/// <summary>
/// Recursively descends down the tree and adds valids results to the resultset
/// </summary>
/// <param name="node">subtree to be searched</param>
/// <param name="val">value to be searched for</param>
/// <param name="result">current resultset</param>
private void SearchSubtree(IntervalNode <T> node, T val, List <Interval <T> > result)
{
if (node == Sentinel)
{
return;
}
// Value is higher than any interval in this subtree
if (val.CompareTo(node.MaxEnd) > 0)
{
return;
}
if (node.Left != Sentinel)
{
SearchSubtree(node.Left, val, result);
}
if (node.Interval.Contains(val))
{
result.Add(node.Interval);
}
if (val.CompareTo(node.Interval.Start) < 0)
{
return;
}
if (node.Right != Sentinel)
{
SearchSubtree(node.Right, val, result);
}
}
public IntervalTree()
{
this.head = new IntervalNode <T, D>();
this.intervalList = new List <Interval <T, D> >();
this.inSync = true;
this.size = 0;
}
public IntervalTree()
{
Root = Sentinel;
Root.Left = Sentinel;
Root.Right = Sentinel;
Root.Parent = Sentinel;
}
private IntervalNode <T> FindInterval(IntervalNode <T> tree, Interval <T> i)
{
while (tree != Sentinel)
{
if (tree.Interval.CompareTo(i) > 0)
{
tree = tree.Left;
continue;
}
if (tree.Interval.CompareTo(i) < 0)
{
tree = tree.Right;
continue;
}
if (tree.Interval.CompareTo(i) == 0)
{
return(tree);
}
}
return(Sentinel);
}
/// <summary>
/// General left rotation
/// </summary>
/// <param name="node">top of rotated subtree</param>
private void RotateLeft(IntervalNode <T> node)
{
var pivot = node.Right;
NodeDirection dir = node.ParentDirection;
var parent = node.Parent;
var tempTree = pivot.Left;
pivot.Left = node;
node.Parent = pivot;
node.Right = tempTree;
if (tempTree != Sentinel)
{
tempTree.Parent = node;
}
if (dir == NodeDirection.LEFT)
{
parent.Right = pivot;
}
else if (dir == NodeDirection.RIGHT)
{
parent.Left = pivot;
}
else
{
Root = pivot;
}
pivot.Parent = parent;
pivot.RecalculateMaxEnd();
node.RecalculateMaxEnd();
}
public IntervalNode()
{
intervals = new OrderedDictionary <Interval <T, D>, List <Interval <T, D> > >();
center = default(D);
leftNode = null;
rightNode = null;
}
private void RemoveNode(IntervalNode <T> node)
{
if (node == Sentinel)
{
return;
}
IntervalNode <T> temp = node;
if (node.Right != Sentinel && node.Left != Sentinel)
{
// Trick when deleting node with both children, switch it with closest in order node
// swap values and delete the bottom node converting it to other cases
temp = node.GetSuccessor();
node.Interval = temp.Interval;
node.RecalculateMaxEnd();
while (node.Parent != Sentinel)
{
node = node.Parent;
node.RecalculateMaxEnd();
}
}
node = temp;
temp = node.Left != Sentinel ? node.Left : node.Right;
// we will replace node with temp and delete node
temp.Parent = node.Parent;
if (node.IsRoot)
{
Root = temp; // Set new root
}
else
{
// Reattach node to parent
if (node.ParentDirection == NodeDirection.RIGHT)
{
node.Parent.Left = temp;
}
else
{
node.Parent.Right = temp;
}
IntervalNode <T> maxAux = node.Parent;
maxAux.RecalculateMaxEnd();
while (maxAux.Parent != Sentinel)
{
maxAux = maxAux.Parent;
maxAux.RecalculateMaxEnd();
}
}
if (node.Color == NodeColor.BLACK)
{
RenewConstraintsAfterDelete(temp);
}
}
public IntervalTree(List <Interval <T, D> > intervalList)
{
this.head = new IntervalNode <T, D>(intervalList);
this.intervalList = new List <Interval <T, D> >();
this.intervalList.AddRange(intervalList);
this.inSync = true;
this.size = intervalList.Count;
}
/// <summary>
/// Finds the min.
