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// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the MIT license.
#if DEBUG
//#define VerifyIndex
#define VerifyPath
#define VerifySort
#endif
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.CodeAnalysis;
namespace System.Data
{
internal enum RBTreeError
{
InvalidPageSize = 1,
// InvalidCompareDelegate = 2,
PagePositionInSlotInUse = 3,
NoFreeSlots = 4,
InvalidStateinInsert = 5,
// InvalidStateinEndInsert = 6,
InvalidNextSizeInDelete = 7,
InvalidStateinDelete = 8,
InvalidNodeSizeinDelete = 9,
InvalidStateinEndDelete = 10,
CannotRotateInvalidsuccessorNodeinDelete = 11,
// IndexOutOfRange = 12,
IndexOutOFRangeinGetNodeByIndex = 13,
RBDeleteFixup = 14,
UnsupportedAccessMethod1 = 15,
UnsupportedAccessMethod2 = 16,
UnsupportedAccessMethodInNonNillRootSubtree = 17,
AttachedNodeWithZerorbTreeNodeId = 18, // DataRowCollection
CompareNodeInDataRowTree = 19, // DataRowCollection
CompareSatelliteTreeNodeInDataRowTree = 20, // DataRowCollection
NestedSatelliteTreeEnumerator = 21,
}
internal enum TreeAccessMethod
{
KEY_SEARCH_AND_INDEX = 1,
INDEX_ONLY = 2,
}
// an index represents location the tree
// a tree has an array of pages (max 2^16) (top 16 bits)
// a page has an array of nodes (max 2^16) (bottom 16 bits)
// nodes are indexed by RBTree.PageTable[index>>16].Slots[index&0xFFFF]
// a tree has an PageTableBitmap to indicate which allocated pages have free nodes
// a page has a SlotBitmap to indicate which slots are free
// initial page allocation (assuming no deletes)
// #page * #slot = #total, #cumulative
// ( 4) * 32 = 128, 127 (subtract 1 for NIL node)
// ( 32 - 4) * 256 = 7168, 7,295
// ( 128 - 32) * 1024 = 98304, 105,599
// ( 4096 - 128) * 4096 = 16252928, 16,358,527
// (32768 - 4096) * 8192 = 234881024, 251,239,551
// (65535 - 32768) * 65536 = 2147418112, 2,398,657,663 (excess nodes 251,174,016 > Int32.MaxValue)
// tree page size is GetIntValueFromBitMap(inUsePageCount) // return highest bit in array
//private static readonly int[] PageSize = new int[17] { // nobit + 16 bits == 17 position
// 32, 32, 32, // inUsePageCount < 4 0, 1, 2,
// 256, 256, 256, // inUsePageCount < 32 4, 8, 16,
// 1024, 1024, // inUsePageCount < 128 32, 64,
// 4096, 4096, 4096, 4096, 4096, // inUsePageCount < 4096 128, 256, 512, 1024, 2048,
// 8192, 8192, 8192, // inUsePageCount < 32768 4096, 8192, 16384
// 65535 // inUsePageCount <= 65535
//};
// the in-ordering of nodes in the tree (the second graph has duplicate nodes)
// for the satellite tree, the main tree node is the clone, GetNodeByIndex always returns the satelliteRootid
// 4 | 4
// / \ | / \
// 2 6 | 3 - 3 7
// / \ / \ | / \ / \ / \
// 1 3 5 7 | 1 5 2 4 8 9
// PageTable (starting at 32) doubles in size on demand (^16 - ^5 = 11 grows to reach max PageTable size)
// if a page has no allocated slots, it will be dropped
// worst case scenario is to repeatedly add/remove on a boundary condition
// the primary change to support Index using Predicate<DataRow> or Comparison<DataRow> was to eliminate all
// unnecessary searching for the node in the main tree when operating on a node in the satellite branch
// in all cases except GetNodeByKey(K)& GetIndexByNode(int), we know what that mainTreeNodeID is and can avoid searching
internal abstract class RBTree<K> : IEnumerable
{
// 2^16 #pages * 2^n == total number of nodes. 512 = 32 million, 1024 = 64 million, 2048 = 128m, 4096=256m, 8192=512m, 16284=1 billion
// 32K=2 billion.
internal const int DefaultPageSize = 32; /* 512 = 2^9 32 million nodes*/
internal const int NIL = 0; // 0th page, 0th slot for each tree till CLR static & generics issue is fixed
private TreePage?[] _pageTable; // initial size 4, then doubles (grows) - it never shrinks.
private int[] _pageTableMap;
private int _inUsePageCount; // contains count of allocated pages per tree, its <= the capacity of pageTable
private int _nextFreePageLine; // used for keeping track of position of last used free page in pageTable
public int root;
private int _version;
private int _inUseNodeCount; // total number of nodes currently in use by this tree.
private int _inUseSatelliteTreeCount; // total number of satellite associated with this tree.
private readonly TreeAccessMethod _accessMethod;
protected abstract int CompareNode(K? record1, K? record2);
protected abstract int CompareSatelliteTreeNode(K? record1, K? record2);
protected RBTree(TreeAccessMethod accessMethod)
{
_accessMethod = accessMethod;
InitTree();
}
[MemberNotNull(nameof(_pageTable))]
[MemberNotNull(nameof(_pageTableMap))]
private void InitTree()
{
root = NIL;
_pageTable = new TreePage[1 * TreePage.slotLineSize];
_pageTableMap = new int[(_pageTable.Length + TreePage.slotLineSize - 1) / TreePage.slotLineSize]; // Ceiling(size)
_inUsePageCount = 0;
_nextFreePageLine = 0;
AllocPage(DefaultPageSize);
// alloc storage for reserved NIL node. segment 0, slot 0; Initialize NIL
_pageTable[0]!._slots[0]._nodeColor = NodeColor.black;
_pageTable[0]!._slotMap[0] = 0x1;
_pageTable[0]!.InUseCount = 1;
_inUseNodeCount = 1;
_inUseSatelliteTreeCount = 0; // total number of satellite associated with this tree.
}
private void FreePage(TreePage page)
{
MarkPageFree(page);
_pageTable[page.PageId] = null;
_inUsePageCount--;
}
/* AllocPage()
* size : Allocates a page of the specified size.
*
* Look for an unallocated page entry.
* (1) If entry for an unallocated page exists in current pageTable - use it
* (2) else extend pageTable
*/
private TreePage AllocPage(int size)
{
int freePageIndex = GetIndexOfPageWithFreeSlot(false);
if (freePageIndex != -1)
{
_pageTable[freePageIndex] = new TreePage(size);
_nextFreePageLine = freePageIndex / TreePage.slotLineSize;
}
else
{
// no free position found, increase pageTable size
TreePage[] newPageTable = new TreePage[_pageTable.Length * 2];
Array.Copy(_pageTable, newPageTable, _pageTable.Length);
int[] newPageTableMap = new int[(newPageTable.Length + TreePage.slotLineSize - 1) / TreePage.slotLineSize];
Array.Copy(_pageTableMap, newPageTableMap, _pageTableMap.Length);
_nextFreePageLine = _pageTableMap.Length;
freePageIndex = _pageTable.Length;
_pageTable = newPageTable;
_pageTableMap = newPageTableMap;
_pageTable[freePageIndex] = new TreePage(size);
}
_pageTable[freePageIndex]!.PageId = freePageIndex;
_inUsePageCount++;
return _pageTable[freePageIndex]!;
}
/* MarkPageFull()
* Mark the specified page "Full" as all its slots aer in use
*/
private void MarkPageFull(TreePage page)
{
// set bit associated with page to mark it as full
/*
int pageTableMapIndex = (page.PageId / TreePage.slotLineSize);
int pageTableMapOffset = (page.PageId % TreePage.slotLineSize);
Int32 pageBitMask = ((Int32)1) << pageTableMapOffset;
_pageTableMap[pageTableMapIndex] |= (pageBitMask);
*/
_pageTableMap[page.PageId / TreePage.slotLineSize] |= (1 << (page.PageId % TreePage.slotLineSize));
}
/* MarkPageFree()
* Mark the specified page as "Free". It has atleast 1 available slot.
