/** @file
An OrderedCollectionLib instance that provides a red-black tree
implementation, and allocates and releases tree nodes with
MemoryAllocationLib.
This library instance is useful when a fast associative container is needed.
Worst case time complexity is O(log n) for Find(), Next(), Prev(), Min(),
Max(), Insert(), and Delete(), where "n" is the number of elements in the
tree. Complete ordered traversal takes O(n) time.
The implementation is also useful as a fast priority queue.
Copyright (C) 2014, Red Hat, Inc.
Copyright (c) 2014, Intel Corporation. All rights reserved.<BR>
This program and the accompanying materials are licensed and made available
under the terms and conditions of the BSD License that accompanies this
distribution. The full text of the license may be found at
http://opensource.org/licenses/bsd-license.php.
THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS, WITHOUT
WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
**/
#include <Library/OrderedCollectionLib.h>
#include <Library/DebugLib.h>
#include <Library/MemoryAllocationLib.h>
typedef enum {
RedBlackTreeRed,
RedBlackTreeBlack
} RED_BLACK_TREE_COLOR;
//
// Incomplete types and convenience typedefs are present in the library class
// header. Beside completing the types, we introduce typedefs here that reflect
// the implementation closely.
//
typedef ORDERED_COLLECTION RED_BLACK_TREE;
typedef ORDERED_COLLECTION_ENTRY RED_BLACK_TREE_NODE;
typedef ORDERED_COLLECTION_USER_COMPARE RED_BLACK_TREE_USER_COMPARE;
typedef ORDERED_COLLECTION_KEY_COMPARE RED_BLACK_TREE_KEY_COMPARE;
struct ORDERED_COLLECTION {
RED_BLACK_TREE_NODE *Root;
RED_BLACK_TREE_USER_COMPARE UserStructCompare;
RED_BLACK_TREE_KEY_COMPARE KeyCompare;
};
struct ORDERED_COLLECTION_ENTRY {
VOID *UserStruct;
RED_BLACK_TREE_NODE *Parent;
RED_BLACK_TREE_NODE *Left;
RED_BLACK_TREE_NODE *Right;
RED_BLACK_TREE_COLOR Color;
};
/**
Retrieve the user structure linked by the specified tree node.
Read-only operation.
@param[in] Node Pointer to the tree node whose associated user structure we
want to retrieve. The caller is responsible for passing a
non-NULL argument.
@return Pointer to user structure linked by Node.
**/
VOID *
EFIAPI
OrderedCollectionUserStruct (
IN CONST RED_BLACK_TREE_NODE *Node
)
{
return Node->UserStruct;
}
/**
A slow function that asserts that the tree is a valid red-black tree, and
that it orders user structures correctly.
Read-only operation.
This function uses the stack for recursion and is not recommended for
"production use".
@param[in] Tree The tree to validate.
**/
VOID
RedBlackTreeValidate (
IN CONST RED_BLACK_TREE *Tree
);
/**
Allocate and initialize the RED_BLACK_TREE structure.
Allocation occurs via MemoryAllocationLib's AllocatePool() function.
@param[in] UserStructCompare This caller-provided function will be used to
order two user structures linked into the
tree, during the insertion procedure.
@param[in] KeyCompare This caller-provided function will be used to
order the standalone search key against user
structures linked into the tree, during the
lookup procedure.
@retval NULL If allocation failed.
@return Pointer to the allocated, initialized RED_BLACK_TREE structure,
otherwise.
**/
RED_BLACK_TREE *
EFIAPI
OrderedCollectionInit (
IN RED_BLACK_TREE_USER_COMPARE UserStructCompare,
IN RED_BLACK_TREE_KEY_COMPARE KeyCompare
)
{
RED_BLACK_TREE *Tree;
Tree = AllocatePool (sizeof *Tree);
if (Tree == NULL) {
return NULL;
}
Tree->Root = NULL;
Tree->UserStructCompare = UserStructCompare;
Tree->KeyCompare = KeyCompare;
if (FeaturePcdGet (PcdValidateOrderedCollection)) {
RedBlackTreeValidate (Tree);
}
return Tree;
}
/**
Check whether the tree is empty (has no nodes).
Read-only operation.
@param[in] Tree The tree to check for emptiness.
@retval TRUE The tree is empty.
@retval FALSE The tree is not empty.
**/
BOOLEAN
EFIAPI
OrderedCollectionIsEmpty (
IN CONST RED_BLACK_TREE *Tree
)
{
return (BOOLEAN)(Tree->Root == NULL);
}
/**
Uninitialize and release an empty RED_BLACK_TREE structure.
Read-write operation.
Release occurs via MemoryAllocationLib's FreePool() function.
It is the caller's responsibility to delete all nodes from the tree before
calling this function.
@param[in] Tree The empty tree to uninitialize and release.
**/
VOID
EFIAPI
OrderedCollectionUninit (
IN RED_BLACK_TREE *Tree
)
{
ASSERT (OrderedCollectionIsEmpty (Tree));
FreePool (Tree);
}
/**
Look up the tree node that links the user structure that matches the
specified standalone key.
