Red Black Tree
//******************************
// Written by Peter Golde
// Copyright (c) 2004-2007, Wintellect
//
// Use and restribution of this code is subject to the license agreement
// contained in the file "License.txt" accompanying this file.
//******************************
using System;
using System.Diagnostics;
using System.Collections.Generic;
namespace Wintellect.PowerCollections
{
/// <summary>
/// Describes what to do if a key is already in the tree when doing an
/// insertion.
/// </summary>
internal enum DuplicatePolicy
{
InsertFirst, // Insert a new node before duplicates
InsertLast, // Insert a new node after duplicates
ReplaceFirst, // Replace the first of the duplicate nodes
ReplaceLast, // Replace the last of the duplicate nodes
DoNothing // Do nothing to the tree
};
/// <summary>
/// The base implementation for various collections classes that use Red-Black trees
/// as part of their implementation. This class should not (and can not) be
/// used directly by end users; it's only for internal use by the collections package.
/// </summary>
/// <remarks>
/// The Red-Black tree manages items of type T, and uses a IComparer<T> that
/// compares items to sort the tree. Multiple items can compare equal and be stored
/// in the tree. Insert, Delete, and Find operations are provided in their full generality;
/// all operations allow dealing with either the first or last of items that compare equal.
///</remarks>
internal class RedBlackTree<T> : IEnumerable<T>
{
private readonly IComparer<T> comparer; // interface for comparing elements, only Compare is used.
private Node root; // The root of the tree. Can be null when tree is empty.
private int count; // The count of elements in the tree.
private int changeStamp; // An integer that is changed every time the tree structurally changes.
// Used so that enumerations throw an exception if the tree is changed
// during enumeration.
private Node[] stack; // A stack of nodes. This is cached locally to avoid constant re-allocated it.
/// <summary>
/// Create an array of Nodes big enough for any path from top
/// to bottom. This is cached, and reused from call-to-call, so only one
/// can be around at a time per tree.
/// </summary>
/// <returns>The node stack.</returns>
private Node[] GetNodeStack()
{
// Maximum depth needed is 2 * lg count + 1.
int maxDepth;
if (count < 0x400)
maxDepth = 21;
else if (count < 0x10000)
maxDepth = 41;
else
maxDepth = 65;
if (stack == null || stack.Length < maxDepth)
stack = new Node[maxDepth];
return stack;
}
/// <summary>
/// The class that is each node in the red-black tree.
/// </summary>
private class Node
{
public Node left, right;
public T item;
private const uint REDMASK = 0x80000000;
private uint count;
/// <summary>
/// Is this a red node?
/// </summary>
public bool IsRed
{
get { return (count & REDMASK) != 0; }
set
{
if (value)
count |= REDMASK;
else
count &= ~REDMASK;
}
}
/// <summary>
/// Get or set the Count field -- a 31-bit field
/// that holds the number of nodes at or below this
/// level.
/// </summary>
public int Count
{
get { return (int)(count & ~REDMASK); }
set { count = (count & REDMASK) | (uint)value; }
}
/// <summary>
/// Add one to the Count.
/// </summary>
public void IncrementCount()
{
++count;
}
/// <summary>
/// Subtract one from the Count. The current
/// Count must be non-zero.
/// </summary>
public void DecrementCount()
{
Debug.Assert(Count != 0);
--count;
}
/// <summary>
/// Clones a node and all its descendants.
/// </summary>
/// <returns>The cloned node.</returns>
public Node Clone()
{
Node newNode = new Node();
newNode.item = item;
newNode.count = count;
if (left != null)
newNode.left = left.Clone();
if (right != null)
newNode.right = right.Clone();
return newNode;
}
}
/// <summary>
/// Must be called whenever there is a structural change in the tree. Causes
/// changeStamp to be changed, which causes any in-progress enumerations
/// to throw exceptions.
/// </summary>
internal void StopEnumerations()
{
++changeStamp;
}
/// <summary>
/// Checks the given stamp against the current change stamp. If different, the
/// collection has changed during enumeration and an InvalidOperationException
/// must be thrown
/// </summary>
/// <param name="startStamp">changeStamp at the start of the enumeration.</param>
private void CheckEnumerationStamp(int startStamp)
{
if (startStamp != changeStamp)
{
throw new InvalidOperationException("Change During Enumeration");
}
}
/// <summary>
/// Initialize a red-black tree, using the given interface instance to compare elements. Only
/// Compare is used on the IComparer interface.
/// </summary>
/// <param name="comparer">The IComparer<T> used to sort keys.</param>
public RedBlackTree(IComparer<T> comparer)
{
this.comparer = comparer;
this.count = 0;
this.root = null;
}
/// <summary>
/// Returns the number of elements in the tree.