*/
private void MarkPageFree(TreePage page)
{
// set bit associated with page to mark it as free
/*
int pageTableMapIndex = (page.PageId / TreePage.slotLineSize);
int pageTableMapOffset = (page.PageId % TreePage.slotLineSize);
Int32 pageBitMask = ((Int32)1) << pageTableMapOffset;
_pageTableMap[pageTableMapIndex] &= ~(pageBitMask);
*/
_pageTableMap[page.PageId / TreePage.slotLineSize] &= ~(1 << (page.PageId % TreePage.slotLineSize));
}
private static int GetIntValueFromBitMap(uint bitMap)
{
int value = 0; // 0 based slot position
/*
* Assumption: bitMap can have max, exactly 1 bit set.
* convert bitMap to int value giving number of 0's to its right
* return value between 0 and 31
*/
if ((bitMap & 0xFFFF0000) != 0)
{
value += 16;
bitMap >>= 16;
}
if ((bitMap & 0x0000FF00) != 0)
{
value += 8;
bitMap >>= 8;
}
if ((bitMap & 0x000000F0) != 0)
{
value += 4;
bitMap >>= 4;
}
if ((bitMap & 0x0000000C) != 0)
{
value += 2;
bitMap >>= 2;
}
if ((bitMap & 0x00000002) != 0)
value += 1;
return value;
}
/*
* FreeNode()
* nodeId: The nodeId of the node to be freed
*/
private void FreeNode(int nodeId)
{
TreePage page = _pageTable[nodeId >> 16]!;
int slotIndex = nodeId & 0xFFFF;
page._slots[slotIndex] = default(Node);
// clear slotMap entry associated with nodeId
page._slotMap[slotIndex / TreePage.slotLineSize] &= ~(1 << slotIndex % TreePage.slotLineSize);
page.InUseCount--;
_inUseNodeCount--;
if (page.InUseCount == 0)
FreePage(page);
else if (page.InUseCount == page._slots.Length - 1)
MarkPageFree(page); // With freeing of a node, a previous full page has a free slot.
}
/*
* GetIndexOfPageWithFreeSlot()
* allocatedPage: If true, look for an allocatedPage with free slot else look for an unallocated page entry in pageTable
* return: if allocatedPage is true, return index of a page with at least 1 free slot
* else return index of an unallocated page, pageTable[index] is empty.
*/
private int GetIndexOfPageWithFreeSlot(bool allocatedPage)
{
int pageTableMapPos = _nextFreePageLine;
int pageIndex = -1;
while (pageTableMapPos < _pageTableMap.Length)
{
if (((uint)_pageTableMap[pageTableMapPos]) < 0xFFFFFFFF)
{
uint pageSegmentMap = (uint)_pageTableMap[pageTableMapPos];
while ((pageSegmentMap ^ (0xFFFFFFFF)) != 0) //atleast one "0" is there (same as <0xFFFFFFFF)
{
uint pageWithFreeSlot = (~(pageSegmentMap)) & (pageSegmentMap + 1);
if ((_pageTableMap[pageTableMapPos] & pageWithFreeSlot) != 0) //paranoia check
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.PagePositionInSlotInUse);
pageIndex = (pageTableMapPos * TreePage.slotLineSize) + GetIntValueFromBitMap(pageWithFreeSlot); // segment + offset
if (allocatedPage)
{
if (_pageTable[pageIndex] != null)
return pageIndex;
}
else
{
if (_pageTable[pageIndex] == null)
return pageIndex; // pageIndex points to an unallocated Page
}
pageIndex = -1;
pageSegmentMap |= pageWithFreeSlot; // found "reset bit", but unallocated page, mark it as unavaiable and continue search
}
}
pageTableMapPos++;
}
if (_nextFreePageLine != 0)
{
//Try one more time, starting from 0th page segment position to locate a page with free slots
_nextFreePageLine = 0;
pageIndex = GetIndexOfPageWithFreeSlot(allocatedPage);
}
return pageIndex;
}
public int Count
{
get
{
Debug.Assert(_inUseNodeCount - 1 == SubTreeSize(root), "count mismatch");
return (_inUseNodeCount - 1);
}
}
public bool HasDuplicates
{
get
{
return (0 != _inUseSatelliteTreeCount);
}
}
/*
* GetNewNode()
* Allocate storage for a new node and assign in the specified key.
*
* Find a page with free slots or allocate a new page.
* Use bitmap associated with page to allocate a slot.
* mark the slot as used and return its index.
*/
private int GetNewNode(K? key)
{
// find page with free slots, if none, allocate a new page
TreePage? page;
int freePageIndex = GetIndexOfPageWithFreeSlot(true);
if (freePageIndex != -1)
page = _pageTable[freePageIndex];
else if (_inUsePageCount < (4))
page = AllocPage(DefaultPageSize); // First 128 slots
else if (_inUsePageCount < (32))
page = AllocPage(256);
else if (_inUsePageCount < (128))
page = AllocPage(1024);
else if (_inUsePageCount < (4096))
page = AllocPage(4096);
else if (_inUsePageCount < (32 * 1024))
page = AllocPage(8192); // approximately First 16 million slots (2^24)
else
page = AllocPage(64 * 1024); // Page size to accommodate more than 16 million slots (Max 2 Billion and 16 million slots)
// page contains atleast 1 free slot.
int slotId = page!.AllocSlot(this);
if (slotId == -1)
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.NoFreeSlots);
// NodeId: Upper 16 bits pageId, lower bits slotId
page._slots[slotId]._selfId = (int)(((uint)page.PageId) << 16) | slotId;
Debug.Assert(page._slots[slotId]._leftId == NIL, "node not cleared");
Debug.Assert(page._slots[slotId]._rightId == NIL, "node not cleared");
Debug.Assert(page._slots[slotId]._parentId == NIL, "node not cleared");
Debug.Assert(page._slots[slotId]._nextId == NIL, "node not cleared");
page._slots[slotId]._subTreeSize = 1; // new Nodes have size 1.
page._slots[slotId]._keyOfNode = key;
Debug.Assert(page._slots[slotId]._nodeColor == NodeColor.red, "node not cleared");
return page._slots[slotId]._selfId;
}
private int Successor(int x_id)
{
if (Right(x_id) != NIL)
return Minimum(Right(x_id)); //return left most node in right sub-tree.