Read-only operation.
@param[in] Tree The tree to search for StandaloneKey.
@param[in] StandaloneKey The key to locate among the user structures linked
into Tree. StandaloneKey will be passed to
Tree->KeyCompare().
@retval NULL StandaloneKey could not be found.
@return The tree node that links to the user structure matching
StandaloneKey, otherwise.
**/
RED_BLACK_TREE_NODE *
EFIAPI
OrderedCollectionFind (
IN CONST RED_BLACK_TREE *Tree,
IN CONST VOID *StandaloneKey
)
{
RED_BLACK_TREE_NODE *Node;
Node = Tree->Root;
while (Node != NULL) {
INTN Result;
Result = Tree->KeyCompare (StandaloneKey, Node->UserStruct);
if (Result == 0) {
break;
}
Node = (Result < 0) ? Node->Left : Node->Right;
}
return Node;
}
/**
Find the tree node of the minimum user structure stored in the tree.
Read-only operation.
@param[in] Tree The tree to return the minimum node of. The user structure
linked by the minimum node compares less than all other user
structures in the tree.
@retval NULL If Tree is empty.
@return The tree node that links the minimum user structure, otherwise.
**/
RED_BLACK_TREE_NODE *
EFIAPI
OrderedCollectionMin (
IN CONST RED_BLACK_TREE *Tree
)
{
RED_BLACK_TREE_NODE *Node;
Node = Tree->Root;
if (Node == NULL) {
return NULL;
}
while (Node->Left != NULL) {
Node = Node->Left;
}
return Node;
}
/**
Find the tree node of the maximum user structure stored in the tree.
Read-only operation.
@param[in] Tree The tree to return the maximum node of. The user structure
linked by the maximum node compares greater than all other
user structures in the tree.
@retval NULL If Tree is empty.
@return The tree node that links the maximum user structure, otherwise.
**/
RED_BLACK_TREE_NODE *
EFIAPI
OrderedCollectionMax (
IN CONST RED_BLACK_TREE *Tree
)
{
RED_BLACK_TREE_NODE *Node;
Node = Tree->Root;
if (Node == NULL) {
return NULL;
}
while (Node->Right != NULL) {
Node = Node->Right;
}
return Node;
}
/**
Get the tree node of the least user structure that is greater than the one
linked by Node.
Read-only operation.
@param[in] Node The node to get the successor node of.
@retval NULL If Node is NULL, or Node is the maximum node of its containing
tree (ie. Node has no successor node).
@return The tree node linking the least user structure that is greater
than the one linked by Node, otherwise.
**/
RED_BLACK_TREE_NODE *
EFIAPI
OrderedCollectionNext (
IN CONST RED_BLACK_TREE_NODE *Node
)
{
RED_BLACK_TREE_NODE *Walk;
CONST RED_BLACK_TREE_NODE *Child;
if (Node == NULL) {
return NULL;
}
//
// If Node has a right subtree, then the successor is the minimum node of
// that subtree.
//
Walk = Node->Right;
if (Walk != NULL) {
while (Walk->Left != NULL) {
Walk = Walk->Left;
}
return Walk;
}
//
// Otherwise we have to ascend as long as we're our parent's right child (ie.
// ascending to the left).
//
Child = Node;
Walk = Child->Parent;
while (Walk != NULL && Child == Walk->Right) {
Child = Walk;
Walk = Child->Parent;
}
return Walk;
}
/**
Get the tree node of the greatest user structure that is less than the one
linked by Node.
Read-only operation.
@param[in] Node The node to get the predecessor node of.
@retval NULL If Node is NULL, or Node is the minimum node of its containing
tree (ie. Node has no predecessor node).
@return The tree node linking the greatest user structure that is less
than the one linked by Node, otherwise.
**/
RED_BLACK_TREE_NODE *
EFIAPI
OrderedCollectionPrev (
IN CONST RED_BLACK_TREE_NODE *Node
)
{
RED_BLACK_TREE_NODE *Walk;
CONST RED_BLACK_TREE_NODE *Child;
if (Node == NULL) {
return NULL;
}
//
// If Node has a left subtree, then the predecessor is the maximum node of
// that subtree.
//
Walk = Node->Left;
if (Walk != NULL) {
while (Walk->Right != NULL) {
Walk = Walk->Right;
}
return Walk;
}
//
// Otherwise we have to ascend as long as we're our parent's left child (ie.
// ascending to the right).
//
Child = Node;
Walk = Child->Parent;
while (Walk != NULL && Child == Walk->Left) {
Child = Walk;
Walk = Child->Parent;
}
return Walk;
}
/**
Rotate tree nodes around Pivot to the right.
Parent Parent
| |
Pivot LeftChild
/ . . \_
LeftChild Node1 ---> Node2 Pivot
. \ / .
Node2 LeftRightChild LeftRightChild Node1
The ordering Node2 < LeftChild < LeftRightChild < Pivot < Node1 is kept
intact. Parent (if any) is either at the left extreme or the right extreme of
this ordering, and that relation is also kept intact.
Edges marked with a dot (".") don't change during rotation.
