It's not easy to find red-black tree implementations on the net, especially for learning.
Where can I find a simple red-black tree implementation (C# preferred)?
Generic red-black trees aren't "simple" by default.
But if you put a small restriction on them and make them "left-leaning", then they become simpler.
Take a look at this MSDN blog post.
I've copy-pasted (with slight modifications) the code from that post here (in C#):
using System;
using System.Collections.Generic;
using System.Diagnostics;
/// <summary>Implements a left-leaning red-black tree.</summary>
/// <remarks>
/// Based on the research paper "Left-leaning Red-Black Trees"
/// by Robert Sedgewick. More information available at:
/// http://www.cs.princeton.edu/~rs/talks/LLRB/RedBlack.pdf
/// http://www.cs.princeton.edu/~rs/talks/LLRB/08Penn.pdf
/// </remarks>
/// <typeparam name="TKey">Type of keys.</typeparam>
/// <typeparam name="TValue">Type of values.</typeparam>
public class LeftLeaningRedBlackTree<TKey, TValue>
{
/// <summary>Stores the key comparison function.</summary>
private Comparison<TKey> _keyComparison;
/// <summary>Stores the value comparison function.</summary>
private Comparison<TValue> _valueComparison;
/// <summary>Stores the root node of the tree.</summary>
private Node _rootNode;
/// <summary>Represents a node of the tree.</summary>
/// <remarks>Using fields instead of properties drops execution time by about 40%.</remarks>
[DebuggerDisplay("Key={Key}, Value={Value}, Siblings={Siblings}")]
private class Node
{
/// <summary>Gets or sets the node's key.</summary>
public TKey Key;
/// <summary>Gets or sets the node's value.</summary>
public TValue Value;
/// <summary>Gets or sets the left node.</summary>
public Node Left;
/// <summary>Gets or sets the right node.</summary>
public Node Right;
/// <summary>Gets or sets the color of the node.</summary>
public bool IsBlack;
/// <summary>Gets or sets the number of "siblings" (nodes with the same key/value).</summary>
public int Siblings;
}
/// <summary>Initializes a new instance of the LeftLeaningRedBlackTree class implementing a normal dictionary.</summary>
/// <param name="keyComparison">The key comparison function.</param>
public LeftLeaningRedBlackTree(Comparison<TKey> keyComparison)
{
if (null == keyComparison)
{
throw new ArgumentNullException("keyComparison");
}
_keyComparison = keyComparison;
}
/// <summary>Initializes a new instance of the LeftLeaningRedBlackTree class implementing an ordered multi-dictionary.</summary>
/// <param name="keyComparison">The key comparison function.</param>
/// <param name="valueComparison">The value comparison function.</param>
public LeftLeaningRedBlackTree(Comparison<TKey> keyComparison, Comparison<TValue> valueComparison)
: this(keyComparison)
{
if (null == valueComparison)
{
throw new ArgumentNullException("valueComparison");
}
_valueComparison = valueComparison;
}
/// <summary>Gets a value indicating whether the tree is acting as an ordered multi-dictionary.</summary>
private bool IsMultiDictionary
{
get { return null != _valueComparison; }
}
/// <summary>Adds a key/value pair to the tree.</summary>
/// <param name="key">Key to add.</param>
/// <param name="value">Value to add.</param>
public void Add(TKey key, TValue value)
{
_rootNode = Add(_rootNode, key, value);
_rootNode.IsBlack = true;
AssertInvariants();
}
/// <summary>Removes a key (and its associated value) from a normal (non-multi) dictionary.</summary>
/// <param name="key">Key to remove.</param>
/// <returns>True if key present and removed.</returns>
public bool Remove(TKey key)
{
if (IsMultiDictionary)
{
throw new InvalidOperationException("Remove is only supported when acting as a normal (non-multi) dictionary.");
}
return Remove(key, default(TValue));
}
/// <summary>Removes a key/value pair from the tree.</summary>
/// <param name="key">Key to remove.</param>
/// <param name="value">Value to remove.</param>
/// <returns>True if key/value present and removed.</returns>
public bool Remove(TKey key, TValue value)
{
int initialCount = Count;
if (null != _rootNode)
{
_rootNode = Remove(_rootNode, key, value);
if (null != _rootNode)
{
_rootNode.IsBlack = true;
}
}
AssertInvariants();
return initialCount != Count;
}
/// <summary>Removes all nodes in the tree.</summary>
public void Clear()
{
_rootNode = null;
Count = 0;