int y_id = Parent(x_id);
while (y_id != NIL && x_id == Right(y_id))
{
x_id = y_id;
y_id = Parent(y_id);
}
return y_id;
}
private bool Successor(ref int nodeId, ref int mainTreeNodeId)
{
if (NIL == nodeId)
{ // find first node, using branchNodeId as the root
nodeId = Minimum(mainTreeNodeId);
mainTreeNodeId = NIL;
}
else
{ // find next node
nodeId = Successor(nodeId);
if ((NIL == nodeId) && (NIL != mainTreeNodeId))
{ // done with satellite branch, move back to main tree
nodeId = Successor(mainTreeNodeId);
mainTreeNodeId = NIL;
}
}
if (NIL != nodeId)
{ // test for satellite branch
if (NIL != Next(nodeId))
{ // find first node of satellite branch
if (NIL != mainTreeNodeId)
{ // satellite branch has satellite branch - very bad
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.NestedSatelliteTreeEnumerator);
}
mainTreeNodeId = nodeId;
nodeId = Minimum(Next(nodeId));
}
// has value
return true;
}
// else no value, done with main tree
return false;
}
private int Minimum(int x_id)
{
while (Left(x_id) != NIL)
{
x_id = Left(x_id);
}
return x_id;
}
/*
* LeftRotate()
*
* It returns the node id for the root of the rotated tree
*/
private int LeftRotate(int root_id, int x_id, int mainTreeNode)
{
int y_id = Right(x_id);
// Turn y's left subtree into x's right subtree
SetRight(x_id, Left(y_id));
if (Left(y_id) != NIL)
{
SetParent(Left(y_id), x_id);
}
SetParent(y_id, Parent(x_id));
if (Parent(x_id) == NIL)
{
if (root_id == NIL)
{
root = y_id;
}
else
{
SetNext(mainTreeNode, y_id);
SetKey(mainTreeNode, Key(y_id));
root_id = y_id;
}
}
else if (x_id == Left(Parent(x_id)))
{ // x is left child of its parent
SetLeft(Parent(x_id), y_id);
}
else
{
SetRight(Parent(x_id), y_id);
}
SetLeft(y_id, x_id);
SetParent(x_id, y_id);
//maintain size: y_id = parent & x_id == child
if (x_id != NIL)
{
SetSubTreeSize(x_id, (SubTreeSize(Left(x_id)) + SubTreeSize(Right(x_id)) + (Next(x_id) == NIL ? 1 : SubTreeSize(Next(x_id)))));
}
if (y_id != NIL)
{
SetSubTreeSize(y_id, (SubTreeSize(Left(y_id)) + SubTreeSize(Right(y_id)) + (Next(y_id) == NIL ? 1 : SubTreeSize(Next(y_id)))));
}
return root_id;
}
/*
* RightRotate()
*
* It returns the node id for the root of the rotated tree
*/
private int RightRotate(int root_id, int x_id, int mainTreeNode)
{
int y_id = Left(x_id);
SetLeft(x_id, Right(y_id)); // Turn y's right subtree into x's left subtree
if (Right(y_id) != NIL)
{
SetParent(Right(y_id), x_id);
}
SetParent(y_id, Parent(x_id));
if (Parent(x_id) == NIL)
{
if (root_id == NIL)
{
root = y_id;
}
else
{
SetNext(mainTreeNode, y_id);
SetKey(mainTreeNode, Key(y_id));
root_id = y_id;
}
}
else if (x_id == Left(Parent(x_id))) // x is left child of its parent
SetLeft(Parent(x_id), y_id);
else
SetRight(Parent(x_id), y_id);
SetRight(y_id, x_id);
SetParent(x_id, y_id);
//maintain size: y_id == parent && x_id == child.
if (x_id != NIL)
{
SetSubTreeSize(x_id, (SubTreeSize(Left(x_id)) + SubTreeSize(Right(x_id)) + (Next(x_id) == NIL ? 1 : SubTreeSize(Next(x_id)))));
}
if (y_id != NIL)
{
SetSubTreeSize(y_id, (SubTreeSize(Left(y_id)) + SubTreeSize(Right(y_id)) + (Next(y_id) == NIL ? 1 : SubTreeSize(Next(y_id)))));
}
return root_id;
}
#if VerifySort
// This helps validate the sorting of the tree to help catch instances of corruption much sooner.
// corruption happens when the data changes without telling the tree or when multi-threads do simultanous write operations
private int Compare(int root_id, int x_id, int z_id)
{
Debug.Assert(NIL != x_id, "nil left");
Debug.Assert(NIL != z_id, "nil right");
return (root_id == NIL) ? CompareNode(Key(x_id), Key(z_id)) : CompareSatelliteTreeNode(Key(x_id), Key(z_id));
}
#endif
/*
* RBInsert()
* root_id: root_id of the tree to which a node has to be inserted. it is NIL for inserting to Main tree.
* x_id : node_id of node to be inserted
*
* returns: The root of the tree to which the specified node was added. its NIL if the node was added to Main RBTree.
*
* if root_id is NIL -> use CompareNode else use CompareSatelliteTreeNode
*
* Satellite tree creation:
* First Duplicate value encountered. Create a *new* tree whose root will have the same key value as the current node.
* The Duplicate tree nodes have same key when used with CompareRecords but distinct record ids.
* The current record at all times will have the same *key* as the duplicate tree root.
*/
private int RBInsert(int root_id, int x_id, int mainTreeNodeID, int position, bool append)
{
unchecked { _version++; }
// Insert Node x at the appropriate position
int y_id = NIL;
int z_id = (root_id == NIL) ? root : root_id; //if non NIL, then use the specifid root_id as tree's root.
if (_accessMethod == TreeAccessMethod.KEY_SEARCH_AND_INDEX && !append)
{
Debug.Assert(-1 == position, "KEY_SEARCH_AND_INDEX with bad position");
while (z_id != NIL) // in-order traverse and find node with a NILL left or right child
{
IncreaseSize(z_id);
y_id = z_id; // y_id set to the proposed parent of x_id
int c = (root_id == NIL) ? CompareNode(Key(x_id), Key(z_id)) : CompareSatelliteTreeNode(Key(x_id), Key(z_id));
if (c < 0)
{
#if VerifySort
Debug.Assert((NIL == Left(z_id)) || (0 > Compare(root_id, Left(z_id), z_id)), "Left is not left");
#endif
z_id = Left(z_id);
}
else if (c > 0)
{
#if VerifySort
Debug.Assert((NIL == Right(z_id)) || (0 < Compare(root_id, Right(z_id), z_id)), "Right is not right");
#endif
z_id = Right(z_id);
}
else
{
// Multiple records with same key - insert it to the duplicate record tree associated with current node
if (root_id != NIL)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.InvalidStateinInsert);
}
if (Next(z_id) != NIL)
{
root_id = RBInsert(Next(z_id), x_id, z_id, -1, false); // z_id is existing mainTreeNodeID
SetKey(z_id, Key(Next(z_id)));
#if VerifyPath
(new NodePath(x_id, z_id)).VerifyPath(this); // verify x_id after its been added
#endif
}
else
{
int newMainTreeNodeId = NIL;
// The existing node is pushed into the Satellite Tree and a new Node
// is created in the main tree, whose's next points to satellite root.
newMainTreeNodeId = GetNewNode(Key(z_id));
_inUseSatelliteTreeCount++;
// copy contents of z_id to dupRootId (main tree node).
SetNext(newMainTreeNodeId, z_id);
SetColor(newMainTreeNodeId, color(z_id));
SetParent(newMainTreeNodeId, Parent(z_id));
SetLeft(newMainTreeNodeId, Left(z_id));
SetRight(newMainTreeNodeId, Right(z_id));
// Update z_id's non-nil parent
if (Left(Parent(z_id)) == z_id)
SetLeft(Parent(z_id), newMainTreeNodeId);
else if (Right(Parent(z_id)) == z_id)
SetRight(Parent(z_id), newMainTreeNodeId);
// update children.
if (Left(z_id) != NIL)
SetParent(Left(z_id), newMainTreeNodeId);
if (Right(z_id) != NIL)
SetParent(Right(z_id), newMainTreeNodeId);
if (root == z_id)
root = newMainTreeNodeId;
// Reset z_id's pointers to NIL. It will start as the satellite tree's root.
SetColor(z_id, NodeColor.black);
SetParent(z_id, NIL);
SetLeft(z_id, NIL);
SetRight(z_id, NIL);
int savedSize = SubTreeSize(z_id);
SetSubTreeSize(z_id, 1);
// With z_id as satellite root, insert x_id
root_id = RBInsert(z_id, x_id, newMainTreeNodeId, -1, false);
SetSubTreeSize(newMainTreeNodeId, savedSize);
#if VerifyPath
(new NodePath(x_id, newMainTreeNodeId)).VerifyPath(this); // verify x_id after its been added
#endif
}
return root_id;
}
}
}
else if (_accessMethod == TreeAccessMethod.INDEX_ONLY || append)
{
if (position == -1)
{
position = SubTreeSize(root); // append
}
while (z_id != NIL) // in-order traverse and find node with a NILL left or right child
{
IncreaseSize(z_id);
y_id = z_id; // y_id set to the proposed parent of x_id
//int c = (SubTreeSize(y_id)-(position)); // Actually it should be: SubTreeSize(y_id)+1 - (position + 1)
int c = (position) - (SubTreeSize(Left(y_id)));
if (c <= 0)
{
z_id = Left(z_id);
}
else
{
//position = position - SubTreeSize(z_id);
z_id = Right(z_id);
if (z_id != NIL)
{
position = c - 1; //skip computation of position for leaf node
}
}
}
}
else
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.UnsupportedAccessMethod1);
}
SetParent(x_id, y_id);
if (y_id == NIL)
{
if (root_id == NIL)
{
root = x_id;
}
else
{
// technically we should never come here. Satellite tree always has a root and atleast 1 child.