Internal read-write operation.
@param[in,out] Pivot The tree node to rotate other nodes right around. It
is the caller's responsibility to ensure that
Pivot->Left is not NULL.
@param[out] NewRoot If Pivot has a parent node on input, then the
function updates Pivot's original parent on output
according to the rotation, and NewRoot is not
accessed.
If Pivot has no parent node on input (ie. Pivot is
the root of the tree), then the function stores the
new root node of the tree in NewRoot.
**/
VOID
RedBlackTreeRotateRight (
IN OUT RED_BLACK_TREE_NODE *Pivot,
OUT RED_BLACK_TREE_NODE **NewRoot
)
{
RED_BLACK_TREE_NODE *Parent;
RED_BLACK_TREE_NODE *LeftChild;
RED_BLACK_TREE_NODE *LeftRightChild;
Parent = Pivot->Parent;
LeftChild = Pivot->Left;
LeftRightChild = LeftChild->Right;
Pivot->Left = LeftRightChild;
if (LeftRightChild != NULL) {
LeftRightChild->Parent = Pivot;
}
LeftChild->Parent = Parent;
if (Parent == NULL) {
*NewRoot = LeftChild;
} else {
if (Pivot == Parent->Left) {
Parent->Left = LeftChild;
} else {
Parent->Right = LeftChild;
}
}
LeftChild->Right = Pivot;
Pivot->Parent = LeftChild;
}
/**
Rotate tree nodes around Pivot to the left.
Parent Parent
| |
Pivot RightChild
. \ / .
Node1 RightChild ---> Pivot Node2
/. . \_
RightLeftChild Node2 Node1 RightLeftChild
The ordering Node1 < Pivot < RightLeftChild < RightChild < Node2 is kept
intact. Parent (if any) is either at the left extreme or the right extreme of
this ordering, and that relation is also kept intact.
Edges marked with a dot (".") don't change during rotation.
Internal read-write operation.
@param[in,out] Pivot The tree node to rotate other nodes left around. It
is the caller's responsibility to ensure that
Pivot->Right is not NULL.
@param[out] NewRoot If Pivot has a parent node on input, then the
function updates Pivot's original parent on output
according to the rotation, and NewRoot is not
accessed.
If Pivot has no parent node on input (ie. Pivot is
the root of the tree), then the function stores the
new root node of the tree in NewRoot.
**/
VOID
RedBlackTreeRotateLeft (
IN OUT RED_BLACK_TREE_NODE *Pivot,
OUT RED_BLACK_TREE_NODE **NewRoot
)
{
RED_BLACK_TREE_NODE *Parent;
RED_BLACK_TREE_NODE *RightChild;
RED_BLACK_TREE_NODE *RightLeftChild;
Parent = Pivot->Parent;
RightChild = Pivot->Right;
RightLeftChild = RightChild->Left;
Pivot->Right = RightLeftChild;
if (RightLeftChild != NULL) {
RightLeftChild->Parent = Pivot;
}
RightChild->Parent = Parent;
if (Parent == NULL) {
*NewRoot = RightChild;
} else {
if (Pivot == Parent->Left) {
Parent->Left = RightChild;
} else {
Parent->Right = RightChild;
}
}
RightChild->Left = Pivot;
Pivot->Parent = RightChild;
}
/**
Insert (link) a user structure into the tree.
Read-write operation.
This function allocates the new tree node with MemoryAllocationLib's
AllocatePool() function.
@param[in,out] Tree The tree to insert UserStruct into.
@param[out] Node The meaning of this optional, output-only
parameter depends on the return value of the
function.
When insertion is successful (RETURN_SUCCESS),
Node is set on output to the new tree node that
now links UserStruct.
When insertion fails due to lack of memory
(RETURN_OUT_OF_RESOURCES), Node is not changed.
When insertion fails due to key collision (ie.
another user structure is already in the tree that
compares equal to UserStruct), with return value
RETURN_ALREADY_STARTED, then Node is set on output
to the node that links the colliding user
structure. This enables "find-or-insert" in one
function call, or helps with later removal of the
colliding element.
@param[in] UserStruct The user structure to link into the tree.
UserStruct is ordered against in-tree user
structures with the Tree->UserStructCompare()
function.
@retval RETURN_SUCCESS Insertion successful. A new tree node has
been allocated, linking UserStruct. The new
tree node is reported back in Node (if the
caller requested it).
Existing RED_BLACK_TREE_NODE pointers into
Tree remain valid. For example, on-going
iterations in the caller can continue with
OrderedCollectionNext() /
OrderedCollectionPrev(), and they will
return the new node at some point if user
structure order dictates it.
@retval RETURN_OUT_OF_RESOURCES AllocatePool() failed to allocate memory for
the new tree node. The tree has not been
changed. Existing RED_BLACK_TREE_NODE
pointers into Tree remain valid.
@retval RETURN_ALREADY_STARTED A user structure has been found in the tree
that compares equal to UserStruct. The node
linking the colliding user structure is
reported back in Node (if the caller
requested it). The tree has not been
changed. Existing RED_BLACK_TREE_NODE
pointers into Tree remain valid.