AssertInvariants();
}
/// <summary>Gets a sorted list of keys in the tree.</summary>
/// <returns>Sorted list of keys.</returns>
public IEnumerable<TKey> GetKeys()
{
TKey lastKey = default(TKey);
bool lastKeyValid = false;
return Traverse(
_rootNode,
n => !lastKeyValid || !object.Equals(lastKey, n.Key),
n =>
{
lastKey = n.Key;
lastKeyValid = true;
return lastKey;
});
}
/// <summary>Gets the value associated with the specified key in a normal (non-multi) dictionary.</summary>
/// <param name="key">Specified key.</param>
/// <returns>Value associated with the specified key.</returns>
public TValue GetValueForKey(TKey key)
{
if (IsMultiDictionary)
{
throw new InvalidOperationException("GetValueForKey is only supported when acting as a normal (non-multi) dictionary.");
}
Node node = GetNodeForKey(key);
if (null != node)
{
return node.Value;
}
else
{
throw new KeyNotFoundException();
}
}
/// <summary>Gets a sequence of the values associated with the specified key.</summary>
/// <param name="key">Specified key.</param>
/// <returns>Sequence of values.</returns>
public IEnumerable<TValue> GetValuesForKey(TKey key)
{
return Traverse(GetNodeForKey(key), n => 0 == _keyComparison(n.Key, key), n => n.Value);
}
/// <summary>Gets a sequence of all the values in the tree.</summary>
/// <returns>Sequence of all values.</returns>
public IEnumerable<TValue> GetValuesForAllKeys()
{
return Traverse(_rootNode, n => true, n => n.Value);
}
/// <summary>Gets the count of key/value pairs in the tree.</summary>
public int Count { get; private set; }
/// <summary>Gets the minimum key in the tree.</summary>
public TKey MinimumKey
{
get { return GetExtreme(_rootNode, n => n.Left, n => n.Key); }
}
/// <summary>Gets the maximum key in the tree.</summary>
public TKey MaximumKey
{
get { return GetExtreme(_rootNode, n => n.Right, n => n.Key); }
}
/// <summary>Returns true if the specified node is red.</summary>
/// <param name="node">Specified node.</param>
/// <returns>True if specified node is red.</returns>
private static bool IsRed(Node node)
{
if (null == node)
{
// "Virtual" leaf nodes are always black
return false;
}
return !node.IsBlack;
}
/// <summary>Adds the specified key/value pair below the specified root node.</summary>
/// <param name="node">Specified node.</param>
/// <param name="key">Key to add.</param>
/// <param name="value">Value to add.</param>
/// <returns>New root node.</returns>
private Node Add(Node node, TKey key, TValue value)
{
if (null == node)
{
// Insert new node
Count++;
return new Node { Key = key, Value = value };
}
if (IsRed(node.Left) && IsRed(node.Right))
{
// Split node with two red children
FlipColor(node);
}
// Find right place for new node
int comparisonResult = KeyAndValueComparison(key, value, node.Key, node.Value);
if (comparisonResult < 0)
{
node.Left = Add(node.Left, key, value);
}
else if (0 < comparisonResult)
{
node.Right = Add(node.Right, key, value);
}
else
{
if (IsMultiDictionary)
{
// Store the presence of a "duplicate" node
node.Siblings++;
Count++;
}
else
{
// Replace the value of the existing node
node.Value = value;
}
}
if (IsRed(node.Right))
{
// Rotate to prevent red node on right
node = RotateLeft(node);
}
if (IsRed(node.Left) && IsRed(node.Left.Left))
{
// Rotate to prevent consecutive red nodes
node = RotateRight(node);
}
return node;
}
/// <summary>Removes the specified key/value pair from below the specified node.</summary>
/// <param name="node">Specified node.</param>
/// <param name="key">Key to remove.</param>
/// <param name="value">Value to remove.</param>
/// <returns>True if key/value present and removed.</returns>
private Node Remove(Node node, TKey key, TValue value)
{
int comparisonResult = KeyAndValueComparison(key, value, node.Key, node.Value);
if (comparisonResult < 0)
{
// * Continue search if left is present
if (null != node.Left)
{
if (!IsRed(node.Left) && !IsRed(node.Left.Left))
{
// Move a red node over
node = MoveRedLeft(node);
}
// Remove from left
node.Left = Remove(node.Left, key, value);
}
}
else
{
if (IsRed(node.Left))
{
// Flip a 3 node or unbalance a 4 node
node = RotateRight(node);
}
if ((0 == KeyAndValueComparison(key, value, node.Key, node.Value)) && (null == node.Right))
{
// Remove leaf node
Debug.Assert(null == node.Left, "About to remove an extra node.");
Count--;
if (0 < node.Siblings)