/// </summary>
public int ElementCount
{
get
{
return count;
}
}
/// <summary>
/// Clone the tree, returning a new tree containing the same items. Should
/// take O(N) take.
/// </summary>
/// <returns>Clone version of this tree.</returns>
public RedBlackTree<T> Clone()
{
RedBlackTree<T> newTree = new RedBlackTree<T>(comparer);
newTree.count = this.count;
if (this.root != null)
newTree.root = this.root.Clone();
return newTree;
}
/// <summary>
/// Finds the key in the tree. If multiple items in the tree have
/// compare equal to the key, finds the first or last one. Optionally replaces the item
/// with the one searched for.
/// </summary>
/// <param name="key">Key to search for.</param>
/// <param name="findFirst">If true, find the first of duplicates, else finds the last of duplicates.</param>
/// <param name="replace">If true, replaces the item with key (if function returns true)</param>
/// <param name="item">Returns the found item, before replacing (if function returns true).</param>
/// <returns>True if the key was found.</returns>
public bool Find(T key, bool findFirst, bool replace, out T item)
{
Node current = root; // current search location in the tree
Node found = null; // last node found with the key, or null if none.
while (current != null)
{
int compare = comparer.Compare(key, current.item);
if (compare < 0)
{
current = current.left;
}
else if (compare > 0)
{
current = current.right;
}
else
{
// Go left/right on equality to find first/last of elements with this key.
Debug.Assert(compare == 0);
found = current;
if (findFirst)
current = current.left;
else
current = current.right;
}
}
if (found != null)
{
item = found.item;
if (replace)
found.item = key;
return true;
}
else
{
item = default(T);
return false;
}
}
/// <summary>
/// Finds the index of the key in the tree. If multiple items in the tree have
/// compare equal to the key, finds the first or last one.
/// </summary>
/// <param name="key">Key to search for.</param>
/// <param name="findFirst">If true, find the first of duplicates, else finds the last of duplicates.</param>
/// <returns>Index of the item found if the key was found, -1 if not found.</returns>
public int FindIndex(T key, bool findFirst)
{
T dummy;
if (findFirst)
return FirstItemInRange(EqualRangeTester(key), out dummy);
else
return LastItemInRange(EqualRangeTester(key), out dummy);
}
/// <summary>
/// Find the item at a particular index in the tree.
/// </summary>
/// <param name="index">The zero-based index of the item. Must be >= 0 and < Count.</param>
/// <returns>The item at the particular index.</returns>
public T GetItemByIndex(int index)
{
if (index < 0 || index >= count)
throw new ArgumentOutOfRangeException("index");
Node current = root; // current search location in the tree
for (; ; )
{
int leftCount;
if (current.left != null)
leftCount = current.left.Count;
else
leftCount = 0;
if (leftCount > index)
current = current.left;
else if (leftCount == index)
return current.item;
else
{
index -= leftCount + 1;
current = current.right;
}
}
}
/// <summary>
/// Insert a new node into the tree, maintaining the red-black invariants.
/// </summary>
/// <remarks>Algorithm from Sedgewick, "Algorithms".</remarks>
/// <param name="item">The new item to insert</param>
/// <param name="dupPolicy">What to do if equal item is already present.</param>
/// <param name="previous">If false, returned, the previous item.</param>
/// <returns>false if duplicate exists, otherwise true.</returns>
public bool Insert(T item, DuplicatePolicy dupPolicy, out T previous)
{
Node node = root;
Node parent = null, gparent = null, ggparent = null; // parent, grand, a great-grantparent of node.
bool wentLeft = false, wentRight = false; // direction from parent to node.
bool rotated;
Node duplicateFound = null;
// The tree may be changed.
StopEnumerations();
// We increment counts on the way down the tree. If we end up not inserting an items due
// to a duplicate, we need a stack to adjust the counts back. We don't need the stack if the duplicate
// policy means that we will always do an insertion.
bool needStack = !((dupPolicy == DuplicatePolicy.InsertFirst) || (dupPolicy == DuplicatePolicy.InsertLast));
Node[] nodeStack = null;
int nodeStackPtr = 0; // first free item on the stack.
if (needStack)
nodeStack = GetNodeStack();
while (node != null)
{
// If we find a node with two red children, split it so it doesn't cause problems
// when inserting a node.
