/** @brief Validate and fix-up tree properties for a new insert/colored node
*
* This routine checks and fixes the Red-Black Tree properties based on
* @a the_node being just added to the tree.
*
* @note It does NOT disable interrupts to ensure the atomicity of the
* append operation.
*/
static void _RBTree_Validate_insert( RBTree_Node *the_node )
{
RBTree_Node *parent = _RBTree_Parent( the_node );
RBTree_Color parentcolor;
RBTree_Node *grandparent = _RBTree_Parent_and_color( parent, &parentcolor );
/* note: the insert root case is handled already */
/* if the parent is black, nothing needs to be done
* otherwise may need to loop a few times */
while ( parentcolor == RBT_RED ) {
/* The root is black, so the grandparent must exist */
RBTree_Node *uncle = _RBTree_Sibling( parent, grandparent );
RBTree_Node *grandgrandparent = _RBTree_Parent( grandparent );
/*
* If uncle exists and is red, repaint uncle/parent black and grandparent
* red.
*/
if ( uncle != NULL && _RBTree_Color( uncle ) == RBT_RED ) {
_RBTree_Set_parent_and_color( parent, grandparent, RBT_BLACK );
_RBTree_Set_parent_and_color( uncle, grandparent, RBT_BLACK );
_RBTree_Set_parent_and_color( grandparent, grandgrandparent, RBT_RED );
the_node = grandparent;
parent = grandgrandparent;
grandparent = _RBTree_Parent_and_color( parent, &parentcolor );
if ( grandparent == NULL )
break;
} else { /* If uncle does not exist or is black */
RBTree_Direction dir = _RBTree_Direction( the_node, parent );
RBTree_Direction parentdir = _RBTree_Direction( parent, grandparent );
/* ensure node is on the same branch direction as parent */
if ( dir != parentdir ) {
RBTree_Node *oldparent = parent;
parent = the_node;
the_node = oldparent;
_RBTree_Rotate( oldparent, parentdir );
}
_RBTree_Set_color( parent, RBT_BLACK );
_RBTree_Set_parent_and_color( grandparent, grandgrandparent, RBT_RED );
/* now rotate grandparent in the other branch direction (toward uncle) */
_RBTree_Rotate( grandparent, _RBTree_Opposite_direction( parentdir ) );
grandparent = _RBTree_Parent( parent );
break;
}
}
if ( grandparent == NULL )
_RBTree_Set_parent_and_color( the_node, parent, RBT_BLACK );
}
/** @brief Validate and fix-up tree properties after deleting a node
*
* This routine is called on a black node, @a the_node, after its deletion.
* This function maintains the properties of the red-black tree.
*/
static void rtems_rbtree_extract_validate( RBTree_Node *the_node )
{
RBTree_Color color;
RBTree_Node *parent = _RBTree_Parent_and_color( the_node, &color );
RBTree_Color parentcolor;
RBTree_Node *grandparent = _RBTree_Parent_and_color( parent, &parentcolor );
if ( grandparent == NULL )
return;
/* continue to correct tree as long as the_node is black and not the root */
while ( grandparent != NULL && color == RBT_BLACK ) {
RBTree_Node *sibling = _RBTree_Sibling( the_node, parent );
/* if sibling is red, switch parent (black) and sibling colors,
* then rotate parent left, making the sibling be the_node's grandparent.
* Now the_node has a black sibling and red parent. After rotation,
* update sibling pointer.
*/
if ( _RBTree_Color( sibling ) == RBT_RED ) {
RBTree_Direction dir = _RBTree_Direction( the_node, parent );
RBTree_Direction opp_dir = _RBTree_Opposite_direction( dir );
parentcolor = RBT_RED;
_RBTree_Set_parent_and_color( parent, grandparent, parentcolor );
_RBTree_Set_parent_and_color( sibling, parent, RBT_BLACK );
_RBTree_Rotate( parent, dir );
grandparent = sibling;
sibling = parent->child[ opp_dir ];
}
/* sibling is black, see if both of its children are also black. */
if ( _RBTree_Is_null_or_black( sibling->child[ RBT_RIGHT ] ) &&
_RBTree_Is_null_or_black( sibling->child[ RBT_LEFT ] ) ) {
_RBTree_Set_parent_and_color( sibling, parent, RBT_RED );
if ( parentcolor == RBT_RED ) {
_RBTree_Set_parent_and_color( parent, grandparent, RBT_BLACK );
break;
}
the_node = parent; /* done if parent is red */
parent = grandparent;
grandparent = _RBTree_Parent_and_color( parent, &parentcolor );
} else {
/* at least one of sibling's children is red. we now proceed in two
* cases, either the_node is to the left or the right of the parent.