**/
RETURN_STATUS
EFIAPI
OrderedCollectionInsert (
IN OUT RED_BLACK_TREE *Tree,
OUT RED_BLACK_TREE_NODE **Node OPTIONAL,
IN VOID *UserStruct
)
{
RED_BLACK_TREE_NODE *Tmp;
RED_BLACK_TREE_NODE *Parent;
INTN Result;
RETURN_STATUS Status;
RED_BLACK_TREE_NODE *NewRoot;
Tmp = Tree->Root;
Parent = NULL;
Result = 0;
//
// First look for a collision, saving the last examined node for the case
// when there's no collision.
//
while (Tmp != NULL) {
Result = Tree->UserStructCompare (UserStruct, Tmp->UserStruct);
if (Result == 0) {
break;
}
Parent = Tmp;
Tmp = (Result < 0) ? Tmp->Left : Tmp->Right;
}
if (Tmp != NULL) {
if (Node != NULL) {
*Node = Tmp;
}
Status = RETURN_ALREADY_STARTED;
goto Done;
}
//
// no collision, allocate a new node
//
Tmp = AllocatePool (sizeof *Tmp);
if (Tmp == NULL) {
Status = RETURN_OUT_OF_RESOURCES;
goto Done;
}
if (Node != NULL) {
*Node = Tmp;
}
//
// reference the user structure from the node
//
Tmp->UserStruct = UserStruct;
//
// Link the node as a child to the correct side of the parent.
// If there's no parent, the new node is the root node in the tree.
//
Tmp->Parent = Parent;
Tmp->Left = NULL;
Tmp->Right = NULL;
if (Parent == NULL) {
Tree->Root = Tmp;
Tmp->Color = RedBlackTreeBlack;
Status = RETURN_SUCCESS;
goto Done;
}
if (Result < 0) {
Parent->Left = Tmp;
} else {
Parent->Right = Tmp;
}
Tmp->Color = RedBlackTreeRed;
//
// Red-black tree properties:
//
// #1 Each node is either red or black (RED_BLACK_TREE_NODE.Color).
//
// #2 Each leaf (ie. a pseudo-node pointed-to by a NULL valued
// RED_BLACK_TREE_NODE.Left or RED_BLACK_TREE_NODE.Right field) is black.
//
// #3 Each red node has two black children.
//
// #4 For any node N, and for any leaves L1 and L2 reachable from N, the
// paths N..L1 and N..L2 contain the same number of black nodes.
//
// #5 The root node is black.
//
// By replacing a leaf with a red node above, only property #3 may have been
// broken. (Note that this is the only edge across which property #3 might
// not hold in the entire tree.) Restore property #3.
//
NewRoot = Tree->Root;
while (Tmp != NewRoot && Parent->Color == RedBlackTreeRed) {
RED_BLACK_TREE_NODE *GrandParent;
RED_BLACK_TREE_NODE *Uncle;
//
// Tmp is not the root node. Tmp is red. Tmp's parent is red. (Breaking
// property #3.)
//
// Due to property #5, Tmp's parent cannot be the root node, hence Tmp's
// grandparent exists.
//
// Tmp's grandparent is black, because property #3 is only broken between
// Tmp and Tmp's parent.
//
GrandParent = Parent->Parent;
if (Parent == GrandParent->Left) {
Uncle = GrandParent->Right;
if (Uncle != NULL && Uncle->Color == RedBlackTreeRed) {
//
// GrandParent (black)
// / \_
// Parent (red) Uncle (red)
// |
// Tmp (red)
//
Parent->Color = RedBlackTreeBlack;
Uncle->Color = RedBlackTreeBlack;
GrandParent->Color = RedBlackTreeRed;
//
// GrandParent (red)
// / \_
// Parent (black) Uncle (black)
// |
// Tmp (red)
//
// We restored property #3 between Tmp and Tmp's parent, without
// breaking property #4. However, we may have broken property #3
// between Tmp's grandparent and Tmp's great-grandparent (if any), so
// repeat the loop for Tmp's grandparent.
//
// If Tmp's grandparent has no parent, then the loop will terminate,
// and we will have broken property #5, by coloring the root red. We'll
// restore property #5 after the loop, without breaking any others.
//
Tmp = GrandParent;
Parent = Tmp->Parent;
} else {
//
// Tmp's uncle is black (satisfied by the case too when Tmp's uncle is
// NULL, see property #2).
//
if (Tmp == Parent->Right) {
//
// GrandParent (black): D
// / \_
// Parent (red): A Uncle (black): E
// \_
// Tmp (red): B
// \_
// black: C
//
// Rotate left, pivoting on node A. This keeps the breakage of
// property #3 in the same spot, and keeps other properties intact
// (because both Tmp and its parent are red).
//
Tmp = Parent;
RedBlackTreeRotateLeft (Tmp, &NewRoot);
Parent = Tmp->Parent;
//
// With the rotation we reached the same configuration as if Tmp had
// been a left child to begin with.