if (node.left != null && node.left.IsRed && node.right != null && node.right.IsRed)
{
node = InsertSplit(ggparent, gparent, parent, node, out rotated);
if (needStack && rotated)
{
nodeStackPtr -= 2;
if (nodeStackPtr < 0)
nodeStackPtr = 0;
}
}
// Keep track of parent, grandparent, great-grand parent.
ggparent = gparent; gparent = parent; parent = node;
// Compare the key and the node.
int compare = comparer.Compare(item, node.item);
if (compare == 0)
{
// Found a node with the data already. Check duplicate policy.
if (dupPolicy == DuplicatePolicy.DoNothing)
{
previous = node.item;
// Didn't insert after all. Return counts back to their previous value.
for (int i = 0; i < nodeStackPtr; ++i)
nodeStack[i].DecrementCount();
return false;
}
else if (dupPolicy == DuplicatePolicy.InsertFirst || dupPolicy == DuplicatePolicy.ReplaceFirst)
{
// Insert first by treating the key as less than nodes in the tree.
duplicateFound = node;
compare = -1;
}
else
{
Debug.Assert(dupPolicy == DuplicatePolicy.InsertLast || dupPolicy == DuplicatePolicy.ReplaceLast);
// Insert last by treating the key as greater than nodes in the tree.
duplicateFound = node;
compare = 1;
}
}
Debug.Assert(compare != 0);
node.IncrementCount();
if (needStack)
nodeStack[nodeStackPtr++] = node;
// Move to the left or right as needed to find the insertion point.
if (compare < 0)
{
node = node.left;
wentLeft = true; wentRight = false;
}
else
{
node = node.right;
wentRight = true; wentLeft = false;
}
}
if (duplicateFound != null)
{
previous = duplicateFound.item;
// Are we replacing instread of inserting?
if (dupPolicy == DuplicatePolicy.ReplaceFirst || dupPolicy == DuplicatePolicy.ReplaceLast)
{
duplicateFound.item = item;
// Didn't insert after all. Return counts back to their previous value.
for (int i = 0; i < nodeStackPtr; ++i)
nodeStack[i].DecrementCount();
return false;
}
}
else
{
previous = default(T);
}
// Create a new node.
node = new Node();
node.item = item;
node.Count = 1;
// Link the node into the tree.
if (wentLeft)
parent.left = node;
else if (wentRight)
parent.right = node;
else
{
Debug.Assert(root == null);
root = node;
}
// Maintain the red-black policy.
InsertSplit(ggparent, gparent, parent, node, out rotated);
// We've added a node to the tree, so update the count.
count += 1;
return (duplicateFound == null);
}
/// <summary>
/// Split a node with two red children (a 4-node in the 2-3-4 tree formalism), as
/// part of an insert operation.
/// </summary>
/// <param name="ggparent">great grand-parent of "node", can be null near root</param>
/// <param name="gparent">grand-parent of "node", can be null near root</param>
/// <param name="parent">parent of "node", can be null near root</param>
/// <param name="node">Node to split, can't be null</param>
/// <param name="rotated">Indicates that rotation(s) occurred in the tree.</param>
/// <returns>Node to continue searching from.</returns>
private Node InsertSplit(Node ggparent, Node gparent, Node parent, Node node, out bool rotated)
{
if (node != root)
node.IsRed = true;
if (node.left != null)
node.left.IsRed = false;
if (node.right != null)
node.right.IsRed = false;
if (parent != null && parent.IsRed)
{
// Since parent is red, gparent can't be null (root is always black). ggparent
// might be null, however.
Debug.Assert(gparent != null);
// if links from gparent and parent are opposite (left/right or right/left),
// then rotate.
if ((gparent.left == parent) != (parent.left == node))
{
Rotate(gparent, parent, node);
parent = node;
}
gparent.IsRed = true;
// Do a rotate to prevent two red links in a row.
Rotate(ggparent, gparent, parent);
parent.IsRed = false;
rotated = true;
return parent;
}
else
{
rotated = false;
return node;
}
}
/// <summary>
/// Performs a rotation involving the node, it's child and grandchild. The counts of
/// childs and grand-child are set the correct values from their children; this is important
/// if they have been adjusted on the way down the try as part of an insert/delete.