/// </summary>
/// <param name="node">The node.</param>
/// <returns></returns>
public static IntervalNode FindMin(IntervalNode node)
{
while (node != null && node.Left != null)
{
node = node.Left;
}
return(node);
}
/// <summary>
/// Finds the max.
/// </summary>
/// <param name="node">The node.</param>
/// <returns></returns>
public static IntervalNode FindMax(IntervalNode node)
{
while (node != null && node.Right != null)
{
node = node.Right;
}
return(node);
}
/// <summary>
/// Adds the specified arg.
/// </summary>
/// <param name="arg">The arg.</param>
public void Add(KeyValuePair <IInterval <T>, TypeValue> arg)
{
bool wasAdded = false;
bool wasSuccessful = false;
this.Root = IntervalNode.Add(this.Root, arg, ref wasAdded, ref wasSuccessful);
IntervalNode.ComputeMax(this.Root);
}
public void Build()
{
if (!inSync)
{
head = new IntervalNode <T, D>(intervalList);
inSync = true;
size = intervalList.Count;
}
}
/// <summary>
/// Validates and applies RB-tree constaints to node
/// </summary>
/// <param name="node">node to be validated and fixed</param>
private void RenewConstraintsAfterInsert(IntervalNode <T> node)
{
if (node.Parent == Sentinel)
{
return;
}
if (node.Parent.Color == NodeColor.BLACK)
{
return;
}
var uncle = node.Uncle;
if (uncle != Sentinel && uncle.Color == NodeColor.RED)
{
node.Parent.Color = uncle.Color = NodeColor.BLACK;
var gparent = node.GrandParent;
if (gparent != Sentinel && !gparent.IsRoot)
{
gparent.Color = NodeColor.RED;
RenewConstraintsAfterInsert(gparent);
}
}
else
{
if (node.ParentDirection == NodeDirection.LEFT && node.Parent.ParentDirection == NodeDirection.RIGHT)
{
RotateLeft(node.Parent);
node = node.Left;
}
else if (node.ParentDirection == NodeDirection.RIGHT && node.Parent.ParentDirection == NodeDirection.LEFT)
{
RotateRight(node.Parent);
node = node.Right;
}
node.Parent.Color = NodeColor.BLACK;
if (node.GrandParent == Sentinel)
{
return;
}
node.GrandParent.Color = NodeColor.RED;
if (node.ParentDirection == NodeDirection.RIGHT)
{
RotateRight(node.GrandParent);
}
else
{
RotateLeft(node.GrandParent);
}
}
}
/// <summary>
/// Insert new interval to interval tree
/// </summary>
/// <param name="interval">interval to add</param>
public void Add(Interval <T> interval)
{
var node = new IntervalNode <T>(interval);
if (Root == Sentinel)
{
node.Color = NodeColor.BLACK;
Root = node;
}
else
{
InsertInterval(interval, Root);
}
}
public IntervalNode(List <Interval <T, D> > intervalList)
{
intervals = new OrderedDictionary <Interval <T, D>, List <Interval <T, D> > >();
var endpoints = new OrderedSet <D>();
foreach (var interval in intervalList)
{
endpoints.Add(interval.Start);
endpoints.Add(interval.End);
}
Nullable <D> median = GetMedian(endpoints);
center = median.GetValueOrDefault();
List <Interval <T, D> > left = new List <Interval <T, D> >();
List <Interval <T, D> > right = new List <Interval <T, D> >();
foreach (Interval <T, D> interval in intervalList)
{
if (interval.End.CompareTo(center) < 0)
{
left.Add(interval);
}
else if (interval.Start.CompareTo(center) > 0)
{
right.Add(interval);
}
else
{
List <Interval <T, D> > posting;
if (!intervals.TryGetValue(interval, out posting))
{
posting = new List <Interval <T, D> >();
intervals.Add(interval, posting);
}
posting.Add(interval);
}
}
if (left.Count > 0)
{
leftNode = new IntervalNode <T, D>(left);
}
if (right.Count > 0)
{
rightNode = new IntervalNode <T, D>(right);
}
}
/// <summary>
/// Deletes the interval starting at x.