//
// GrandParent (black): D
// / \_
// Parent (red): B Uncle (black): E
// / \_
// Tmp (red): A black: C
//
ASSERT (GrandParent == Parent->Parent);
}
Parent->Color = RedBlackTreeBlack;
GrandParent->Color = RedBlackTreeRed;
//
// Property #3 is now restored, but we've broken property #4. Namely,
// paths going through node E now see a decrease in black count, while
// paths going through node B don't.
//
// GrandParent (red): D
// / \_
// Parent (black): B Uncle (black): E
// / \_
// Tmp (red): A black: C
//
RedBlackTreeRotateRight (GrandParent, &NewRoot);
//
// Property #4 has been restored for node E, and preserved for others.
//
// Parent (black): B
// / \_
// Tmp (red): A [GrandParent] (red): D
// / \_
// black: C [Uncle] (black): E
//
// This configuration terminates the loop because Tmp's parent is now
// black.
//
}
} else {
//
// Symmetrical to the other branch.
//
Uncle = GrandParent->Left;
if (Uncle != NULL && Uncle->Color == RedBlackTreeRed) {
Parent->Color = RedBlackTreeBlack;
Uncle->Color = RedBlackTreeBlack;
GrandParent->Color = RedBlackTreeRed;
Tmp = GrandParent;
Parent = Tmp->Parent;
} else {
if (Tmp == Parent->Left) {
Tmp = Parent;
RedBlackTreeRotateRight (Tmp, &NewRoot);
Parent = Tmp->Parent;
ASSERT (GrandParent == Parent->Parent);
}
Parent->Color = RedBlackTreeBlack;
GrandParent->Color = RedBlackTreeRed;
RedBlackTreeRotateLeft (GrandParent, &NewRoot);
}
}
}
NewRoot->Color = RedBlackTreeBlack;
Tree->Root = NewRoot;
Status = RETURN_SUCCESS;
Done:
if (FeaturePcdGet (PcdValidateOrderedCollection)) {
RedBlackTreeValidate (Tree);
}
return Status;
}
/**
Check if a node is black, allowing for leaf nodes (see property #2).
This is a convenience shorthand.
param[in] Node The node to check. Node may be NULL, corresponding to a leaf.
@return If Node is NULL or colored black.
**/
BOOLEAN
NodeIsNullOrBlack (
IN CONST RED_BLACK_TREE_NODE *Node
)
{
return (BOOLEAN)(Node == NULL || Node->Color == RedBlackTreeBlack);
}
/**
Delete a node from the tree, unlinking the associated user structure.
Read-write operation.
@param[in,out] Tree The tree to delete Node from.
@param[in] Node The tree node to delete from Tree. The caller is
responsible for ensuring that Node belongs to
Tree, and that Node is non-NULL and valid. Node is
typically an earlier return value, or output
parameter, of:
- OrderedCollectionFind(), for deleting a node by
user structure key,
- OrderedCollectionMin() / OrderedCollectionMax(),
for deleting the minimum / maximum node,
- OrderedCollectionNext() /
OrderedCollectionPrev(), for deleting a node
found during an iteration,
- OrderedCollectionInsert() with return value
RETURN_ALREADY_STARTED, for deleting a node
whose linked user structure caused collision
during insertion.
Given a non-empty Tree, Tree->Root is also a valid
Node argument (typically used for simplicity in
loops that empty the tree completely).
Node is released with MemoryAllocationLib's
FreePool() function.
Existing RED_BLACK_TREE_NODE pointers (ie.
iterators) *different* from Node remain valid. For
example:
- OrderedCollectionNext() /
OrderedCollectionPrev() iterations in the caller
can be continued from Node, if
OrderedCollectionNext() or
OrderedCollectionPrev() is called on Node
*before* OrderedCollectionDelete() is. That is,
fetch the successor / predecessor node first,
then delete Node.
- On-going iterations in the caller that would
have otherwise returned Node at some point, as
dictated by user structure order, will correctly
reflect the absence of Node after
OrderedCollectionDelete() is called
mid-iteration.
@param[out] UserStruct If the caller provides this optional output-only
parameter, then on output it is set to the user
structure originally linked by Node (which is now
freed).
This is a convenience that may save the caller a
OrderedCollectionUserStruct() invocation before
calling OrderedCollectionDelete(), in order to
retrieve the user structure being unlinked.
**/
VOID
EFIAPI
OrderedCollectionDelete (
IN OUT RED_BLACK_TREE *Tree,
IN RED_BLACK_TREE_NODE *Node,
OUT VOID **UserStruct OPTIONAL
)
{
RED_BLACK_TREE_NODE *NewRoot;
RED_BLACK_TREE_NODE *OrigLeftChild;
RED_BLACK_TREE_NODE *OrigRightChild;
RED_BLACK_TREE_NODE *OrigParent;
RED_BLACK_TREE_NODE *Child;
RED_BLACK_TREE_NODE *Parent;
RED_BLACK_TREE_COLOR ColorOfUnlinked;
NewRoot = Tree->Root;
OrigLeftChild = Node->Left,
OrigRightChild = Node->Right,
OrigParent = Node->Parent;
if (UserStruct != NULL) {
*UserStruct = Node->UserStruct;
}
//
// After this block, no matter which branch we take:
// - Child will point to the unique (or NULL) original child of the node that
// we will have unlinked,
// - Parent will point to the *position* of the original parent of the node
// that we will have unlinked.
