt, or NULL if there is none.

RB_TREE_PREV(rbt, rb)

Return the previous node in rbt, or NULL if there is none.

RB_TREE_FOREACH(rb, rbt)

RB_TREE_FOREACH is a macro to be used in the place of a for header preceding a statement to traverse the nodes in rbt from least to greatest, assigning rb to each node in turn and executing the statement.

RB_TREE_FOREACH_SAFE(rb, rbt, tmp)

Allows both the removal of rb as well as freeing it from within the loop safely without interfering with the traversal.

RB_TREE_FOREACH_REVERSE(rb, rbt)

RB_TREE_FOREACH_REVERSE is a macro to be used in the place of a for header preceding a statement to traverse the nodes in rbt from greatest to least, assigning rb to each node in turn and executing the statement.

RB_TREE_FOREACH_REVERSE_SAFE(rb, rbt, tmp)

Allows both the removal of rb as well as freeing it from within the loop safely without interfering with the traversal.

CODE REFERENCES

The rbtree interface is implemented in common/lib/libc/gen/rb.c.

SEE ALSO

queue(3), tree(3)

HISTORY

The rbtree interface first appeared in NetBSD 6.0.

AUTHORS

Matt Thomas <matt@NetBSD.org> wrote rbtree.

Niels Provos <provos@citi.umich.edu> wrote the tree(3) manual page. Portions of this page derive from that page.