/// </summary>
/// <param name="arg">The arg.</param>
public void Delete(IInterval <T> arg)
{
if (Root != null)
{
bool wasDeleted = false;
bool wasSuccessful = false;
Root = IntervalNode.Delete(Root, arg, ref wasDeleted, ref wasSuccessful);
if (this.Root != null)
{
IntervalNode.ComputeMax(this.Root);
}
}
}
/// <summary>
/// Recursively descends to the correct spot for interval insertion in the tree
/// When a free spot is found for the node, it is attached and tree state is validated
/// </summary>
/// <param name="interval">interval to be added</param>
/// <param name="currentNode">subtree accessed in recursion</param>
private void InsertInterval(Interval <T> interval, IntervalNode <T> currentNode)
{
IntervalNode <T> addedNode = Sentinel;
if (interval.CompareTo(currentNode.Interval) < 0)
{
if (currentNode.Left == Sentinel)
{
addedNode = new IntervalNode <T>(interval);
addedNode.Color = NodeColor.RED;
currentNode.Left = addedNode;
addedNode.Parent = currentNode;
}
else
{
InsertInterval(interval, currentNode.Left);
return;
}
}
else if (interval.CompareTo(currentNode.Interval) > 0)
{
if (currentNode.Right == Sentinel)
{
addedNode = new IntervalNode <T>(interval);
addedNode.Color = NodeColor.RED;
currentNode.Right = addedNode;
addedNode.Parent = currentNode;
}
else
{
InsertInterval(interval, currentNode.Right);
return;
}
}
else
{
return;
}
addedNode.Parent.RecalculateMaxEnd();
RenewConstraintsAfterInsert(addedNode);
Root.Color = NodeColor.BLACK;
}
private String NodeString(IntervalNode <T, D> node, int level)
{
if (node == null)
{
return("");
}
var sb = new StringBuilder();
for (int i = 0; i < level; i++)
{
sb.Append("\t");
}
sb.Append(node + "\n");
sb.Append(NodeString(node.Left, level + 1));
sb.Append(NodeString(node.Right, level + 1));
return(sb.ToString());
}
/// <summary>
/// Computes the max.
/// </summary>
/// <param name="node">The node.</param>
public static void ComputeMax(IntervalNode node)
{
if (node.Left == null && node.Right == null)
{
node.Max = node.MaxRange;
}
else if (node.Left == null)
{
node.Max = Max(node.MaxRange, node.Right.Max);
}
else if (node.Right == null)
{
node.Max = Max(node.MaxRange, node.Left.Max);
}
else
{
node.Max = Max(node.MaxRange, Max(node.Left.Max, node.Right.Max));
}
}
/// <summary>
/// Searches the specified subtree.
/// </summary>
/// <param name="subtree">The subtree.</param>
/// <param name="data">The data.</param>
/// <returns></returns>
public static IntervalNode Search(IntervalNode subtree, IInterval <T> data)
{
if (subtree != null)
{
if (data.Start.CompareTo(subtree.Data.Key.Start) < 0)
{
return(Search(subtree.Left, data));
}
else if (data.Start.CompareTo(subtree.Data.Key.Start) > 0)
{
return(Search(subtree.Right, data));
}
else
{
return(subtree);
}
}
else
{
return(null);
}
}
private void SearchSubtree(IntervalNode <T> node, Interval <T> i, List <Interval <T> > result)
{
if (node == Sentinel)
{
return;
}
if (node.Left != Sentinel)
{
SearchSubtree(node.Left, i, result);
}
if (i.Overlaps(node.Interval))
{
result.Add(node.Interval);
}
// Interval start is greater than largest endpoint in this subtree
if (node.Right != Sentinel && i.Start.CompareTo(node.MaxEnd) <= 0)
{
SearchSubtree(node.Right, i, result);
}
}
private IEnumerable <Interval <T> > InOrderWalk(IntervalNode <T> node)
{
if (node.Left != Sentinel)
{
foreach (Interval <T> val in InOrderWalk(node.Left))
{
yield return(val);
}
}
if (node != Sentinel)
{
yield return(node.Interval);
}
if (node.Right != Sentinel)
{
foreach (Interval <T> val in InOrderWalk(node.Right))
{
yield return(val);
}
}
}
/// <summary>
/// Rotates lefts this instance.