//
if (OrigLeftChild == NULL || OrigRightChild == NULL) {
//
// Node has at most one child. We can connect that child (if any) with
// Node's parent (if any), unlinking Node. This will preserve ordering
// because the subtree rooted in Node's child (if any) remains on the same
// side of Node's parent (if any) that Node was before.
//
Parent = OrigParent;
Child = (OrigLeftChild != NULL) ? OrigLeftChild : OrigRightChild;
ColorOfUnlinked = Node->Color;
if (Child != NULL) {
Child->Parent = Parent;
}
if (OrigParent == NULL) {
NewRoot = Child;
} else {
if (Node == OrigParent->Left) {
OrigParent->Left = Child;
} else {
OrigParent->Right = Child;
}
}
} else {
//
// Node has two children. We unlink Node's successor, and then link it into
// Node's place, keeping Node's original color. This preserves ordering
// because:
// - Node's left subtree is less than Node, hence less than Node's
// successor.
// - Node's right subtree is greater than Node. Node's successor is the
// minimum of that subtree, hence Node's successor is less than Node's
// right subtree with its minimum removed.
// - Node's successor is in Node's subtree, hence it falls on the same side
// of Node's parent as Node itself. The relinking doesn't change this
// relation.
//
RED_BLACK_TREE_NODE *ToRelink;
ToRelink = OrigRightChild;
if (ToRelink->Left == NULL) {
//
// OrigRightChild itself is Node's successor, it has no left child:
//
// OrigParent
// |
// Node: B
// / \_
// OrigLeftChild: A OrigRightChild: E <--- Parent, ToRelink
// \_
// F <--- Child
//
Parent = OrigRightChild;
Child = OrigRightChild->Right;
} else {
do {
ToRelink = ToRelink->Left;
} while (ToRelink->Left != NULL);
//
// Node's successor is the minimum of OrigRightChild's proper subtree:
//
// OrigParent
// |
// Node: B
// / \_
// OrigLeftChild: A OrigRightChild: E <--- Parent
// /
// C <--- ToRelink
// \_
// D <--- Child
Parent = ToRelink->Parent;
Child = ToRelink->Right;
//
// Unlink Node's successor (ie. ToRelink):
//
// OrigParent
// |
// Node: B
// / \_
// OrigLeftChild: A OrigRightChild: E <--- Parent
// /
// D <--- Child
//
// C <--- ToRelink
//
Parent->Left = Child;
if (Child != NULL) {
Child->Parent = Parent;
}
//
// We start to link Node's unlinked successor into Node's place:
//
// OrigParent
// |
// Node: B C <--- ToRelink
// / \_
// OrigLeftChild: A OrigRightChild: E <--- Parent
// /
// D <--- Child
//
//
//
ToRelink->Right = OrigRightChild;
OrigRightChild->Parent = ToRelink;
}
//
// The rest handles both cases, attaching ToRelink (Node's original
// successor) to OrigLeftChild and OrigParent.
//
// Parent,
// OrigParent ToRelink OrigParent
// | | |
// Node: B | Node: B Parent
// v |
// OrigRightChild: E C <--- ToRelink |
// / \ / \ v
// OrigLeftChild: A F OrigLeftChild: A OrigRightChild: E
// ^ /
// | D <--- Child
// Child
//
ToRelink->Left = OrigLeftChild;
OrigLeftChild->Parent = ToRelink;
//
// Node's color must be preserved in Node's original place.
//
ColorOfUnlinked = ToRelink->Color;
ToRelink->Color = Node->Color;
//
// Finish linking Node's unlinked successor into Node's place.
//
// Parent,
// Node: B ToRelink Node: B
// |
// OrigParent | OrigParent Parent
// | v | |
// OrigRightChild: E C <--- ToRelink |
// / \ / \ v
// OrigLeftChild: A F OrigLeftChild: A OrigRightChild: E
// ^ /
// | D <--- Child
// Child
//
ToRelink->Parent = OrigParent;
if (OrigParent == NULL) {
NewRoot = ToRelink;
} else {
if (Node == OrigParent->Left) {
OrigParent->Left = ToRelink;
} else {
OrigParent->Right = ToRelink;
}
}
}
FreePool (Node);
//
// If the node that we unlinked from its original spot (ie. Node itself, or
// Node's successor), was red, then we broke neither property #3 nor property
// #4: we didn't create any red-red edge between Child and Parent, and we
// didn't change the black count on any path.
//
if (ColorOfUnlinked == RedBlackTreeBlack) {
//
// However, if the unlinked node was black, then we have to transfer its
// "black-increment" to its unique child (pointed-to by Child), lest we
// break property #4 for its ancestors.
//
// If Child is red, we can simply color it black. If Child is black
// already, we can't technically transfer a black-increment to it, due to
// property #1.