* In both cases, first check if one of sibling's children is black,
* and if so rotate in the proper direction and update sibling pointer.
* Then switch the sibling and parent colors, and rotate through parent.
*/
RBTree_Direction dir = _RBTree_Direction( the_node, parent );
RBTree_Direction opp_dir = _RBTree_Opposite_direction( dir );
if ( _RBTree_Is_null_or_black( sibling->child[ opp_dir ] ) ) {
_RBTree_Set_parent_and_color( sibling, parent, RBT_RED );
_RBTree_Set_parent_and_color(
sibling->child[ dir ],
sibling,
RBT_BLACK
);
_RBTree_Rotate( sibling, opp_dir );
sibling = parent->child[ opp_dir ];
}
_RBTree_Set_parent_and_color( sibling, parent, parentcolor );
_RBTree_Set_parent_and_color( parent, grandparent, RBT_BLACK );
_RBTree_Set_parent_and_color(
sibling->child[ opp_dir ],
sibling,
RBT_BLACK
);
_RBTree_Rotate( parent, dir );
grandparent = sibling;
break; /* done */
}
} /* while */
if ( grandparent == NULL )
_RBTree_Set_parent_and_color( the_node, parent, RBT_BLACK );
}
/** @brief Validate and fix-up tree properties after deleting a node
*
* This routine is called on a black node, @a the_node, after its deletion.
* This function maintains the properties of the red-black tree.
*
* @note It does NOT disable interrupts to ensure the atomicity
* of the extract operation.
*/
static void _RBTree_Extract_validate( RBTree_Node *the_node )
{
RBTree_Node *parent;
parent = the_node->parent;
if ( !parent->parent )
return;
/* continue to correct tree as long as the_node is black and not the root */
while ( !_RBTree_Is_red( the_node ) && parent->parent ) {
RBTree_Node *sibling = _RBTree_Sibling( the_node, parent );
/* if sibling is red, switch parent (black) and sibling colors,
* then rotate parent left, making the sibling be the_node's grandparent.
* Now the_node has a black sibling and red parent. After rotation,
* update sibling pointer.
*/
if ( _RBTree_Is_red( sibling ) ) {
RBTree_Direction dir = _RBTree_Direction( the_node, parent );
RBTree_Direction opp_dir = _RBTree_Opposite_direction( dir );
parent->color = RBT_RED;
sibling->color = RBT_BLACK;
_RBTree_Rotate( parent, dir );
sibling = parent->child[ opp_dir ];
}
/* sibling is black, see if both of its children are also black. */
if ( !_RBTree_Is_red( sibling->child[ RBT_RIGHT ] ) &&
!_RBTree_Is_red( sibling->child[ RBT_LEFT ] ) ) {
sibling->color = RBT_RED;
if ( _RBTree_Is_red( parent ) ) {
parent->color = RBT_BLACK;
break;
}
the_node = parent; /* done if parent is red */
parent = the_node->parent;
} else {
/* at least one of sibling's children is red. we now proceed in two
* cases, either the_node is to the left or the right of the parent.
* In both cases, first check if one of sibling's children is black,
* and if so rotate in the proper direction and update sibling pointer.
* Then switch the sibling and parent colors, and rotate through parent.
*/
RBTree_Direction dir = _RBTree_Direction( the_node, parent );
RBTree_Direction opp_dir = _RBTree_Opposite_direction( dir );
if (
!_RBTree_Is_red( sibling->child[ opp_dir ] )
) {
sibling->color = RBT_RED;
sibling->child[ dir ]->color = RBT_BLACK;
_RBTree_Rotate( sibling, opp_dir );
sibling = parent->child[ opp_dir ];
}
sibling->color = parent->color;
parent->color = RBT_BLACK;
sibling->child[ opp_dir ]->color = RBT_BLACK;
_RBTree_Rotate( parent, dir );
break; /* done */
}
} /* while */
if ( !the_node->parent->parent )
the_node->color = RBT_BLACK;
}
void rtems_rbtree_compact_extract(
RBTree_Control *the_rbtree,
RBTree_Node *the_node
)
{
RBTree_Node *leaf;
RBTree_Color color;
RBTree_Node *parent;
RBTree_Color victim_color;
RBTree_Direction dir;
/* check if min needs to be updated */
if ( the_node == the_rbtree->first[ RBT_LEFT ] ) {
the_rbtree->first[ RBT_LEFT ] = _RBTree_Successor( the_node );
}
/* Check if max needs to be updated. min=max for 1 element trees so
* do not use else if here. */
if ( the_node == the_rbtree->first[ RBT_RIGHT ] ) {
the_rbtree->first[ RBT_RIGHT ] = _RBTree_Predecessor( the_node );
}
/* if the_node has at most one non-null child then it is safe to proceed
* check if both children are non-null, if so then we must find a target node
* either max in node->child[RBT_LEFT] or min in node->child[RBT_RIGHT],
* and replace the_node with the target node. This maintains the binary
* search tree property, but may violate the red-black properties.