/// </summary>
/// <param name="node">Top node of the rotation. Can be null if child==root.</param>
/// <param name="child">One child of "node". Not null.</param>
/// <param name="gchild">One child of "child". Not null.</param>
private void Rotate(Node node, Node child, Node gchild)
{
if (gchild == child.left)
{
child.left = gchild.right;
gchild.right = child;
}
else
{
Debug.Assert(gchild == child.right);
child.right = gchild.left;
gchild.left = child;
}
// Restore the counts.
child.Count = (child.left != null ? child.left.Count : 0) + (child.right != null ? child.right.Count : 0) + 1;
gchild.Count = (gchild.left != null ? gchild.left.Count : 0) + (gchild.right != null ? gchild.right.Count : 0) + 1;
if (node == null)
{
Debug.Assert(child == root);
root = gchild;
}
else if (child == node.left)
{
node.left = gchild;
}
else
{
Debug.Assert(child == node.right);
node.right = gchild;
}
}
/// <summary>
/// Deletes a key from the tree. If multiple elements are equal to key,
/// deletes the first or last. If no element is equal to the key,
/// returns false.
/// </summary>
/// <remarks>Top-down algorithm from Weiss. Basic plan is to move down in the tree,
/// rotating and recoloring along the way to always keep the current node red, which
/// ensures that the node we delete is red. The details are quite complex, however! </remarks>
/// <param name="key">Key to delete.</param>
/// <param name="deleteFirst">Which item to delete if multiple are equal to key. True to delete the first, false to delete last.</param>
/// <param name="item">Returns the item that was deleted, if true returned.</param>
/// <returns>True if an element was deleted, false if no element had
/// specified key.</returns>
public bool Delete(T key, bool deleteFirst, out T item)
{
return DeleteItemFromRange(EqualRangeTester(key), deleteFirst, out item);
}
///
/// <summary>
/// Enumerate all the items in-order
/// </summary>
/// <returns>An enumerator for all the items, in order.</returns>
/// <exception cref="InvalidOperationException">The tree has an item added or deleted during the enumeration.</exception>
public IEnumerator<T> GetEnumerator()
{
return EnumerateRange(EntireRangeTester).GetEnumerator();
}
/// <summary>
/// Enumerate all the items in-order
/// </summary>
/// <returns>An enumerator for all the items, in order.</returns>
/// <exception cref="InvalidOperationException">The tree has an item added or deleted during the enumeration.</exception>
System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()
{
return GetEnumerator();
}
#region Ranges
/// <summary>
/// A delegate that tests if an item is within a custom range. The range must be a contiguous
/// range of items with the ordering of this tree. The range test function must test
/// if an item is before, withing, or after the range.
/// </summary>
/// <param name="item">Item to test against the range.</param>
/// <returns>Returns negative if item is before the range, zero if item is withing the range,
/// and positive if item is after the range.</returns>
public delegate int RangeTester(T item);
/// <summary>
/// Gets a range tester that defines a range by first and last items.
/// </summary>
/// <param name="useFirst">If true, bound the range on the bottom by first.</param>
/// <param name="first">If useFirst is true, the inclusive lower bound.</param>
/// <param name="useLast">If true, bound the range on the top by last.</param>
/// <param name="last">If useLast is true, the exclusive upper bound.</param>
/// <returns>A RangeTester delegate that tests for an item in the given range.</returns>
public RangeTester BoundedRangeTester(bool useFirst, T first, bool useLast, T last)
{
return delegate(T item)
{
if (useFirst && comparer.Compare(first, item) > 0)
return -1; // item is before first.
else if (useLast && comparer.Compare(last, item) <= 0)
return 1; // item is after or equal to last.
else
return 0; // item is greater or equal to first, and less than last.
};
}
/// <summary>
/// Gets a range tester that defines a range by first and last items.
/// </summary>
/// <param name="first">The lower bound.</param>
/// <param name="firstInclusive">True if the lower bound is inclusive, false if exclusive.</param>
/// <param name="last">The upper bound.</param>
/// <param name="lastInclusive">True if the upper bound is inclusive, false if exclusive.</param>
/// <returns>A RangeTester delegate that tests for an item in the given range.</returns>
public RangeTester DoubleBoundedRangeTester(T first, bool firstInclusive, T last, bool lastInclusive)
{
return delegate(T item)
{
if (firstInclusive)
{
if (comparer.Compare(first, item) > 0)
return -1; // item is before first.
}
else
{
if (comparer.Compare(first, item) >= 0)
return -1; // item is before or equal to first.
}
if (lastInclusive)
{
if (comparer.Compare(last, item) < 0)
return 1; // item is after last.
}
else
{
if (comparer.Compare(last, item) <= 0)
return 1; // item is after or equal to last
}
return 0; // item is between first and last.
};
}
/// <summary>
/// Gets a range tester that defines a range by a lower bound.