// if it has only root as it's node, then the satellite tree gets collapsed into the main tree.
#if VerifyPath
(new NodePath(x_id, mainTreeNodeID)).VerifyPath(this); // verify x_id after its been added
#endif
SetNext(mainTreeNodeID, x_id);
SetKey(mainTreeNodeID, Key(x_id));
root_id = x_id;
}
}
else
{
int c = 0;
if (_accessMethod == TreeAccessMethod.KEY_SEARCH_AND_INDEX)
c = (root_id == NIL) ? CompareNode(Key(x_id), Key(y_id)) : CompareSatelliteTreeNode(Key(x_id), Key(y_id));
else if (_accessMethod == TreeAccessMethod.INDEX_ONLY)
c = (position <= 0) ? -1 : 1;
else
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.UnsupportedAccessMethod2);
}
if (c < 0)
SetLeft(y_id, x_id);
else
SetRight(y_id, x_id);
}
SetLeft(x_id, NIL);
SetRight(x_id, NIL);
SetColor(x_id, NodeColor.red);
z_id = x_id; // for verification later
// fix the tree
while (color(Parent(x_id)) == NodeColor.red)
{
if (Parent(x_id) == Left(Parent(Parent(x_id)))) // if x.parent is a left child
{
y_id = Right(Parent(Parent(x_id))); // x.parent.parent.right;
if (color(y_id) == NodeColor.red) // my right uncle is red
{
SetColor(Parent(x_id), NodeColor.black); // x.parent.color = Color.black;
SetColor(y_id, NodeColor.black);
SetColor(Parent(Parent(x_id)), NodeColor.red); // x.parent.parent.color = Color.red;
x_id = Parent(Parent(x_id)); // x = x.parent.parent;
}
else
{ // my right uncle is black
if (x_id == Right(Parent(x_id)))
{
x_id = Parent(x_id);
root_id = LeftRotate(root_id, x_id, mainTreeNodeID);
}
SetColor(Parent(x_id), NodeColor.black); // x.parent.color = Color.black;
SetColor(Parent(Parent(x_id)), NodeColor.red); // x.parent.parent.color = Color.red;
root_id = RightRotate(root_id, Parent(Parent(x_id)), mainTreeNodeID); // RightRotate (x.parent.parent);
}
}
else
{ // x.parent is a right child
y_id = Left(Parent(Parent(x_id))); // y = x.parent.parent.left;
if (color(y_id) == NodeColor.red) // if (y.color == Color.red) // my right uncle is red
{
SetColor(Parent(x_id), NodeColor.black);
SetColor(y_id, NodeColor.black);
SetColor(Parent(Parent(x_id)), NodeColor.red); // x.parent.parent.color = Color.red;
x_id = Parent(Parent(x_id));
}
else
{// my right uncle is black
if (x_id == Left(Parent(x_id)))
{
x_id = Parent(x_id);
root_id = RightRotate(root_id, x_id, mainTreeNodeID);
}
SetColor(Parent(x_id), NodeColor.black); // x.parent.color = Color.black;
SetColor(Parent(Parent(x_id)), NodeColor.red); // x.parent.parent.color = Color.red;
root_id = LeftRotate(root_id, Parent(Parent(x_id)), mainTreeNodeID);
}
}
}
if (root_id == NIL)
SetColor(root, NodeColor.black);
else
SetColor(root_id, NodeColor.black);
#if VerifyPath
(new NodePath(z_id, mainTreeNodeID)).VerifyPath(this); // verify x_id after its been added
#endif
return root_id;
} //Insert
public void UpdateNodeKey(K currentKey, K newKey)
{
// swap oldRecord with NewRecord in nodeId associated with oldRecord
// if the matched node is a satellite root then also change the key in the associated main tree node.
NodePath x_id = GetNodeByKey(currentKey);
if (Parent(x_id._nodeID) == NIL && x_id._nodeID != root) //determine if x_id is a satellite root.
{
#if VerifyPath
x_id.VerifyPath(this);
#endif
SetKey(x_id._mainTreeNodeID, newKey);
}
SetKey(x_id._nodeID, newKey);
}
public K DeleteByIndex(int i)
{
// This check was not correct, it should have been ((uint)this.Count <= (uint)i)
// Even then, the index will be checked by GetNodebyIndex which will throw either
// using RowOutOfRange or InternalRBTreeError depending on _accessMethod
//
//if (i >= (_inUseNodeCount - 1)) {
// throw ExceptionBuilder.InternalRBTreeError(RBTreeError.IndexOutOfRange);
//}
K key;
NodePath x_id = GetNodeByIndex(i); // it'l throw if corresponding node does not exist
key = Key(x_id._nodeID);
RBDeleteX(NIL, x_id._nodeID, x_id._mainTreeNodeID);
return key;
}
public int RBDelete(int z_id)
{
// always perform delete operation on the main tree
Debug.Assert(_accessMethod == TreeAccessMethod.INDEX_ONLY, "not expecting anything else");
return RBDeleteX(NIL, z_id, NIL);
}
/*
* RBDelete()
* root_id: root_id of the tree. it is NIL for Main tree.
* z_id : node_id of node to be deleted
*
* returns: The id of the spliced node
*
* Case 1: Node is in main tree only (decrease size in main tree)
* Case 2: Node's key is shared with a main tree node whose next is non-NIL
* (decrease size in both trees)
* Case 3: special case of case 2: After deletion, node leaves satellite tree with only 1 node (only root),
* it should collapse the satellite tree - go to case 4. (decrease size in both trees)
* Case 4: (1) Node is in Main tree and is a satellite tree root AND
* (2) It is the only node in Satellite tree
* (Do not decrease size in any tree, as its a collpase operation)
*
*/
private int RBDeleteX(int root_id, int z_id, int mainTreeNodeID)
{
int x_id = NIL; // used for holding spliced node (y_id's) child
int y_id; // the spliced node
int py_id; // for holding spliced node (y_id's) parent
#if VerifyPath
// by knowing the NodePath, when z_id is in a satellite branch we don't have to Search for mainTreeNodeID
(new NodePath(z_id, mainTreeNodeID)).VerifyPath(this);
#endif
if (Next(z_id) != NIL)
return RBDeleteX(Next(z_id), Next(z_id), z_id); // delete root of satellite tree.
// if we reach here, we are guaranteed z_id.next is NIL.
bool isCase3 = false;
int mNode = ((_accessMethod == TreeAccessMethod.KEY_SEARCH_AND_INDEX) ? mainTreeNodeID : z_id);
if (Next(mNode) != NIL)
root_id = Next(mNode);
if (SubTreeSize(Next(mNode)) == 2) // Next(mNode) == root_id
isCase3 = true;
else if (SubTreeSize(Next(mNode)) == 1)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.InvalidNextSizeInDelete);
}
if (Left(z_id) == NIL || Right(z_id) == NIL)
y_id = z_id;
else
y_id = Successor(z_id);
if (Left(y_id) != NIL)
x_id = Left(y_id);
else
x_id = Right(y_id);
py_id = Parent(y_id);
if (x_id != NIL)
SetParent(x_id, py_id);
if (py_id == NIL) // if the spliced node is the root.
