/// <summary>
/// Finds the node whose key is immediately less than <paramref name="node"/>.
/// </summary>
/// <param name="node">Node to find the predecessor of</param>
/// <returns>Predecessor of <paramref name="node"/></returns>
private static IntervalTreeNode <K, V> PredecessorOf(IntervalTreeNode <K, V> node)
{
if (node.Left != null)
{
return(Maximum(node.Left));
}
IntervalTreeNode <K, V> parent = node.Parent;
while (parent != null && node == parent.Left)
{
node = parent;
parent = parent.Parent;
}
return(parent);
}
/// <summary>
/// Removes the value from the dictionary after searching for it with <paramref name="key">.
/// </summary>
/// <param name="key">Tree node to be removed</param>
private void Delete(IntervalTreeNode <K, V> nodeToDelete)
{
IntervalTreeNode <K, V> replacementNode;
if (LeftOf(nodeToDelete) == null || RightOf(nodeToDelete) == null)
{
replacementNode = nodeToDelete;
}
else
{
replacementNode = PredecessorOf(nodeToDelete);
}
IntervalTreeNode <K, V> tmp = LeftOf(replacementNode) ?? RightOf(replacementNode);
if (tmp != null)
{
tmp.Parent = ParentOf(replacementNode);
}
if (ParentOf(replacementNode) == null)
{
_root = tmp;
}
else if (replacementNode == LeftOf(ParentOf(replacementNode)))
{
ParentOf(replacementNode).Left = tmp;
}
else
{
ParentOf(replacementNode).Right = tmp;
}
if (replacementNode != nodeToDelete)
{
nodeToDelete.Start = replacementNode.Start;
nodeToDelete.Value = replacementNode.Value;
nodeToDelete.End = replacementNode.End;
nodeToDelete.Max = replacementNode.Max;
}
PropagateFull(replacementNode);
if (tmp != null && ColorOf(replacementNode) == Black)
{
RestoreBalanceAfterRemoval(tmp);
}
}
/// <summary>
/// Propagate an increase in max value starting at the given node, heading up the tree.
/// This should only be called if the max increases - not for rebalancing or removals.
/// </summary>
/// <param name="node">The node to start propagating from</param>
private void PropagateIncrease(IntervalTreeNode <K, V> node)
{
K max = node.Max;
IntervalTreeNode <K, V> ptr = node;
while ((ptr = ptr.Parent) != null)
{
if (max.CompareTo(ptr.Max) > 0)
{
ptr.Max = max;
}
else
{
break;
}
}
}
/// <summary>
/// Propagate recalculating max value starting at the given node, heading up the tree.
/// This fully recalculates the max value from all children when there is potential for it to decrease.
/// </summary>
/// <param name="node">The node to start propagating from</param>
private void PropagateFull(IntervalTreeNode <K, V> node)
{
IntervalTreeNode <K, V> ptr = node;
do
{
K max = ptr.End;
if (ptr.Left != null && ptr.Left.Max.CompareTo(max) > 0)
{
max = ptr.Left.Max;
}
if (ptr.Right != null && ptr.Right.Max.CompareTo(max) > 0)
{
max = ptr.Right.Max;
}
ptr.Max = max;
} while ((ptr = ptr.Parent) != null);
}
public void Clear()
{
_root = null;
_count = 0;
}
/// <summary>
/// Returns the parent node of <paramref name="node"/>, or null if <paramref name="node"/> is null.
/// </summary>
/// <param name="node">Node to retrieve the parent from</param>
/// <returns>Parent of <paramref name="node"/></returns>
private static IntervalTreeNode <K, V> ParentOf(IntervalTreeNode <K, V> node)
{
return(node?.Parent);
}
/// <summary>
/// This method returns the right node of <paramref name="node"/>, or null if <paramref name="node"/> is null.
/// </summary>
/// <param name="node">Node to retrieve the right child from</param>
/// <returns>Right child of <paramref name="node"/></returns>
private static IntervalTreeNode <K, V> RightOf(IntervalTreeNode <K, V> node)
{
return(node?.Right);
}
/// <summary>
/// This method returns the left node of <paramref name="node"/>, or null if <paramref name="node"/> is null.
/// </summary>
/// <param name="node">Node to retrieve the left child from</param>
/// <returns>Left child of <paramref name="node"/></returns>
private static IntervalTreeNode <K, V> LeftOf(IntervalTreeNode <K, V> node)
{
return(node?.Left);
}
// These methods save memory by allowing us to forego sentinel nil nodes, as well as serve as protection against NullReferenceExceptions.
/// <summary>
/// Returns the color of <paramref name="node"/>, or Black if it is null.