{
// Record the removal of the "duplicate" node
Debug.Assert(IsMultiDictionary, "Should not have siblings if tree is not a multi-dictionary.");
node.Siblings--;
return node;
}
else
{
// Leaf node is gone
return null;
}
}
// * Continue search if right is present
if (null != node.Right)
{
if (!IsRed(node.Right) && !IsRed(node.Right.Left))
{
// Move a red node over
node = MoveRedRight(node);
}
if (0 == KeyAndValueComparison(key, value, node.Key, node.Value))
{
// Remove leaf node
Count--;
if (0 < node.Siblings)
{
// Record the removal of the "duplicate" node
Debug.Assert(IsMultiDictionary, "Should not have siblings if tree is not a multi-dictionary.");
node.Siblings--;
}
else
{
// Find the smallest node on the right, swap, and remove it
Node m = GetExtreme(node.Right, n => n.Left, n => n);
node.Key = m.Key;
node.Value = m.Value;
node.Siblings = m.Siblings;
node.Right = DeleteMinimum(node.Right);
}
}
else
{
// Remove from right
node.Right = Remove(node.Right, key, value);
}
}
}
// Maintain invariants
return FixUp(node);
}
/// <summary>Flip the colors of the specified node and its direct children.</summary>
/// <param name="node">Specified node.</param>
private static void FlipColor(Node node)
{
node.IsBlack = !node.IsBlack;
node.Left.IsBlack = !node.Left.IsBlack;
node.Right.IsBlack = !node.Right.IsBlack;
}
/// <summary>Rotate the specified node "left".</summary>
/// <param name="node">Specified node.</param>
/// <returns>New root node.</returns>
private static Node RotateLeft(Node node)
{
Node x = node.Right;
node.Right = x.Left;
x.Left = node;
x.IsBlack = node.IsBlack;
node.IsBlack = false;
return x;
}
/// <summary>Rotate the specified node "right".</summary>
/// <param name="node">Specified node.</param>
/// <returns>New root node.</returns>
private static Node RotateRight(Node node)
{
Node x = node.Left;
node.Left = x.Right;
x.Right = node;
x.IsBlack = node.IsBlack;
node.IsBlack = false;
return x;
}
/// <summary>Moves a red node from the right child to the left child.</summary>
/// <param name="node">Parent node.</param>
/// <returns>New root node.</returns>
private static Node MoveRedLeft(Node node)
{
FlipColor(node);
if (IsRed(node.Right.Left))
{
node.Right = RotateRight(node.Right);
node = RotateLeft(node);
FlipColor(node);
// * Avoid creating right-leaning nodes
if (IsRed(node.Right.Right))
{
node.Right = RotateLeft(node.Right);
}
}
return node;
}
/// <summary>Moves a red node from the left child to the right child.</summary>
/// <param name="node">Parent node.</param>
/// <returns>New root node.</returns>
private static Node MoveRedRight(Node node)
{
FlipColor(node);
if (IsRed(node.Left.Left))
{
node = RotateRight(node);
FlipColor(node);
}
return node;
}
/// <summary>Deletes the minimum node under the specified node.</summary>
/// <param name="node">Specified node.</param>
/// <returns>New root node.</returns>
private Node DeleteMinimum(Node node)
{
if (null == node.Left)
{
// Nothing to do
return null;
}
if (!IsRed(node.Left) && !IsRed(node.Left.Left))
{
// Move red node left
node = MoveRedLeft(node);
}
// Recursively delete
node.Left = DeleteMinimum(node.Left);
// Maintain invariants
return FixUp(node);
}
/// <summary>Maintains invariants by adjusting the specified nodes children.</summary>
/// <param name="node">Specified node.</param>
/// <returns>New root node.</returns>
private static Node FixUp(Node node)
{
if (IsRed(node.Right))
{
// Avoid right-leaning node
node = RotateLeft(node);
}
if (IsRed(node.Left) && IsRed(node.Left.Left))
{
// Balance 4-node
node = RotateRight(node);
}
if (IsRed(node.Left) && IsRed(node.Right))
{
// Push red up
FlipColor(node);
}
// * Avoid leaving behind right-leaning nodes
if ((null != node.Left) && IsRed(node.Left.Right) && !IsRed(node.Left.Left))
{
node.Left = RotateLeft(node.Left);
if (IsRed(node.Left))
{
// Balance 4-node
node = RotateRight(node);
}
}
return node;
}
/// <summary>Gets the (first) node corresponding to the specified key.</summary>
/// <param name="key">Key to search for.</param>
/// <returns>Corresponding node or null if none found.</returns>
private Node GetNodeForKey(TKey key)
{
// Initialize
Node node = _rootNode;
while (null != node)
{
// Compare keys and go left/right
int comparisonResult = _keyComparison(key, node.Key);
if (comparisonResult < 0)
{
node = node.Left;
}
else if (0 < comparisonResult)