{
// check for main tree or Satellite tree root
if (root_id == NIL)
root = x_id;
else
{
// spliced node is root of satellite tree
root_id = x_id;
}
}
else if (y_id == Left(py_id)) // update y's parent to point to X as its child
SetLeft(py_id, x_id);
else
SetRight(py_id, x_id);
if (y_id != z_id)
{
// assign all values from y (spliced node) to z (node containing key to be deleted)
// -----------
SetKey(z_id, Key(y_id)); // assign all values from y to z
SetNext(z_id, Next(y_id)); //z.value = y.value;
}
if (Next(mNode) != NIL)
{
// update mNode to point to satellite tree root and have the same key value.
// mNode will have to be patched again after RBDeleteFixup as root_id can again change
if (root_id == NIL && z_id != mNode)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.InvalidStateinDelete);
}
// -- it's possible for Next(mNode) to be != NIL and root_id == NIL when, the spliced node is a mNode of some
// -- satellite tree and its "next" gets assigned to mNode
if (root_id != NIL)
{
SetNext(mNode, root_id);
SetKey(mNode, Key(root_id));
}
}
// traverse from y_id's parent to root and decrement size by 1
int tmp_py_id = py_id;
// case: 1, 2, 3
while (tmp_py_id != NIL)
{
//DecreaseSize (py_id, (Next(y_id)==NIL)?1:Size(Next(y_id)));
RecomputeSize(tmp_py_id);
tmp_py_id = Parent(tmp_py_id);
}
//if satellite tree node deleted, decrease size in main tree as well.
if (root_id != NIL)
{
// case 2, 3
int nodeId = mNode;
while (nodeId != NIL)
{
DecreaseSize(nodeId);
nodeId = Parent(nodeId);
}
}
if (color(y_id) == NodeColor.black)
root_id = RBDeleteFixup(root_id, x_id, py_id, mainTreeNodeID); // passing x.parent as y.parent, to handle x=Node.NIL case.
if (isCase3)
{
// Collpase satellite tree, by swapping it with the main tree counterpart and freeing the main tree node
if (mNode == NIL || SubTreeSize(Next(mNode)) != 1)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.InvalidNodeSizeinDelete);
}
_inUseSatelliteTreeCount--;
int satelliteRootId = Next(mNode);
SetLeft(satelliteRootId, Left(mNode));
SetRight(satelliteRootId, Right(mNode));
SetSubTreeSize(satelliteRootId, SubTreeSize(mNode));
SetColor(satelliteRootId, color(mNode)); // Next of satelliteRootId is already NIL
if (Parent(mNode) != NIL)
{
SetParent(satelliteRootId, Parent(mNode));
if (Left(Parent(mNode)) == mNode)
{
SetLeft(Parent(mNode), satelliteRootId);
}
else
{
SetRight(Parent(mNode), satelliteRootId);
}
}
// update mNode's children.
if (Left(mNode) != NIL)
{
SetParent(Left(mNode), satelliteRootId);
}
if (Right(mNode) != NIL)
{
SetParent(Right(mNode), satelliteRootId);
}
if (root == mNode)
{
root = satelliteRootId;
}
FreeNode(mNode);
mNode = NIL;
}
else if (Next(mNode) != NIL)
{
// update mNode to point to satellite tree root and have the same key value
if (root_id == NIL && z_id != mNode)
{ //if mNode being deleted, its OK for root_id (it should be) NIL.
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.InvalidStateinEndDelete);
}
if (root_id != NIL)
{
SetNext(mNode, root_id);
SetKey(mNode, Key(root_id));
}
}
// In order to pin a key to it's node, free deleted z_id instead of the spliced y_id
if (y_id != z_id)
{
// we know that key, next and value are same for z_id and y_id
SetLeft(y_id, Left(z_id));
SetRight(y_id, Right(z_id));
SetColor(y_id, color(z_id));
SetSubTreeSize(y_id, SubTreeSize(z_id));
if (Parent(z_id) != NIL)
{
SetParent(y_id, Parent(z_id));
if (Left(Parent(z_id)) == z_id)
{
SetLeft(Parent(z_id), y_id);
}
else
{
SetRight(Parent(z_id), y_id);
}
}
else
{
SetParent(y_id, NIL);
}
// update children.
if (Left(z_id) != NIL)
{
SetParent(Left(z_id), y_id);
}
if (Right(z_id) != NIL)
{
SetParent(Right(z_id), y_id);
}
if (root == z_id)
{
root = y_id;
}
else if (root_id == z_id)
{
root_id = y_id;
}
// update a next reference to z_id (if any)
if (mNode != NIL && Next(mNode) == z_id)
{
SetNext(mNode, y_id);
}
}
FreeNode(z_id);
unchecked { _version++; }
return z_id;
}
/*
* RBDeleteFixup()
* Fix the specified tree for RedBlack properties
*
* returns: The id of the root
*/
private int RBDeleteFixup(int root_id, int x_id, int px_id /* px is parent of x */, int mainTreeNodeID)
{ //x is successor's non nil child or nil if both children are nil
int w_id;
#if VerifyPath
// by knowing the NodePath, when z_id is in a satellite branch we don't have to Search for mainTreeNodeID
(new NodePath(root_id, mainTreeNodeID)).VerifyPath(this);
#endif
if (x_id == NIL && px_id == NIL)
{
return NIL; //case of satellite tree root being deleted.
}
while (((root_id == NIL ? root : root_id) != x_id) && color(x_id) == NodeColor.black)
{
// (1) x's parent should have aleast 1 non-NIL child.
// (2) check if x is a NIL left child or a non NIL left child
if ((x_id != NIL && x_id == Left(Parent(x_id))) || (x_id == NIL && Left(px_id) == NIL))
{
// we have from DELETE, then x cannot be NIL and be a right child of its parent
// also from DELETE, if x is non nil, it will be a left child.
w_id = (x_id == NIL) ? Right(px_id) : Right(Parent(x_id)); // w is x's right sibling and it cannot be NIL
if (w_id == NIL)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.RBDeleteFixup);
}
if (color(w_id) == NodeColor.red)
{
SetColor(w_id, NodeColor.black);
SetColor(px_id, NodeColor.red);
root_id = LeftRotate(root_id, px_id, mainTreeNodeID);
w_id = (x_id == NIL) ? Right(px_id) : Right(Parent(x_id));
}
if (color(Left(w_id)) == NodeColor.black && color(Right(w_id)) == NodeColor.black)
{
SetColor(w_id, NodeColor.red);
x_id = px_id;
px_id = Parent(px_id); //maintain px_id
}
else
{
if (color(Right(w_id)) == NodeColor.black)
{
SetColor(Left(w_id), NodeColor.black);
SetColor(w_id, NodeColor.red);
root_id = RightRotate(root_id, w_id, mainTreeNodeID);
w_id = (x_id == NIL) ? Right(px_id) : Right(Parent(x_id));
}
SetColor(w_id, color(px_id));
SetColor(px_id, NodeColor.black);
SetColor(Right(w_id), NodeColor.black);
root_id = LeftRotate(root_id, px_id, mainTreeNodeID);
x_id = (root_id == NIL) ? root : root_id;
px_id = Parent(x_id);
}
}
else
{ //x is a right child or it is NIL
w_id = Left(px_id);
if (color(w_id) == NodeColor.red)
{ // x_id is y's (the spliced node) sole non-NIL child or NIL if y had no children
SetColor(w_id, NodeColor.black);
if (x_id != NIL)
{
SetColor(px_id, NodeColor.red);
root_id = RightRotate(root_id, px_id, mainTreeNodeID);
w_id = (x_id == NIL) ? Left(px_id) : Left(Parent(x_id));
}
else
{
//we have from DELETE, then x cannot be NIL and be a right child of its parent
// w_id cannot be nil.