/// Assumes that this.Right != null
/// </summary>
/// <returns></returns>
private IntervalNode RotateLeft()
{
var right = this.Right;
Debug.Assert(this.Right != null);
this.Right = right.Left;
ComputeMax(this);
#if TREE_WITH_PARENT_POINTERS
var parent = this.Parent;
if (right.Left != null)
{
right.Left.Parent = this;
}
#endif
right.Left = this;
ComputeMax(right);
#if TREE_WITH_PARENT_POINTERS
this.Parent = right;
if (parent != null)
{
if (parent.Left == this)
{
parent.Left = right;
}
else
{
parent.Right = right;
}
}
right.Parent = parent;
#endif
return(right);
}
public int CompareTo(IntervalNode <T> other)
{
return(Interval.CompareTo(other.Interval));
}
/// <summary>
/// Returns all intervals beginning at the specified start value
/// </summary>
/// <param name="subtree">The subtree.</param>
/// <param name="data">The data.</param>
/// <returns></returns>
public static List <KeyValuePair <IInterval <T>, TypeValue> > GetIntervalsStartingAt(IntervalNode subtree, T start)
{
if (subtree != null)
{
if (start.CompareTo(subtree.Data.Key.Start) < 0)
{
return(GetIntervalsStartingAt(subtree.Left, start));
}
else if (start.CompareTo(subtree.Data.Key.Start) > 0)
{
return(GetIntervalsStartingAt(subtree.Right, start));
}
else
{
var result = new List <KeyValuePair <IInterval <T>, TypeValue> >();
result.Add(subtree.Data);
if (subtree.Range != null)
{
foreach (var value in subtree.Range)
{
var kInterval = new Interval <T>(start, value.Key);
result.Add(new KeyValuePair <IInterval <T>, TypeValue>(kInterval, value.Value));
}
}
return(result);
}
}
else
{
return(null);
}
}
/// <summary>
/// Deletes the specified node.
/// </summary>
/// <param name="node">The node.</param>
/// <param name="arg">The arg.</param>
/// <returns></returns>
public static IntervalNode Delete(IntervalNode node, IInterval <T> arg, ref bool wasDeleted, ref bool wasSuccessful)
{
int cmp = arg.Start.CompareTo(node.Data.Key.Start);
if (cmp < 0)
{
if (node.Left != null)
{
node.Left = Delete(node.Left, arg, ref wasDeleted, ref wasSuccessful);
if (wasDeleted)
{
node.Balance++;
}
}
}
else if (cmp == 0)
{
int position = -1;
// find the exact interval to delete based on the Y value.. consider changing this code
if (arg.End.CompareTo(node.Data.Key.End) == 0)
{
position = 0;
}
else
{
if (node.Range != null && node.Range.Count > 0)
{
for (int k = 0; k < node.Range.Count; k++)
{
if (arg.End.CompareTo(node.Range[k].Key) == 0)
{
position = k + 1;
}
}
}
}
// couldn't find the interval in the tree, throw an exception
if (position == -1)
{
throw new ArgumentOutOfRangeException("arg", "cannot delete the specified interval. invalid argument.");
}
if (position > 0)
{
// we're counting the value stored in the node.Data.Value as position 0, all values stored in Range represent position + 1, position + 2, ...etc
if (node.Range != null && position - 1 < node.Range.Count)
{
node.Range.RemoveAt(position - 1);
if (node.Range.Count == 0)
{
node.Range = null;
}
wasSuccessful = true;
}
}
else if (position == 0 && node.Range != null && node.Range.Count > 0)
{
node.Data = new KeyValuePair <IInterval <T>, TypeValue>(
new Interval <T>(node.Data.Key.Start, node.Range[0].Key),
node.Range[0].Value);
node.Range.RemoveAt(0);
if (node.Range.Count == 0)
{
node.Range = null;
}
wasSuccessful = true;
}
else
{
if (node.Left != null && node.Right != null)
{
var min = FindMin(node.Right);
var data = node.Data;
var range = node.Range;
node.Data = min.Data;
node.Range = min.Range;