*/
if ( the_node->child[ RBT_LEFT ] && the_node->child[ RBT_RIGHT ] ) {
/* find max in node->child[RBT_LEFT] */
RBTree_Node *target = the_node->child[ RBT_LEFT ];
RBTree_Color targetcolor;
RBTree_Node *targetparent;
while ( target->child[ RBT_RIGHT ] != NULL )
target = target->child[ RBT_RIGHT ];
/* if the target node has a child, need to move it up the tree into
* target's position (target is the right child of target->parent)
* when target vacates it. if there is no child, then target->parent
* should become NULL. This may cause the coloring to be violated.
* For now we store the color of the node being deleted in victim_color.
*/
leaf = target->child[ RBT_LEFT ];
targetparent = _RBTree_Parent_and_color( target, &targetcolor );
if ( leaf != NULL ) {
_RBTree_Set_parent( leaf, targetparent );
} else {
/* fix the tree here if the child is a null leaf. */
rtems_rbtree_extract_validate( target );
targetparent = _RBTree_Parent_and_color( target, &targetcolor );
}
victim_color = targetcolor;
dir = _RBTree_Direction( target, targetparent );
targetparent->child[ dir ] = leaf;
/* now replace the_node with target */
parent = _RBTree_Parent_and_color( the_node, &color );
dir = _RBTree_Direction( the_node, parent );
parent->child[ dir ] = target;
/* set target's new children to the original node's children */
target->child[ RBT_RIGHT ] = the_node->child[ RBT_RIGHT ];
if ( the_node->child[ RBT_RIGHT ] )
_RBTree_Set_parent( the_node->child[ RBT_RIGHT ], target );
target->child[ RBT_LEFT ] = the_node->child[ RBT_LEFT ];
if ( the_node->child[ RBT_LEFT ] )
_RBTree_Set_parent( the_node->child[ RBT_LEFT ], target );
/* finally, update the parent node and recolor. target has completely
* replaced the_node, and target's child has moved up the tree if needed.
* the_node is no longer part of the tree, although it has valid pointers
* still.
*/
_RBTree_Set_parent_and_color( target, parent, color );
} else {
parent = _RBTree_Parent_and_color( the_node, &color );
/* the_node has at most 1 non-null child. Move the child in to
* the_node's location in the tree. This may cause the coloring to be
* violated. We will fix it later.
* For now we store the color of the node being deleted in victim_color.
*/
leaf = the_node->child[ RBT_LEFT ] ?
the_node->child[ RBT_LEFT ] : the_node->child[ RBT_RIGHT ];
if ( leaf != NULL ) {
_RBTree_Set_parent( leaf, parent );
} else {
/* fix the tree here if the child is a null leaf. */
rtems_rbtree_extract_validate( the_node );
parent = _RBTree_Parent_and_color( the_node, &color );
}
victim_color = color;
/* remove the_node from the tree */
dir = _RBTree_Direction( the_node, parent );
parent->child[ dir ] = leaf;
}
/* fix coloring. leaf has moved up the tree. The color of the deleted
* node is in victim_color. There are two cases:
* 1. Deleted a red node, its child must be black. Nothing must be done.
* 2. Deleted a black node, its child must be red. Paint child black.
*/
if ( victim_color == RBT_BLACK ) { /* eliminate case 1 */
if ( leaf != NULL ) {
_RBTree_Set_color( leaf, RBT_BLACK ); /* case 2 */
}
}
/* set root to black, if it exists */
if ( the_rbtree->root != NULL )
_RBTree_Set_color( the_rbtree->root, RBT_BLACK );
}