SetColor(px_id, NodeColor.red);
root_id = RightRotate(root_id, px_id, mainTreeNodeID);
w_id = (x_id == NIL) ? Left(px_id) : Left(Parent(x_id));
if (w_id == NIL)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.CannotRotateInvalidsuccessorNodeinDelete);
}
}
}
if (color(Right(w_id)) == NodeColor.black && color(Left(w_id)) == NodeColor.black)
{
SetColor(w_id, NodeColor.red);
x_id = px_id;
px_id = Parent(px_id);
}
else
{
if (color(Left(w_id)) == NodeColor.black)
{
SetColor(Right(w_id), NodeColor.black);
SetColor(w_id, NodeColor.red);
root_id = LeftRotate(root_id, w_id, mainTreeNodeID);
w_id = (x_id == NIL) ? Left(px_id) : Left(Parent(x_id));
}
SetColor(w_id, color(px_id));
SetColor(px_id, NodeColor.black);
SetColor(Left(w_id), NodeColor.black);
root_id = RightRotate(root_id, px_id, mainTreeNodeID);
x_id = (root_id == NIL) ? root : root_id;
px_id = Parent(x_id);
}
}
}
SetColor(x_id, NodeColor.black);
return root_id;
}
private int SearchSubTree(int root_id, K? key)
{
if (root_id != NIL && _accessMethod != TreeAccessMethod.KEY_SEARCH_AND_INDEX)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.UnsupportedAccessMethodInNonNillRootSubtree);
}
int x_id = (root_id == NIL) ? root : root_id;
int c;
while (x_id != NIL)
{
c = (root_id == NIL) ? CompareNode(key, Key(x_id)) : CompareSatelliteTreeNode(key, Key(x_id));
if (c == 0)
{
break;
}
if (c < 0)
{
#if VerifySort
Debug.Assert((NIL == Left(x_id)) || (0 > Compare(root_id, Left(x_id), x_id)), "Search duplicate Left is not left");
#endif
x_id = Left(x_id);
}
else
{
#if VerifySort
Debug.Assert((NIL == Right(x_id)) || (0 < Compare(root_id, Right(x_id), x_id)), "Search duplicate Right is not right");
#endif
x_id = Right(x_id);
}
}
return x_id;
}
// only works on the main tree - does not work with satellite tree
public int Search(K key)
{ // for performance reasons, written as a while loop instead of a recursive method
int x_id = root;
int c;
while (x_id != NIL)
{
c = CompareNode(key, Key(x_id));
if (c == 0)
{
break;
}
if (c < 0)
{
#if VerifySort
Debug.Assert((NIL == Left(x_id)) || (0 > Compare(NIL, Left(x_id), x_id)), "Search Left is not left");
#endif
x_id = Left(x_id);
}
else
{
#if VerifySort
Debug.Assert((NIL == Right(x_id)) || (0 < Compare(NIL, Right(x_id), x_id)), "Search Right is not right");
#endif
x_id = Right(x_id);
}
}
return x_id;
}
// To simulate direct access for records[index]= record
/// <summary>
/// return key associated with the specified value. Specifically, return record for specified index/value
/// indexer
/// </summary>
/// <exception cref="IndexOutOfRangeException"></exception>
// return record i.e key at specified index
public K this[int index]
{
get
{
return Key(GetNodeByIndex(index)._nodeID);
}
}
// Get Record(s) having same key value as that of specified record. Then scan the matched nodes
// and return the node with the matching record
/// <returns>Determine node and the branch it took to get there.</returns>
private NodePath GetNodeByKey(K key) //i.e. GetNodeByKey
{
int nodeId = SearchSubTree(NIL, key);
if (Next(nodeId) != NIL)
{
return new NodePath(SearchSubTree(Next(nodeId), key), nodeId);
}
else if (!Key(nodeId)!.Equals(key))
{
nodeId = NIL;
}
return new NodePath(nodeId, NIL);
}
/*
* GetIndexByRecord()
* Gets index of the specified record. returns (-1) if specified record is not found.
*/
public int GetIndexByKey(K key)
{
int nodeIndex = -1;
NodePath nodeId = GetNodeByKey(key);
if (nodeId._nodeID != NIL)
{
nodeIndex = GetIndexByNodePath(nodeId);
}
return nodeIndex;
}
/*
* GetIndexByNode()
*
* If I am right child then size=my size + size of left child of my parent + 1
* go up till root, if right child keep adding to the size.
* (1) compute rank in main tree.
* (2) if node member of a satellite tree, add to rank its relative rank in that tree.
*
* Rank:
* Case 1: Node is in Main RBTree only
* Its rank/index is its main tree index
* Case 2: Node is in a Satellite tree only
* Its rank/index is its satellite tree index
* Case 3: Nodes is in both Main and Satellite RBTree (a main tree node can be a satellite tree root)
* Its rank/index is its main tree index + its satellite tree index - 1
* Returns the index of the specified node.
* returns -1, if the specified Node is tree.NIL.
*
* Assumption: The specified node always exist in the tree.
*/
// this improves performance when used heavily, like with the default view (creating before rows added)
public int GetIndexByNode(int node)
{
Debug.Assert(NIL != node, "GetIndexByNode(NIL)");
if (0 == _inUseSatelliteTreeCount)
{ // compute from the main tree when no satellite branches exist
return ComputeIndexByNode(node);
}
else if (NIL != Next(node))
{ // node is a main tree node
#if VerifyIndex && VerifyPath
(new NodePath(Next(node), node)).VerifyPath(this);
#endif
return ComputeIndexWithSatelliteByNode(node);
}
else
{
int mainTreeNodeId = SearchSubTree(NIL, Key(node));
if (mainTreeNodeId == node)
{ // node is a main tree node
#if VerifyIndex && VerifyPath
(new NodePath(node, NIL)).VerifyPath(this);
#endif
return ComputeIndexWithSatelliteByNode(node);
}
else
{ //compute the main tree rank + satellite branch rank
#if VerifyIndex && VerifyPath
(new NodePath(node, mainTreeNodeId)).VerifyPath(this);
#endif
return ComputeIndexWithSatelliteByNode(mainTreeNodeId) +
ComputeIndexByNode(node);
}
}
}
/// <summary>Determine tree index position from node path.</summary>
/// <remarks>This differs from GetIndexByNode which would search for the main tree node instead of just knowing it</remarks>
private int GetIndexByNodePath(NodePath path)
{
#if VerifyIndex && VerifyPath
path.VerifyPath(this);
#endif
if (0 == _inUseSatelliteTreeCount)
{ // compute from the main tree when no satellite branches exist
return ComputeIndexByNode(path._nodeID);
}
else if (NIL == path._mainTreeNodeID)
{ // compute from the main tree accounting for satellite branches
return ComputeIndexWithSatelliteByNode(path._nodeID);
}
else
{ //compute the main tree rank + satellite branch rank
return ComputeIndexWithSatelliteByNode(path._mainTreeNodeID) +
ComputeIndexByNode(path._nodeID);
}
}
private int ComputeIndexByNode(int nodeId)
{
#if VerifyIndex
Debug.Assert(NIL != nodeId, "ComputeIndexByNode(NIL)");
#endif
int myRank = SubTreeSize(Left(nodeId));
while (nodeId != NIL)
{
#if VerifyIndex && VerifyPath
Debug.Assert(NIL == Next(nodeId), "Next not NIL");
#endif
int parent = Parent(nodeId);
if (nodeId == Right(parent))
{
myRank += (SubTreeSize(Left(parent)) + 1);
}
nodeId = parent;
}
return myRank;
}
private int ComputeIndexWithSatelliteByNode(int nodeId)
{
#if VerifyIndex
Debug.Assert(NIL != nodeId, "ComputeIndexWithSatelliteByNode(NIL)");
#endif
int myRank = SubTreeSize(Left(nodeId));
while (nodeId != NIL)
{
int parent = Parent(nodeId);
if (nodeId == Right(parent))
{
myRank += (SubTreeSize(Left(parent)) + ((Next(parent) == NIL) ? 1 : SubTreeSize(Next(parent))));
}
nodeId = parent;
}
return myRank;
}
/// <returns>Determine node and the branch it took to get there.</returns>
/// <exception cref="IndexOutOfRangeException"></exception>
private NodePath GetNodeByIndex(int userIndex)
{
int x_id, satelliteRootId;
if (0 == _inUseSatelliteTreeCount)
{
// if rows were only contiguously append, then using (userIndex -= _pageTable[i].InUseCount) would
// be faster for the first 12 pages (about 5248) nodes before (log2 of Count) becomes faster again.