min.Data = data;
min.Range = range;
wasDeleted = false;
node.Right = Delete(node.Right, data.Key, ref wasDeleted, ref wasSuccessful);
if (wasDeleted)
{
node.Balance--;
}
}
else if (node.Left == null)
{
wasDeleted = true;
wasSuccessful = true;
return(node.Right);
}
else
{
wasDeleted = true;
wasSuccessful = true;
return(node.Left);
}
}
}
else
{
if (node.Right != null)
{
node.Right = Delete(node.Right, arg, ref wasDeleted, ref wasSuccessful);
if (wasDeleted)
{
node.Balance--;
}
}
}
ComputeMax(node);
if (wasDeleted)
{
if (node.Balance == 1 || node.Balance == -1)
{
wasDeleted = false;
return(node);
}
else if (node.Balance == -2)
{
if (node.Left.Balance == 1)
{
int leftRightBalance = node.Left.Right.Balance;
node.Left = node.Left.RotateLeft();
node = node.RotateRight();
node.Balance = 0;
node.Left.Balance = (leftRightBalance == 1) ? -1 : 0;
node.Right.Balance = (leftRightBalance == -1) ? 1 : 0;
}
else if (node.Left.Balance == -1)
{
node = node.RotateRight();
node.Balance = 0;
node.Right.Balance = 0;
}
else if (node.Left.Balance == 0)
{
node = node.RotateRight();
node.Balance = 1;
node.Right.Balance = -1;
wasDeleted = false;
}
}
else if (node.Balance == 2)
{
if (node.Right.Balance == -1)
{
int rightLeftBalance = node.Right.Left.Balance;
node.Right = node.Right.RotateRight();
node = node.RotateLeft();
node.Balance = 0;
node.Left.Balance = (rightLeftBalance == 1) ? -1 : 0;
node.Right.Balance = (rightLeftBalance == -1) ? 1 : 0;
}
else if (node.Right.Balance == 1)
{
node = node.RotateLeft();
node.Balance = 0;
node.Left.Balance = 0;
}
else if (node.Right.Balance == 0)
{
node = node.RotateLeft();
node.Balance = -1;
node.Left.Balance = 1;
wasDeleted = false;
}
}
}
return(node);
}
/// <summary>
/// Ensures constraints still apply after node deletion
///
/// - made with the help of algorithm from Cormen et Al. Introduction to Algorithms 2nd ed.
/// </summary>
/// <param name="node"></param>
private void RenewConstraintsAfterDelete(IntervalNode <T> node)
{
// Need to bubble up and fix
while (node != Root && node.Color == NodeColor.BLACK)
{
if (node.ParentDirection == NodeDirection.RIGHT)
{
IntervalNode <T> aux = node.Parent.Right;
if (aux.Color == NodeColor.RED)
{
aux.Color = NodeColor.BLACK;
node.Parent.Color = NodeColor.RED;
RotateLeft(node.Parent);
aux = node.Parent.Right;
}
if (aux.Left.Color == NodeColor.BLACK && aux.Right.Color == NodeColor.BLACK)
{
aux.Color = NodeColor.RED;
node = node.Parent;
}
else
{
if (aux.Right.Color == NodeColor.BLACK)
{
aux.Left.Color = NodeColor.BLACK;
aux.Color = NodeColor.RED;
RotateRight(aux);
aux = node.Parent.Right;
}
aux.Color = node.Parent.Color;
node.Parent.Color = NodeColor.BLACK;
aux.Right.Color = NodeColor.BLACK;
RotateLeft(node.Parent);
node = Root;
}
}
else
{
IntervalNode <T> aux = node.Parent.Left;
if (aux.Color == NodeColor.RED)
{
aux.Color = NodeColor.BLACK;
node.Parent.Color = NodeColor.RED;
RotateRight(node.Parent);
aux = node.Parent.Left;
}
if (aux.Left.Color == NodeColor.BLACK && aux.Right.Color == NodeColor.BLACK)
{
aux.Color = NodeColor.RED;
node = node.Parent;
}
else
{
if (aux.Left.Color == NodeColor.BLACK)
{
aux.Right.Color = NodeColor.BLACK;
aux.Color = NodeColor.RED;
RotateLeft(aux);
aux = node.Parent.Left;
}
aux.Color = node.Parent.Color;
node.Parent.Color = NodeColor.BLACK;
aux.Left.Color = NodeColor.BLACK;
RotateRight(node.Parent);
node = Root;
}
}
}
node.Color = NodeColor.BLACK;
}
/// <summary>
/// Searches the specified arg.