//
// In the following loop we ascend searching for a red node to color black,
// or until we reach the root (in which case we can drop the
// black-increment). Inside the loop body, Child has a black value of 2,
// transitorily breaking property #1 locally, but maintaining property #4
// globally.
//
// Rotations in the loop preserve property #4.
//
while (Child != NewRoot && NodeIsNullOrBlack (Child)) {
RED_BLACK_TREE_NODE *Sibling;
RED_BLACK_TREE_NODE *LeftNephew;
RED_BLACK_TREE_NODE *RightNephew;
if (Child == Parent->Left) {
Sibling = Parent->Right;
//
// Sibling can never be NULL (ie. a leaf).
//
// If Sibling was NULL, then the black count on the path from Parent to
// Sibling would equal Parent's black value, plus 1 (due to property
// #2). Whereas the black count on the path from Parent to any leaf via
// Child would be at least Parent's black value, plus 2 (due to Child's
// black value of 2). This would clash with property #4.
//
// (Sibling can be black of course, but it has to be an internal node.
// Internality allows Sibling to have children, bumping the black
// counts of paths that go through it.)
//
ASSERT (Sibling != NULL);
if (Sibling->Color == RedBlackTreeRed) {
//
// Sibling's red color implies its children (if any), node C and node
// E, are black (property #3). It also implies that Parent is black.
//
// grandparent grandparent
// | |
// Parent,b:B b:D
// / \ / \_
// Child,2b:A Sibling,r:D ---> Parent,r:B b:E
// /\ /\_
// b:C b:E Child,2b:A Sibling,b:C
//
Sibling->Color = RedBlackTreeBlack;
Parent->Color = RedBlackTreeRed;
RedBlackTreeRotateLeft (Parent, &NewRoot);
Sibling = Parent->Right;
//
// Same reasoning as above.
//
ASSERT (Sibling != NULL);
}
//
// Sibling is black, and not NULL. (Ie. Sibling is a black internal
// node.)
//
ASSERT (Sibling->Color == RedBlackTreeBlack);
LeftNephew = Sibling->Left;
RightNephew = Sibling->Right;
if (NodeIsNullOrBlack (LeftNephew) &&
NodeIsNullOrBlack (RightNephew)) {
//
// In this case we can "steal" one black value from Child and Sibling
// each, and pass it to Parent. "Stealing" means that Sibling (black
// value 1) becomes red, Child (black value 2) becomes singly-black,
// and Parent will have to be examined if it can eat the
// black-increment.
//
// Sibling is allowed to become red because both of its children are
// black (property #3).
//
// grandparent Parent
// | |
// Parent,x:B Child,x:B
// / \ / \_
// Child,2b:A Sibling,b:D ---> b:A r:D
// /\ /\_
// LeftNephew,b:C RightNephew,b:E b:C b:E
//
Sibling->Color = RedBlackTreeRed;
Child = Parent;
Parent = Parent->Parent;
//
// Continue ascending.
//
} else {
//
// At least one nephew is red.
//
if (NodeIsNullOrBlack (RightNephew)) {
//
// Since the right nephew is black, the left nephew is red. Due to
// property #3, LeftNephew has two black children, hence node E is
// black.
//
// Together with the rotation, this enables us to color node F red
// (because property #3 will be satisfied). We flip node D to black
// to maintain property #4.
//
// grandparent grandparent
// | |
// Parent,x:B Parent,x:B
// /\ /\_
// Child,2b:A Sibling,b:F ---> Child,2b:A Sibling,b:D
// /\ / \_
// LeftNephew,r:D RightNephew,b:G b:C RightNephew,r:F
// /\ /\_
// b:C b:E b:E b:G
//
LeftNephew->Color = RedBlackTreeBlack;
Sibling->Color = RedBlackTreeRed;
RedBlackTreeRotateRight (Sibling, &NewRoot);
Sibling = Parent->Right;
RightNephew = Sibling->Right;
//
// These operations ensure that...
//
}
//
// ... RightNephew is definitely red here, plus Sibling is (still)
// black and non-NULL.
//
ASSERT (RightNephew != NULL);
ASSERT (RightNephew->Color == RedBlackTreeRed);
ASSERT (Sibling != NULL);
ASSERT (Sibling->Color == RedBlackTreeBlack);
//
// In this case we can flush the extra black-increment immediately,
// restoring property #1 for Child (node A): we color RightNephew
// (node E) from red to black.
//
// In order to maintain property #4, we exchange colors between
// Parent and Sibling (nodes B and D), and rotate left around Parent
// (node B). The transformation doesn't change the black count
// increase incurred by each partial path, eg.
// - ascending from node A: 2 + x == 1 + 1 + x
// - ascending from node C: y + 1 + x == y + 1 + x
// - ascending from node E: 0 + 1 + x == 1 + x
//
// The color exchange is valid, because even if x stands for red,
// both children of node D are black after the transformation
// (preserving property #3).