// the additional complexity was deemed not worthy for the possible perf gain
// computation cost is (log2 of Count)
x_id = ComputeNodeByIndex(root, unchecked(userIndex + 1));
satelliteRootId = NIL;
}
else
{
// computation cost is ((log2 of Distinct Count) + (log2 of Duplicate Count))
x_id = ComputeNodeByIndex(userIndex, out satelliteRootId);
}
if (x_id == NIL)
{
if (TreeAccessMethod.INDEX_ONLY == _accessMethod)
{
throw ExceptionBuilder.RowOutOfRange(userIndex);
}
else
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.IndexOutOFRangeinGetNodeByIndex);
}
}
return new NodePath(x_id, satelliteRootId);
}
private int ComputeNodeByIndex(int index, out int satelliteRootId)
{
index = unchecked(index + 1); // index is 0 based, while size is 1 based.
satelliteRootId = NIL;
int x_id = root;
int rank;
while (x_id != NIL && !(((rank = SubTreeSize(Left(x_id)) + 1) == index) && Next(x_id) == NIL))
{
if (index < rank)
{
x_id = Left(x_id);
}
else if (Next(x_id) != NIL && index >= rank && index <= rank + SubTreeSize(Next(x_id)) - 1)
{
// node with matching index is in the associated satellite tree. continue searching for index in satellite tree.
satelliteRootId = x_id;
index = index - rank + 1; // rank is SubTreeSize(Node.left)+1, we do +1 here to offset +1 done in rank. index -= rank;
return ComputeNodeByIndex(Next(x_id), index); //satellite tree root
}
else
{
if (Next(x_id) == NIL)
index -= rank;
else
index -= rank + SubTreeSize(Next(x_id)) - 1;
x_id = Right(x_id);
}
}
return x_id;
}
private int ComputeNodeByIndex(int x_id, int index)
{
while (x_id != NIL)
{
Debug.Assert(NIL == Next(x_id), "has unexpected satellite tree");
int y_id = Left(x_id);
int rank = SubTreeSize(y_id) + 1;
if (index < rank)
{
x_id = y_id;
}
else if (rank < index)
{
x_id = Right(x_id);
index -= rank;
}
else
{
break;
}
}
return x_id;
}
#if DEBUG
// return true if all nodes are unique; i.e. no satellite trees.
public bool CheckUnique(int curNodeId)
{
if (curNodeId != NIL)
{
if (Next(curNodeId) != NIL)
return false; // atleast 1 duplicate found
if (!CheckUnique(Left(curNodeId)) || !CheckUnique(Right(curNodeId)))
return false;
}
return true;
}
#endif
public int Insert(K item)
{
int nodeId = GetNewNode(item);
RBInsert(NIL, nodeId, NIL, -1, false);
return nodeId;
}
// Begin: List of methods for making it easy to work with ArrayList
public int Add(K? item) //Insert (int record)
{
int nodeId = GetNewNode(item);
RBInsert(NIL, nodeId, NIL, -1, false);
return nodeId;
}
public IEnumerator GetEnumerator()
{
return new RBTreeEnumerator(this);
}
// *****BruteForceImplementation*****
//
// iterate over all nodes, InOrder and return index of node with the specified Item
// For the short term use a recursive method, later re-write it based on a stack data structure (if needed)
public int IndexOf(int nodeId, K item)
{
int index = -1;
// BIG ASSUMPTION: There is not satellite tree, this is INDEX_ONLY.
if (nodeId != NIL)
{
if ((object)Key(nodeId)! == (object)item!)
{
return GetIndexByNode(nodeId);
}
if ((index = IndexOf(Left(nodeId), item)) != -1)
{
return index;
}
if ((index = IndexOf(Right(nodeId), item)) != -1)
{
return index;
}
}
return index;
}
public int Insert(int position, K item) //Insert (int record)
{
return InsertAt(position, item, false);
}
public int InsertAt(int position, K item, bool append)
{
int nodeId = GetNewNode(item);
RBInsert(NIL, nodeId, NIL, position, append);
return nodeId;
}
public void RemoveAt(int position)
{
DeleteByIndex(position);
}
public void Clear()
{
InitTree();
unchecked { _version++; }
}
public void CopyTo(Array array, int index)
{
if (array == null)
{
throw ExceptionBuilder.ArgumentNull(nameof(array));
}
if (index < 0)
{
throw ExceptionBuilder.ArgumentOutOfRange(nameof(index));
}
int count = Count;
if (array.Length - index < Count)
{
throw ExceptionBuilder.InvalidOffsetLength();
}
int x_id = Minimum(root);
for (int i = 0; i < count; ++i)
{
array.SetValue(Key(x_id), index + i);
x_id = Successor(x_id);
}
}
public void CopyTo(K[] array, int index)
{
if (array == null)
{
throw ExceptionBuilder.ArgumentNull(nameof(array));
}
if (index < 0)
{
throw ExceptionBuilder.ArgumentOutOfRange(nameof(index));
}
int count = Count;
if (array.Length - index < Count)
{
throw ExceptionBuilder.InvalidOffsetLength();
}
int x_id = Minimum(root);
for (int i = 0; i < count; ++i)
{
// Can't annotate generic array for element nullability
array[index + i] = Key(x_id)!;
x_id = Successor(x_id);
}
}
// End: List of methods for making it easy to work with ArrayList
private void SetRight(int nodeId, int rightNodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].rightId = rightNodeId;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._rightId = rightNodeId;
}
private void SetLeft(int nodeId, int leftNodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].leftId = leftNodeId;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._leftId = leftNodeId;
}
private void SetParent(int nodeId, int parentNodeId)
{
Debug.Assert(nodeId != NIL, " in SetParent nodeId == NIL");
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].parentId = parentNodeId;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._parentId = parentNodeId;
}
private void SetColor(int nodeId, NodeColor color)
{
Debug.Assert(nodeId != NIL, " in SetColor nodeId == NIL");
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].nodeColor = color;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._nodeColor = color;
}
private void SetKey(int nodeId, K key)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].keyOfNode = key;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._keyOfNode = key;
}
private void SetNext(int nodeId, int nextNodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].nextId = nextNodeId;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._nextId = nextNodeId;
}
private void SetSubTreeSize(int nodeId, int size)
{
Debug.Assert(nodeId != NIL &&
(size != 0 || _pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._selfId == NIL) &&
(size != 1 || _pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._nextId == NIL), "SetSize");
// this improves performance by reducing the impact of this heavily used method
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._subTreeSize = size;
VerifySize(nodeId, size);
}
private void IncreaseSize(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].subTreeSize += 1;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._subTreeSize += 1;
}
private void RecomputeSize(int nodeId)
{
int myCorrectSize = SubTreeSize(Left(nodeId)) + SubTreeSize(Right(nodeId)) + (Next(nodeId) == NIL ? 1 : SubTreeSize(Next(nodeId)));
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].subTreeSize = myCorrectSize;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._subTreeSize = myCorrectSize;
}
private void DecreaseSize(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
page.Slots[slotIndex].subTreeSize -= 1;
*/
_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._subTreeSize -= 1;
VerifySize(nodeId, _pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._subTreeSize);
}
[ConditionalAttribute("DEBUG")]
private void VerifySize(int nodeId, int size)
{
int myCorrectSize = SubTreeSize(Left(nodeId)) + SubTreeSize(Right(nodeId)) + (Next(nodeId) == NIL ? 1 : SubTreeSize(Next(nodeId)));
Debug.Assert(myCorrectSize == size, "VerifySize");
}
public int Right(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
int rightId = page.Slots[slotIndex].rightId;
return rightId;
*/
return (_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._rightId);
}
public int Left(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
int leftId = page.Slots[slotIndex].leftId;
return leftId;
*/
return (_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._leftId);
}
public int Parent(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
int parentId = page.Slots[slotIndex].parentId;
return parentId;
*/
return (_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._parentId);
}
private NodeColor color(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
NodeColor col = page.Slots[slotIndex].nodeColor;
return col;
*/
return (_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._nodeColor);
}
public int Next(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
int nextId = page.Slots[slotIndex].nextId;
return nextId;
*/
return (_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._nextId);
}
public int SubTreeSize(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
int size = page.Slots[slotIndex].subTreeSize;
return size;
*/
return (_pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._subTreeSize);
}
public K Key(int nodeId)
{
/*
TreePage page = _pageTable[nodeId >> 16];
int slotIndex = nodeId & 0xFFFF;
K key = page.Slots[slotIndex].keyOfNode;
return key;
*/
return _pageTable[nodeId >> 16]!._slots[nodeId & 0xFFFF]._keyOfNode!;
}
private enum NodeColor
{
red = 0,
black = 1,
};
private struct Node
{
internal int _selfId;
internal int _leftId;
internal int _rightId;
internal int _parentId;
internal int _nextId; // multiple records associated with same key
internal int _subTreeSize; // number of nodes in subtree rooted at the current node
internal K? _keyOfNode;
internal NodeColor _nodeColor;
}
/// <summary>Represents the node in the tree and the satellite branch it took to get there.</summary>
private readonly struct NodePath
{
/// <summary>Represents the node in the tree</summary>
internal readonly int _nodeID;
/// <summary>
/// When not NIL, it represents the fact NodeID is has duplicate values in the tree.