/// </summary>
/// <param name="first">The lower bound.</param>
/// <param name="inclusive">True if the lower bound is inclusive, false if exclusive.</param>
/// <returns>A RangeTester delegate that tests for an item in the given range.</returns>
public RangeTester LowerBoundedRangeTester(T first, bool inclusive)
{
return delegate(T item)
{
if (inclusive)
{
if (comparer.Compare(first, item) > 0)
return -1; // item is before first.
else
return 0; // item is after or equal to first
}
else
{
if (comparer.Compare(first, item) >= 0)
return -1; // item is before or equal to first.
else
return 0; // item is after first
}
};
}
/// <summary>
/// Gets a range tester that defines a range by upper bound.
/// </summary>
/// <param name="last">The upper bound.</param>
/// <param name="inclusive">True if the upper bound is inclusive, false if exclusive.</param>
/// <returns>A RangeTester delegate that tests for an item in the given range.</returns>
public RangeTester UpperBoundedRangeTester(T last, bool inclusive)
{
return delegate(T item)
{
if (inclusive)
{
if (comparer.Compare(last, item) < 0)
return 1; // item is after last.
else
return 0; // item is before or equal to last.
}
else
{
if (comparer.Compare(last, item) <= 0)
return 1; // item is after or equal to last
else
return 0; // item is before last.
}
};
}
/// <summary>
/// Gets a range tester that defines a range by all items equal to an item.
/// </summary>
/// <param name="equalTo">The item that is contained in the range.</param>
/// <returns>A RangeTester delegate that tests for an item equal to <paramref name="equalTo"/>.</returns>
public RangeTester EqualRangeTester(T equalTo)
{
return delegate(T item)
{
return comparer.Compare(item, equalTo);
};
}
/// <summary>
/// A range tester that defines a range that is the entire tree.
/// </summary>
/// <param name="item">Item to test.</param>
/// <returns>Always returns 0.</returns>
public int EntireRangeTester(T item)
{
return 0;
}
/// <summary>
/// Enumerate the items in a custom range in the tree. The range is determined by
/// a RangeTest delegate.
/// </summary>
/// <param name="rangeTester">Tests an item against the custom range.</param>
/// <returns>An IEnumerable<T> that enumerates the custom range in order.</returns>
/// <exception cref="InvalidOperationException">The tree has an item added or deleted during the enumeration.</exception>
public IEnumerable<T> EnumerateRange(RangeTester rangeTester)
{
return EnumerateRangeInOrder(rangeTester, root);
}
/// <summary>
/// Enumerate all the items in a custom range, under and including node, in-order.
/// </summary>
/// <param name="rangeTester">Tests an item against the custom range.</param>
/// <param name="node">Node to begin enumeration. May be null.</param>
/// <returns>An enumerable of the items.</returns>
/// <exception cref="InvalidOperationException">The tree has an item added or deleted during the enumeration.</exception>
private IEnumerable<T> EnumerateRangeInOrder(RangeTester rangeTester, Node node)
{
int startStamp = changeStamp;
if (node != null)
{
int compare = rangeTester(node.item);
if (compare >= 0)
{
// At least part of the range may lie to the left.
foreach (T item in EnumerateRangeInOrder(rangeTester, node.left))
{
yield return item;
CheckEnumerationStamp(startStamp);
}
}
if (compare == 0)
{
// The item is within the range.
yield return node.item;
CheckEnumerationStamp(startStamp);
}
if (compare <= 0)
{
// At least part of the range lies to the right.
foreach (T item in EnumerateRangeInOrder(rangeTester, node.right))
{
yield return item;
CheckEnumerationStamp(startStamp);
}
}
}
}
/// <summary>
/// Enumerate the items in a custom range in the tree, in reversed order. The range is determined by
/// a RangeTest delegate.
/// </summary>
/// <param name="rangeTester">Tests an item against the custom range.</param>
/// <returns>An IEnumerable<T> that enumerates the custom range in reversed order.</returns>
/// <exception cref="InvalidOperationException">The tree has an item added or deleted during the enumeration.</exception>
public IEnumerable<T> EnumerateRangeReversed(RangeTester rangeTester)
{
return EnumerateRangeInReversedOrder(rangeTester, root);
}
/// <summary>
/// Enumerate all the items in a custom range, under and including node, in reversed order.