{
node = node.Right;
}
else
{
// Match; return node
return node;
}
}
// No match found
return null;
}
/// <summary>Gets an extreme (ex: minimum/maximum) value.</summary>
/// <typeparam name="T">Type of value.</typeparam>
/// <param name="node">Node to start from.</param>
/// <param name="successor">Successor function.</param>
/// <param name="selector">Selector function.</param>
/// <returns>Extreme value.</returns>
private static T GetExtreme<T>(Node node, Func<Node, Node> successor, Func<Node, T> selector)
{
// Initialize
T extreme = default(T);
Node current = node;
while (null != current)
{
// Go to extreme
extreme = selector(current);
current = successor(current);
}
return extreme;
}
/// <summary>Traverses a subset of the sequence of nodes in order and selects the specified nodes.</summary>
/// <typeparam name="T">Type of elements.</typeparam>
/// <param name="node">Starting node.</param>
/// <param name="condition">Condition method.</param>
/// <param name="selector">Selector method.</param>
/// <returns>Sequence of selected nodes.</returns>
private IEnumerable<T> Traverse<T>(Node node, Func<Node, bool> condition, Func<Node, T> selector)
{
// Create a stack to avoid recursion
Stack<Node> stack = new Stack<Node>();
Node current = node;
while (null != current)
{
if (null != current.Left)
{
// Save current state and go left
stack.Push(current);
current = current.Left;
}
else
{
do
{
for (int i = 0; i <= current.Siblings; i++)
{
// Select current node if relevant
if (condition(current))
{
yield return selector(current);
}
}
// Go right - or up if nothing to the right
current = current.Right;
}
while ((null == current) &&
(0 < stack.Count) &&
(null != (current = stack.Pop())));
}
}
}
/// <summary>Compares the specified keys (primary) and values (secondary).</summary>
/// <param name="leftKey">The left key.</param>
/// <param name="leftValue">The left value.</param>
/// <param name="rightKey">The right key.</param>
/// <param name="rightValue">The right value.</param>
/// <returns>CompareTo-style results: -1 if left is less, 0 if equal, and 1 if greater than right.</returns>
private int KeyAndValueComparison(TKey leftKey, TValue leftValue, TKey rightKey, TValue rightValue)
{
// Compare keys
int comparisonResult = _keyComparison(leftKey, rightKey);
if ((0 == comparisonResult) && (null != _valueComparison))
{
// Keys match; compare values
comparisonResult = _valueComparison(leftValue, rightValue);
}
return comparisonResult;
}
/// <summary>Asserts that tree invariants are not violated.</summary>
[Conditional("Debug")]
private void AssertInvariants()
{
// Root is black
Debug.Assert((null == _rootNode) || _rootNode.IsBlack, "Root is not black");
// Every path contains the same number of black nodes
Dictionary<Node, Node> parents = new Dictionary<LeftLeaningRedBlackTree<TKey, TValue>.Node, LeftLeaningRedBlackTree<TKey, TValue>.Node>();
foreach (Node node in Traverse(_rootNode, n => true, n => n))
{
if (null != node.Left)
{
parents[node.Left] = node;
}
if (null != node.Right)
{
parents[node.Right] = node;
}
}
if (null != _rootNode)
{
parents[_rootNode] = null;
}
int treeCount = -1;
foreach (Node node in Traverse(_rootNode, n => (null == n.Left) || (null == n.Right), n => n))
{
int pathCount = 0;
Node current = node;
while (null != current)
{
if (current.IsBlack)
{
pathCount++;
}
current = parents[current];
}
Debug.Assert((-1 == treeCount) || (pathCount == treeCount), "Not all paths have the same number of black nodes.");
treeCount = pathCount;
}
// Verify node properties...
foreach (Node node in Traverse(_rootNode, n => true, n => n))
{
// Left node is less
if (null != node.Left)
{
Debug.Assert(0 > KeyAndValueComparison(node.Left.Key, node.Left.Value, node.Key, node.Value), "Left node is greater than its parent.");
}
// Right node is greater
if (null != node.Right)
{
Debug.Assert(0 < KeyAndValueComparison(node.Right.Key, node.Right.Value, node.Key, node.Value), "Right node is less than its parent.");
}
// Both children of a red node are black
Debug.Assert(!IsRed(node) || (!IsRed(node.Left) && !IsRed(node.Right)), "Red node has a red child.");
// Always left-leaning
Debug.Assert(!IsRed(node.Right) || IsRed(node.Left), "Node is not left-leaning.");
// No consecutive reds (subset of previous rule)
//Debug.Assert(!(IsRed(node) && IsRed(node.Left)));
}
}
}