/// This is the 'fake' node in the main tree that redirects to the root of the satellite tree.
/// By tracking this value, we don't have to repeatedly search for this node.
/// </summary>
internal readonly int _mainTreeNodeID;
internal NodePath(int nodeID, int mainTreeNodeID)
{
_nodeID = nodeID;
_mainTreeNodeID = mainTreeNodeID;
}
#if VerifyPath
internal void VerifyPath(RBTree<K> tree)
{
Debug.Assert(null != tree, "null tree");
Debug.Assert((NIL == _nodeID && NIL == _mainTreeNodeID) || (NIL != _nodeID), "MainTreeNodeID is not NIL");
if (NIL != _mainTreeNodeID)
{
Debug.Assert(NIL != tree.Next(_mainTreeNodeID), "MainTreeNodeID should have a Next");
int node = _mainTreeNodeID;
while (NIL != tree.Parent(node))
{
node = tree.Parent(node);
}
Debug.Assert(tree.root == node, "MainTreeNodeID parent change doesn't align");
}
if (NIL != _nodeID)
{
Debug.Assert(NIL == tree.Next(_nodeID), "NodeID should not have a Next");
int node = _nodeID;
if (NIL == _mainTreeNodeID)
{
while (NIL != tree.Parent(node))
{
node = tree.Parent(node);
}
}
else
{
while (NIL != tree.Parent(node))
{
Debug.Assert(NIL == tree.Next(node), "duplicate node should not have a next");
node = tree.Parent(node);
}
}
Debug.Assert((NIL == _mainTreeNodeID && tree.root == node) ||
(tree.Next(_mainTreeNodeID) == node), "NodeID parent change doesn't align");
}
}
#endif
}
private sealed class TreePage
{
public const int slotLineSize = 32;
internal readonly Node[] _slots; // List of slots
internal readonly int[] _slotMap; // CEILING(slots.size/slotLineSize)
private int _inUseCount; // 0 to _slots.size
private int _pageId; // Page's Id
private int _nextFreeSlotLine; // o based position of next free slot line
/*
* size: number of slots per page. Maximum allowed is 64K
*/
internal TreePage(int size)
{
if (size > 64 * 1024)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.InvalidPageSize);
}
_slots = new Node[size];
_slotMap = new int[(size + slotLineSize - 1) / slotLineSize];
}
/*
* Allocate a free slot from the current page belonging to the specified tree.
* return the Id of the allocated slot, or -1 if the current page does not have any free slots.
*/
internal int AllocSlot(RBTree<K> tree)
{
int segmentPos; // index into _SlotMap
int freeSlot; // Uint, slot offset within the segment
int freeSlotId = -1; // 0 based slot position
if (_inUseCount < _slots.Length)
{
segmentPos = _nextFreeSlotLine;
while (segmentPos < _slotMap.Length)
{
if (unchecked((uint)_slotMap[segmentPos]) < 0xFFFFFFFF)
{
freeSlot = (~(_slotMap[segmentPos])) & unchecked(_slotMap[segmentPos] + 1);
// avoid string concat to allow debug code to run faster
Debug.Assert((_slotMap[segmentPos] & freeSlot) == 0, "Slot position segment[segmentPos ]: [freeSlot] is in use. Expected to be empty");
_slotMap[segmentPos] |= freeSlot; //mark free slot as used.
_inUseCount++;
if (_inUseCount == _slots.Length) // mark page as full
tree.MarkPageFull(this);
tree._inUseNodeCount++;
// convert freeSlotPos to int value giving number of 0's to its right i.e. freeSlotId
freeSlotId = GetIntValueFromBitMap(unchecked((uint)freeSlot));
_nextFreeSlotLine = segmentPos;
freeSlotId = (segmentPos * TreePage.slotLineSize) + freeSlotId;
break;
}
else
{
segmentPos++;
}
}
if (freeSlotId == -1 && _nextFreeSlotLine != 0)
{
//Try one more time, starting from 0th segment position to locate a free slot.
_nextFreeSlotLine = 0;
freeSlotId = AllocSlot(tree);
}
}
return freeSlotId; // 0 based slot position
}
internal int InUseCount
{
get { return _inUseCount; }
set { _inUseCount = value; }
}
internal int PageId
{
get { return _pageId; }
set { _pageId = value; }
}
}
// this improves performance allowing to iterating of the index instead of computing record by index
// changes are required to handle satellite nodes which do not exist in DataRowCollection
// enumerator over index will not be handed to the user, only used internally
// instance of this enumerator will be handed to the user via DataRowCollection.GetEnumerator()
internal struct RBTreeEnumerator : IEnumerator<K>, IEnumerator
{
private readonly RBTree<K> _tree;
private readonly int _version;
private int _index, _mainTreeNodeId;
private K? _current;
internal RBTreeEnumerator(RBTree<K> tree)
{
_tree = tree;
_version = tree._version;
_index = NIL;
_mainTreeNodeId = tree.root;
_current = default(K);
}
internal RBTreeEnumerator(RBTree<K> tree, int position)
{
_tree = tree;
_version = tree._version;
if (0 == position)
{
_index = NIL;
_mainTreeNodeId = tree.root;
}
else
{
_index = tree.ComputeNodeByIndex(position - 1, out _mainTreeNodeId);
if (NIL == _index)
{
throw ExceptionBuilder.InternalRBTreeError(RBTreeError.IndexOutOFRangeinGetNodeByIndex);
}
}
_current = default(K);
}
public void Dispose()
{
}
public bool MoveNext()
{
if (_version != _tree._version)
{
throw ExceptionBuilder.EnumeratorModified();
}
bool hasCurrent = _tree.Successor(ref _index, ref _mainTreeNodeId);
_current = _tree.Key(_index);
return hasCurrent;
}
public K Current
{
get
{
// TODO: Should throw if MoveNext hasn't been called
return _current!;
}
}
object? IEnumerator.Current
{
get
{
return Current;
}
}
void IEnumerator.Reset()
{
if (_version != _tree._version)
{
throw ExceptionBuilder.EnumeratorModified();
}
_index = NIL;
_mainTreeNodeId = _tree.root;
_current = default(K);
}
}
}
}
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