/// </summary>
/// <param name="rangeTester">Tests an item against the custom range.</param>
/// <param name="node">Node to begin enumeration. May be null.</param>
/// <returns>An enumerable of the items, in reversed oreder.</returns>
/// <exception cref="InvalidOperationException">The tree has an item added or deleted during the enumeration.</exception>
private IEnumerable<T> EnumerateRangeInReversedOrder(RangeTester rangeTester, Node node)
{
int startStamp = changeStamp;
if (node != null)
{
int compare = rangeTester(node.item);
if (compare <= 0)
{
// At least part of the range lies to the right.
foreach (T item in EnumerateRangeInReversedOrder(rangeTester, node.right))
{
yield return item;
CheckEnumerationStamp(startStamp);
}
}
if (compare == 0)
{
// The item is within the range.
yield return node.item;
CheckEnumerationStamp(startStamp);
}
if (compare >= 0)
{
// At least part of the range may lie to the left.
foreach (T item in EnumerateRangeInReversedOrder(rangeTester, node.left))
{
yield return item;
CheckEnumerationStamp(startStamp);
}
}
}
}
/// <summary>
/// Deletes either the first or last item from a range, as identified by a RangeTester
/// delegate. If the range is empty, returns false.
/// </summary>
/// <remarks>Top-down algorithm from Weiss. Basic plan is to move down in the tree,
/// rotating and recoloring along the way to always keep the current node red, which
/// ensures that the node we delete is red. The details are quite complex, however! </remarks>
/// <param name="rangeTester">Range to delete from.</param>
/// <param name="deleteFirst">If true, delete the first item from the range, else the last.</param>
/// <param name="item">Returns the item that was deleted, if true returned.</param>
/// <returns>True if an element was deleted, false if the range is empty.</returns>
public bool DeleteItemFromRange(RangeTester rangeTester, bool deleteFirst, out T item)
{
Node node; // The current node.
Node parent; // Parent of the current node.
Node gparent; // Grandparent of the current node.
Node sib; // Sibling of the current node.
Node keyNode; // Node with the key that is being removed.
// The tree may be changed.
StopEnumerations();
if (root == null)
{
// Nothing in the tree. Go home now.
item = default(T);
return false;
}
// We decrement counts on the way down the tree. If we end up not finding an item to delete
// we need a stack to adjust the counts back.
Node[] nodeStack = GetNodeStack();
int nodeStackPtr = 0; // first free item on the stack.
// Start at the root.
node = root;
sib = parent = gparent = null;
keyNode = null;
// Proceed down the tree, making the current node red so it can be removed.
for (; ; )
{
Debug.Assert(parent == null || parent.IsRed);
Debug.Assert(sib == null || !sib.IsRed);
Debug.Assert(!node.IsRed);
if ((node.left == null || !node.left.IsRed) && (node.right == null || !node.right.IsRed))
{
// node has two black children (null children are considered black).
if (parent == null)
{
// Special case for the root.
Debug.Assert(node == root);
node.IsRed = true;
}
else if ((sib.left == null || !sib.left.IsRed) && (sib.right == null || !sib.right.IsRed))
{
// sib has two black children.
node.IsRed = true;
sib.IsRed = true;
parent.IsRed = false;
}
else
{
if (parent.left == node && (sib.right == null || !sib.right.IsRed))
{
// sib has a black child on the opposite side as node.
Node tleft = sib.left;
Rotate(parent, sib, tleft);
sib = tleft;
}
else if (parent.right == node && (sib.left == null || !sib.left.IsRed))
{
// sib has a black child on the opposite side as node.
Node tright = sib.right;
Rotate(parent, sib, tright);
sib = tright;
}
// sib has a red child.
Rotate(gparent, parent, sib);
node.IsRed = true;
sib.IsRed = true;
sib.left.IsRed = false;
sib.right.IsRed = false;
sib.DecrementCount();
nodeStack[nodeStackPtr - 1] = sib;
parent.DecrementCount();
nodeStack[nodeStackPtr++] = parent;
}
}
// Compare the key and move down the tree to the correct child.
do
{
Node nextNode, nextSib; // Node we've moving to, and it's sibling.
node.DecrementCount();
nodeStack[nodeStackPtr++] = node;
// Determine which way to move in the tree by comparing the
// current item to what we're looking for.
int compare = rangeTester(node.item);
if (compare == 0)
{
// We've found the node to remove. Remember it, then keep traversing the
// tree to either find the first/last of equal keys, and if needed, the predecessor
// or successor (the actual node to be removed).
keyNode = node;
if (deleteFirst)
{
nextNode = node.left; nextSib = node.right;
}
else
{
nextNode = node.right; nextSib = node.left;
}
}
else if (compare > 0)
{
nextNode = node.left; nextSib = node.right;
}
else
{
nextNode = node.right; nextSib = node.left;
}
// Have we reached the end of our tree walk?
if (nextNode == null)
goto FINISHED;
// Move down the tree.
gparent = parent;
parent = node;
node = nextNode;
sib = nextSib;
} while (!parent.IsRed && node.IsRed);
if (!parent.IsRed)
{
Debug.Assert(!node.IsRed);
// moved to a black child.