//
// grandparent grandparent
// | |
// Parent,x:B x:D
// / \ / \_
// Child,2b:A Sibling,b:D ---> b:B b:E
// / \ / \_
// y:C RightNephew,r:E b:A y:C
//
//
Sibling->Color = Parent->Color;
Parent->Color = RedBlackTreeBlack;
RightNephew->Color = RedBlackTreeBlack;
RedBlackTreeRotateLeft (Parent, &NewRoot);
Child = NewRoot;
//
// This terminates the loop.
//
}
} else {
//
// Mirrors the other branch.
//
Sibling = Parent->Left;
ASSERT (Sibling != NULL);
if (Sibling->Color == RedBlackTreeRed) {
Sibling->Color = RedBlackTreeBlack;
Parent->Color = RedBlackTreeRed;
RedBlackTreeRotateRight (Parent, &NewRoot);
Sibling = Parent->Left;
ASSERT (Sibling != NULL);
}
ASSERT (Sibling->Color == RedBlackTreeBlack);
RightNephew = Sibling->Right;
LeftNephew = Sibling->Left;
if (NodeIsNullOrBlack (RightNephew) &&
NodeIsNullOrBlack (LeftNephew)) {
Sibling->Color = RedBlackTreeRed;
Child = Parent;
Parent = Parent->Parent;
} else {
if (NodeIsNullOrBlack (LeftNephew)) {
RightNephew->Color = RedBlackTreeBlack;
Sibling->Color = RedBlackTreeRed;
RedBlackTreeRotateLeft (Sibling, &NewRoot);
Sibling = Parent->Left;
LeftNephew = Sibling->Left;
}
ASSERT (LeftNephew != NULL);
ASSERT (LeftNephew->Color == RedBlackTreeRed);
ASSERT (Sibling != NULL);
ASSERT (Sibling->Color == RedBlackTreeBlack);
Sibling->Color = Parent->Color;
Parent->Color = RedBlackTreeBlack;
LeftNephew->Color = RedBlackTreeBlack;
RedBlackTreeRotateRight (Parent, &NewRoot);
Child = NewRoot;
}
}
}
if (Child != NULL) {
Child->Color = RedBlackTreeBlack;
}
}
Tree->Root = NewRoot;
if (FeaturePcdGet (PcdValidateOrderedCollection)) {
RedBlackTreeValidate (Tree);
}
}
/**
Recursively check the red-black tree properties #1 to #4 on a node.
@param[in] Node The root of the subtree to validate.
@retval The black-height of Node's parent.
**/
UINT32
RedBlackTreeRecursiveCheck (
IN CONST RED_BLACK_TREE_NODE *Node
)
{
UINT32 LeftHeight;
UINT32 RightHeight;
//
// property #2
//
if (Node == NULL) {
return 1;
}
//
// property #1
//
ASSERT (Node->Color == RedBlackTreeRed || Node->Color == RedBlackTreeBlack);
//
// property #3
//
if (Node->Color == RedBlackTreeRed) {
ASSERT (NodeIsNullOrBlack (Node->Left));
ASSERT (NodeIsNullOrBlack (Node->Right));
}
//
// property #4
//
LeftHeight = RedBlackTreeRecursiveCheck (Node->Left);
RightHeight = RedBlackTreeRecursiveCheck (Node->Right);
ASSERT (LeftHeight == RightHeight);
return (Node->Color == RedBlackTreeBlack) + LeftHeight;
}
/**
A slow function that asserts that the tree is a valid red-black tree, and
that it orders user structures correctly.
Read-only operation.
This function uses the stack for recursion and is not recommended for
"production use".
@param[in] Tree The tree to validate.
**/
VOID
RedBlackTreeValidate (
IN CONST RED_BLACK_TREE *Tree
)
{
UINT32 BlackHeight;
UINT32 ForwardCount;
UINT32 BackwardCount;
CONST RED_BLACK_TREE_NODE *Last;
CONST RED_BLACK_TREE_NODE *Node;
DEBUG ((DEBUG_VERBOSE, "%a: Tree=%p\n", __FUNCTION__, Tree));
//
// property #5
//
ASSERT (NodeIsNullOrBlack (Tree->Root));
//
// check the other properties
//
BlackHeight = RedBlackTreeRecursiveCheck (Tree->Root) - 1;
//
// forward ordering
//
Last = OrderedCollectionMin (Tree);
ForwardCount = (Last != NULL);
for (Node = OrderedCollectionNext (Last); Node != NULL;
Node = OrderedCollectionNext (Last)) {
ASSERT (Tree->UserStructCompare (Last->UserStruct, Node->UserStruct) < 0);
Last = Node;
++ForwardCount;
}
//
// backward ordering
//
Last = OrderedCollectionMax (Tree);
BackwardCount = (Last != NULL);
for (Node = OrderedCollectionPrev (Last); Node != NULL;
Node = OrderedCollectionPrev (Last)) {
ASSERT (Tree->UserStructCompare (Last->UserStruct, Node->UserStruct) > 0);
Last = Node;
++BackwardCount;
}
ASSERT (ForwardCount == BackwardCount);
DEBUG ((DEBUG_VERBOSE, "%a: Tree=%p BlackHeight=%Ld Count=%Ld\n",
__FUNCTION__, Tree, (INT64)BlackHeight, (INT64)ForwardCount));
}