/// </summary>
/// <param name="node">Node</param>
/// <returns>The boolean color of <paramref name="node"/>, or black if null</returns>
private static bool ColorOf(IntervalTreeNode <K, V> node)
{
return(node == null || node.Color);
}
private void RestoreBalanceAfterRemoval(IntervalTreeNode <K, V> balanceNode)
{
IntervalTreeNode <K, V> ptr = balanceNode;
while (ptr != _root && ColorOf(ptr) == Black)
{
if (ptr == LeftOf(ParentOf(ptr)))
{
IntervalTreeNode <K, V> sibling = RightOf(ParentOf(ptr));
if (ColorOf(sibling) == Red)
{
SetColor(sibling, Black);
SetColor(ParentOf(ptr), Red);
RotateLeft(ParentOf(ptr));
sibling = RightOf(ParentOf(ptr));
}
if (ColorOf(LeftOf(sibling)) == Black && ColorOf(RightOf(sibling)) == Black)
{
SetColor(sibling, Red);
ptr = ParentOf(ptr);
}
else
{
if (ColorOf(RightOf(sibling)) == Black)
{
SetColor(LeftOf(sibling), Black);
SetColor(sibling, Red);
RotateRight(sibling);
sibling = RightOf(ParentOf(ptr));
}
SetColor(sibling, ColorOf(ParentOf(ptr)));
SetColor(ParentOf(ptr), Black);
SetColor(RightOf(sibling), Black);
RotateLeft(ParentOf(ptr));
ptr = _root;
}
}
else
{
IntervalTreeNode <K, V> sibling = LeftOf(ParentOf(ptr));
if (ColorOf(sibling) == Red)
{
SetColor(sibling, Black);
SetColor(ParentOf(ptr), Red);
RotateRight(ParentOf(ptr));
sibling = LeftOf(ParentOf(ptr));
}
if (ColorOf(RightOf(sibling)) == Black && ColorOf(LeftOf(sibling)) == Black)
{
SetColor(sibling, Red);
ptr = ParentOf(ptr);
}
else
{
if (ColorOf(LeftOf(sibling)) == Black)
{
SetColor(RightOf(sibling), Black);
SetColor(sibling, Red);
RotateLeft(sibling);
sibling = LeftOf(ParentOf(ptr));
}
SetColor(sibling, ColorOf(ParentOf(ptr)));
SetColor(ParentOf(ptr), Black);
SetColor(LeftOf(sibling), Black);
RotateRight(ParentOf(ptr));
ptr = _root;
}
}
}
SetColor(ptr, Black);
}
/// <summary>
/// Insertion Mechanism for the interval tree. Similar to a BST insert, with the start of the range as the key.
/// Iterates the tree starting from the root and inserts a new node where all children in the left subtree are less than <paramref name="start"/>, and all children in the right subtree are greater than <paramref name="start"/>.
/// Each node can contain multiple values, and has an end address which is the maximum of all those values.
/// Post insertion, the "max" value of the node and all parents are updated.
/// </summary>
/// <param name="start">Start of the range to insert</param>
/// <param name="end">End of the range to insert</param>
/// <param name="value">Value to insert</param>
/// <param name="updateFactoryCallback">Optional factory used to create a new value if <paramref name="start"/> is already on the tree</param>
/// <param name="outNode">Node that was inserted or modified</param>
/// <returns>True if <paramref name="start"/> was not yet on the tree, false otherwise</returns>
private bool BSTInsert(K start, K end, V value, Func <K, V, V> updateFactoryCallback, out IntervalTreeNode <K, V> outNode)
{
IntervalTreeNode <K, V> parent = null;
IntervalTreeNode <K, V> node = _root;
while (node != null)
{
parent = node;
int cmp = start.CompareTo(node.Start);
if (cmp < 0)
{
node = node.Left;
}
else if (cmp > 0)
{
node = node.Right;
}
else
{
outNode = node;
if (updateFactoryCallback != null)
{
// Replace
node.Value = updateFactoryCallback(start, node.Value);
int endCmp = end.CompareTo(node.End);
if (endCmp > 0)
{
node.End = end;
if (end.CompareTo(node.Max) > 0)
{
node.Max = end;
PropagateIncrease(node);
RestoreBalanceAfterInsertion(node);
}
}
else if (endCmp < 0)
{
node.End = end;
PropagateFull(node);
}
}
return(false);
}
}
IntervalTreeNode <K, V> newNode = new IntervalTreeNode <K, V>(start, end, value, parent);
if (newNode.Parent == null)
{
_root = newNode;
}
else if (start.CompareTo(parent.Start) < 0)
{
parent.Left = newNode;
}
else
{
parent.Right = newNode;
}
PropagateIncrease(newNode);
_count++;
RestoreBalanceAfterInsertion(newNode);
outNode = newNode;
return(true);
}