Rotate(gparent, parent, sib);
sib.DecrementCount();
nodeStack[nodeStackPtr - 1] = sib;
parent.DecrementCount();
nodeStack[nodeStackPtr++] = parent;
sib.IsRed = false;
parent.IsRed = true;
gparent = sib;
sib = (parent.left == node) ? parent.right : parent.left;
}
}
FINISHED:
if (keyNode == null)
{
// We never found a node to delete.
// Return counts back to their previous value.
for (int i = 0; i < nodeStackPtr; ++i)
nodeStack[i].IncrementCount();
// Color the root black, in case it was colored red above.
if (root != null)
root.IsRed = false;
item = default(T);
return false;
}
// Return the item from the node we're deleting.
item = keyNode.item;
// At a leaf or a node with one child which is a leaf. Remove the node.
if (keyNode != node)
{
// The node we want to delete is interior. Move the item from the
// node we're actually deleting to the key node.
keyNode.item = node.item;
}
// If we have one child, replace the current with the child, otherwise,
// replace the current node with null.
Node replacement;
if (node.left != null)
{
replacement = node.left;
Debug.Assert(!node.IsRed && replacement.IsRed);
replacement.IsRed = false;
}
else if (node.right != null)
{
replacement = node.right;
Debug.Assert(!node.IsRed && replacement.IsRed);
replacement.IsRed = false;
}
else
replacement = null;
if (parent == null)
{
Debug.Assert(root == node);
root = replacement;
}
else if (parent.left == node)
parent.left = replacement;
else
{
Debug.Assert(parent.right == node);
parent.right = replacement;
}
// Color the root black, in case it was colored red above.
if (root != null)
root.IsRed = false;
// Update item count.
count -= 1;
// And we're done.
return true;
}
/// <summary>
/// Delete all the items in a range, identified by a RangeTester delegate.
/// </summary>
/// <param name="rangeTester">The delegate that defines the range to delete.</param>
/// <returns>The number of items deleted.</returns>
public int DeleteRange(RangeTester rangeTester)
{
bool deleted;
int counter = 0;
T dummy;
do
{
deleted = DeleteItemFromRange(rangeTester, true, out dummy);
if (deleted)
++counter;
} while (deleted);
return counter;
}
/// <summary>
/// Count the items in a custom range in the tree. The range is determined by
/// a RangeTester delegate.
/// </summary>
/// <param name="rangeTester">The delegate that defines the range.</param>
/// <returns>The number of items in the range.</returns>
public int CountRange(RangeTester rangeTester)
{
return CountRangeUnderNode(rangeTester, root, false, false);
}
/// <summary>
/// Count all the items in a custom range, under and including node.
/// </summary>
/// <param name="rangeTester">The delegate that defines the range.</param>
/// <param name="node">Node to begin enumeration. May be null.</param>
/// <param name="belowRangeTop">This node and all under it are either in the range or below it.</param>
/// <param name="aboveRangeBottom">This node and all under it are either in the range or above it.</param>
/// <returns>The number of items in the range, under and include node.</returns>
private int CountRangeUnderNode(RangeTester rangeTester, Node node, bool belowRangeTop, bool aboveRangeBottom)
{
if (node != null)
{
if (belowRangeTop && aboveRangeBottom)
{
// This node and all below it must be in the range. Use the predefined count.
return node.Count;
}
int compare = rangeTester(node.item);
int counter;
if (compare == 0)
{
counter = 1; // the node itself
counter += CountRangeUnderNode(rangeTester, node.left, true, aboveRangeBottom);
counter += CountRangeUnderNode(rangeTester, node.right, belowRangeTop, true);
}
else if (compare < 0)
{
counter = CountRangeUnderNode(rangeTester, node.right, belowRangeTop, aboveRangeBottom);
}
else
{ // compare > 0
counter = CountRangeUnderNode(rangeTester, node.left, belowRangeTop, aboveRangeBottom);
}
return counter;
}
else
{
return 0;
}
}
/// <summary>
/// Find the first item in a custom range in the tree, and it's index. The range is determined
/// by a RangeTester delegate.
