@c
@c Copyright 2014 Gedare Bloom. 
@c All rights reserved.

@chapter Red-Black Trees

@cindex rbtrees

@section Introduction

The Red-Black Tree API is an interface to the SuperCore (score) rbtree
implementation. Within RTEMS, red-black trees are used when a binary search
tree is needed, including dynamic priority thread queues and non-contiguous
heap memory. The Red-Black Tree API provided by RTEMS is:

@itemize @bullet
@c build_id
@item @code{@value{DIRPREFIX}rtems_rbtree_node} - Red-Black Tree node embedded in another struct
@item @code{@value{DIRPREFIX}rtems_rbtree_control} - Red-Black Tree control node for an entire tree
@item @code{@value{DIRPREFIX}rtems_rbtree_initialize} - initialize the red-black tree with nodes
@item @code{@value{DIRPREFIX}rtems_rbtree_initialize_empty} - initialize the red-black tree as empty
@item @code{@value{DIRPREFIX}rtems_rbtree_set_off_tree} - Clear a node's links
@item @code{@value{DIRPREFIX}rtems_rbtree_root} - Return the red-black tree's root node
@item @code{@value{DIRPREFIX}rtems_rbtree_min} - Return the red-black tree's minimum node
@item @code{@value{DIRPREFIX}rtems_rbtree_max} - Return the red-black tree's maximum node
@item @code{@value{DIRPREFIX}rtems_rbtree_left} - Return a node's left child node
@item @code{@value{DIRPREFIX}rtems_rbtree_right} - Return a node's right child node
@item @code{@value{DIRPREFIX}rtems_rbtree_parent} - Return a node's parent node
@item @code{@value{DIRPREFIX}rtems_rbtree_are_nodes_equal} - Are the node's equal ?
@item @code{@value{DIRPREFIX}rtems_rbtree_is_empty} - Is the red-black tree empty ?
@item @code{@value{DIRPREFIX}rtems_rbtree_is_min} - Is the Node the minimum in the red-black tree ?
@item @code{@value{DIRPREFIX}rtems_rbtree_is_max} - Is the Node the maximum in the red-black tree ?
@item @code{@value{DIRPREFIX}rtems_rbtree_is_root} - Is the Node the root of the red-black tree ?
@item @code{@value{DIRPREFIX}rtems_rbtree_find} - Find the node with a matching key in the red-black tree
@item @code{@value{DIRPREFIX}rtems_rbtree_predecessor} - Return the in-order predecessor of a node.
@item @code{@value{DIRPREFIX}rtems_rbtree_successor} - Return the in-order successor of a node.
@item @code{@value{DIRPREFIX}rtems_rbtree_extract} - Remove the node from the red-black tree
@item @code{@value{DIRPREFIX}rtems_rbtree_get_min} - Remove the minimum node from the red-black tree
@item @code{@value{DIRPREFIX}rtems_rbtree_get_max} - Remove the maximum node from the red-black tree
@item @code{@value{DIRPREFIX}rtems_rbtree_peek_min} - Returns the minimum node from the red-black tree
@item @code{@value{DIRPREFIX}rtems_rbtree_peek_max} - Returns the maximum node from the red-black tree
@item @code{@value{DIRPREFIX}rtems_rbtree_find_control} - Returns the control node of a red-black tree given a node in the tree.
@item @code{@value{DIRPREFIX}rtems_rbtree_insert} - Add the node to the red-black tree
@end itemize

@section Background

The Red-Black Trees API is a thin layer above the SuperCore Red-Black Trees
implementation. A Red-Black Tree is defined by a control node with pointers to
the root, minimum, and maximum nodes in the tree. Each node in the tree
consists of a parent pointer, two children pointers, and a color attribute.  A
tree is parameterized as either unique, meaning identical keys are rejected, or
not, in which case duplicate keys are allowed.

Users must provide a comparison functor that gets passed to functions that need
to compare nodes. In addition, no internal synchronization is offered within
the red-black tree implementation, thus users must ensure at most one thread
accesses a red-black tree instance at a time.

@subsection Nodes

A red-black tree is made up from nodes that orginate from a red-black tree control
object. A node is of type @code{@value{DIRPREFIX}rtems_rbtree_node}. The node
is designed to be part of a user data structure. To obtain the encapsulating
structure users can use the @code{RTEMS_CONTAINER_OF} macro.
The node can be placed anywhere within the user's structure and the macro will
calculate the structure's address from the node's address. 

@subsection Controls

A red-black tree is rooted with a control object. Red-Black Tree control
provide the user with access to the nodes on the red-black tree.  The
implementation does not require special checks for manipulating the root of the
red-black tree. To accomplish this the
@code{@value{DIRPREFIX}rtems_rbtree_control} structure is treated as a
@code{@value{DIRPREFIX}rtems_rbtree_node} structure with a @code{NULL} parent
and left child pointing to the root. 

@section Operations

Examples for using the red-black trees
can be found in the testsuites/sptests/sprbtree01/init.c file.

@section Directives

@subsection Documentation for the Red-Black Tree Directives

@cindex rbtree doc

Source documentation for the Red-Black Tree API can be found in the
generated Doxygen output for cpukit/sapi.