/// </summary>
/// <param name="arg">The arg.</param>
/// <returns></returns>
public List <KeyValuePair <IInterval <T>, TypeValue> > GetIntervalsStartingAt(T arg)
{
return(IntervalNode.GetIntervalsStartingAt(Root, arg));
}
/// <summary>
/// Adds the specified elem.
/// </summary>
/// <param name="elem">The elem.</param>
/// <param name="data">The data.</param>
/// <returns></returns>
public static IntervalNode Add(
IntervalNode elem,
KeyValuePair <IInterval <T>, TypeValue> data,
ref bool wasAdded,
ref bool wasSuccessful)
{
if (elem == null)
{
elem = new IntervalNode {
Data = data, Left = null, Right = null, Balance = 0, Max = data.Key.End
};
wasAdded = true;
wasSuccessful = true;
}
else
{
if (data.Key.Start.CompareTo(elem.Data.Key.Start) < 0)
{
elem.Left = Add(elem.Left, data, ref wasAdded, ref wasSuccessful);
if (wasAdded)
{
elem.Balance--;
if (elem.Balance == 0)
{
wasAdded = false;
}
}
#if TREE_WITH_PARENT_POINTERS
elem.Left.Parent = elem;
#endif
if (elem.Balance == -2)
{
if (elem.Left.Balance == 1)
{
int elemLeftRightBalance = elem.Left.Right.Balance;
elem.Left = elem.Left.RotateLeft();
elem = elem.RotateRight();
elem.Balance = 0;
elem.Left.Balance = elemLeftRightBalance == 1 ? -1 : 0;
elem.Right.Balance = elemLeftRightBalance == -1 ? 1 : 0;
}
else if (elem.Left.Balance == -1)
{
elem = elem.RotateRight();
elem.Balance = 0;
elem.Right.Balance = 0;
}
wasAdded = false;
}
}
else if (data.Key.Start.CompareTo(elem.Data.Key.Start) > 0)
{
elem.Right = Add(elem.Right, data, ref wasAdded, ref wasSuccessful);
if (wasAdded)
{
elem.Balance++;
if (elem.Balance == 0)
{
wasAdded = false;
}
}
#if TREE_WITH_PARENT_POINTERS
elem.Right.Parent = elem;
#endif
if (elem.Balance == 2)
{
if (elem.Right.Balance == -1)
{
int elemRightLeftBalance = elem.Right.Left.Balance;
elem.Right = elem.Right.RotateRight();
elem = elem.RotateLeft();
elem.Balance = 0;
elem.Left.Balance = elemRightLeftBalance == 1 ? -1 : 0;
elem.Right.Balance = elemRightLeftBalance == -1 ? 1 : 0;
}
else if (elem.Right.Balance == 1)
{
elem = elem.RotateLeft();
elem.Balance = 0;
elem.Left.Balance = 0;
}
wasAdded = false;
}
}
else
{
// we allow multiple values per key
if (elem.Range == null)
{
elem.Range = new List <KeyValuePair <T, TypeValue> >();
}
//always store the max Y value in the node.Data itself .. store the Range list in decreasing order
if (data.Key.End.CompareTo(elem.Data.Key.End) > 0)
{
elem.Range.Insert(0, new KeyValuePair <T, TypeValue>(elem.Data.Key.End, elem.Data.Value));
elem.Data = data;
}
else
{
for (int i = 0; i < elem.Range.Count; i++)
{
if (data.Key.End.CompareTo(elem.Range[i].Key) >= 0)
{
elem.Range.Insert(i, new KeyValuePair <T, TypeValue>(data.Key.End, data.Value));
break;
}
}
}
wasSuccessful = true;
}
}
ComputeMax(elem);
return(elem);
}