/// </summary>
/// <param name="rangeTester">The delegate that defines the range.</param>
/// <param name="item">Returns the item found, if true was returned.</param>
/// <returns>Index of first item in range if range is non-empty, -1 otherwise.</returns>
public int FirstItemInRange(RangeTester rangeTester, out T item)
{
Node node = root, found = null;
int curCount = 0, foundIndex = -1;
while (node != null)
{
int compare = rangeTester(node.item);
if (compare == 0)
{
found = node;
if (node.left != null)
foundIndex = curCount + node.left.Count;
else
foundIndex = curCount;
}
if (compare >= 0)
node = node.left;
else
{
if (node.left != null)
curCount += node.left.Count + 1;
else
curCount += 1;
node = node.right;
}
}
if (found != null)
{
item = found.item;
return foundIndex;
}
else
{
item = default(T);
return -1;
}
}
/// <summary>
/// Find the last item in a custom range in the tree, and it's index. The range is determined
/// by a RangeTester delegate.
/// </summary>
/// <param name="rangeTester">The delegate that defines the range.</param>
/// <param name="item">Returns the item found, if true was returned.</param>
/// <returns>Index of the item if range is non-empty, -1 otherwise.</returns>
public int LastItemInRange(RangeTester rangeTester, out T item)
{
Node node = root, found = null;
int curCount = 0, foundIndex = -1;
while (node != null)
{
int compare = rangeTester(node.item);
if (compare == 0)
{
found = node;
if (node.left != null)
foundIndex = curCount + node.left.Count;
else
foundIndex = curCount;
}
if (compare <= 0)
{
if (node.left != null)
curCount += node.left.Count + 1;
else
curCount += 1;
node = node.right;
}
else
node = node.left;
}
if (found != null)
{
item = found.item;
return foundIndex;
}
else
{
item = default(T);
return foundIndex;
}
}
#endregion Ranges
#if DEBUG
/// <summary>
/// Prints out the tree.
/// </summary>
public void Print()
{
PrintSubTree(root, "", "");
Console.WriteLine();
}
/// <summary>
/// Prints a sub-tree.
/// </summary>
/// <param name="node">Node to print from</param>
/// <param name="prefixNode">Prefix for the node</param>
/// <param name="prefixChildren">Prefix for the node's children</param>
private void PrintSubTree(Node node, string prefixNode, string prefixChildren)
{
if (node == null)
return;
// Red nodes marked as "@@", black nodes as "..".
Console.WriteLine("{0}{1} {2,4} {3}", prefixNode, node.IsRed ? "@@" : "..", node.Count, node.item);
PrintSubTree(node.left, prefixChildren + "|-L-", prefixChildren + "| ");
PrintSubTree(node.right, prefixChildren + "|-R-", prefixChildren + " ");
}
/// <summary>
/// Validates that the tree is correctly sorted, and meets the red-black tree
/// axioms.
/// </summary>
public void Validate()
{
Debug.Assert(comparer != null, "Comparer should not be null");
if (root == null)
{
Debug.Assert(0 == count, "Count in empty tree should be 0.");
}
else
{
Debug.Assert(!root.IsRed, "Root is not black");
int blackHeight;
int nodeCount = ValidateSubTree(root, out blackHeight);
Debug.Assert(nodeCount == this.count, "Node count of tree is not correct.");
}
}
/// <summary>
/// Validates a sub-tree and returns the count and black height.
/// </summary>
/// <param name="node">Sub-tree to validate. May be null.</param>
/// <param name="blackHeight">Returns the black height of the tree.</param>
/// <returns>Returns the number of nodes in the sub-tree. 0 if node is null.</returns>
private int ValidateSubTree(Node node, out int blackHeight)
{
if (node == null)
{
blackHeight = 0;
return 0;
}
// Check that this node is sorted with respect to any children.
if (node.left != null)
Debug.Assert(comparer.Compare(node.left.item, node.item) <= 0, "Left child is not less than or equal to node");
if (node.right != null)
Debug.Assert(comparer.Compare(node.right.item, node.item) >= 0, "Right child is not greater than or equal to node");
// Check that the two-red rule is not violated.
if (node.IsRed)
{
if (node.left != null)
Debug.Assert(!node.left.IsRed, "Node and left child both red");
if (node.right != null)
Debug.Assert(!node.right.IsRed, "Node and right child both red");
}
// Validate sub-trees and get their size and heights.
int leftCount, leftBlackHeight;
int rightCount, rightBlackHeight;
int ourCount;
leftCount = ValidateSubTree(node.left, out leftBlackHeight);
rightCount = ValidateSubTree(node.right, out rightBlackHeight);
ourCount = leftCount + rightCount + 1;
Debug.Assert(ourCount == node.Count);
// Validate the equal black-height rule.
Debug.Assert(leftBlackHeight == rightBlackHeight, "Black heights are not equal");
// Calculate our black height and return the count
blackHeight = leftBlackHeight;
if (!node.IsRed)
blackHeight += 1;
return ourCount;
}
#endif //DEBUG
}
}
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