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using System;
using System.Collections.Generic;
namespace ARMeilleure.Translation
{
/// <summary>
/// An Augmented Interval Tree based off of the "TreeDictionary"'s Red-Black Tree. Allows fast overlap checking of ranges.
/// </summary>
/// <typeparam name="K">Key</typeparam>
/// <typeparam name="V">Value</typeparam>
class IntervalTree<K, V> where K : IComparable<K>
{
private const int ArrayGrowthSize = 32;
private const bool Black = true;
private const bool Red = false;
private IntervalTreeNode<K, V> _root = null;
private int _count = 0;
public int Count => _count;
public IntervalTree() { }
#region Public Methods
/// <summary>
/// Gets the values of the interval whose key is <paramref name="key"/>.
/// </summary>
/// <param name="key">Key of the node value to get</param>
/// <param name="value">Value with the given <paramref name="key"/></param>
/// <returns>True if the key is on the dictionary, false otherwise</returns>
public bool TryGet(K key, out V value)
{
IntervalTreeNode<K, V> node = GetNode(key);
if (node == null)
{
value = default;
return false;
}
value = node.Value;
return true;
}
/// <summary>
/// Returns the start addresses of the intervals whose start and end keys overlap the given range.
/// </summary>
/// <param name="start">Start of the range</param>
/// <param name="end">End of the range</param>
/// <param name="overlaps">Overlaps array to place results in</param>
/// <param name="overlapCount">Index to start writing results into the array. Defaults to 0</param>
/// <returns>Number of intervals found</returns>
public int Get(K start, K end, ref K[] overlaps, int overlapCount = 0)
{
GetKeys(_root, start, end, ref overlaps, ref overlapCount);
return overlapCount;
}
/// <summary>
/// Adds a new interval into the tree whose start is <paramref name="start"/>, end is <paramref name="end"/> and value is <paramref name="value"/>.
/// </summary>
/// <param name="start">Start of the range to add</param>
/// <param name="end">End of the range to insert</param>
/// <param name="value">Value to add</param>
/// <param name="updateFactoryCallback">Optional factory used to create a new value if <paramref name="start"/> is already on the tree</param>
/// <exception cref="ArgumentNullException"><paramref name="value"/> is null</exception>
/// <returns>True if the value was added, false if the start key was already in the dictionary</returns>
public bool AddOrUpdate(K start, K end, V value, Func<K, V, V> updateFactoryCallback)
{
if (value == null)
{
throw new ArgumentNullException(nameof(value));
}
return BSTInsert(start, end, value, updateFactoryCallback, out IntervalTreeNode<K, V> node);
}
/// <summary>
/// Gets an existing or adds a new interval into the tree whose start is <paramref name="start"/>, end is <paramref name="end"/> and value is <paramref name="value"/>.
/// </summary>
/// <param name="start">Start of the range to add</param>
/// <param name="end">End of the range to insert</param>
/// <param name="value">Value to add</param>
/// <exception cref="ArgumentNullException"><paramref name="value"/> is null</exception>
/// <returns><paramref name="value"/> if <paramref name="start"/> is not yet on the tree, or the existing value otherwise</returns>
public V GetOrAdd(K start, K end, V value)
{
if (value == null)
{
throw new ArgumentNullException(nameof(value));
}
BSTInsert(start, end, value, null, out IntervalTreeNode<K, V> node);
return node.Value;
}
/// <summary>
/// Removes a value from the tree, searching for it with <paramref name="key"/>.
/// </summary>
/// <param name="key">Key of the node to remove</param>
/// <returns>Number of deleted values</returns>
public int Remove(K key)
{
int removed = Delete(key);
_count -= removed;
return removed;
}
/// <summary>
/// Adds all the nodes in the dictionary into <paramref name="list"/>.
/// </summary>
/// <returns>A list of all values sorted by Key Order</returns>
public List<V> AsList()
{
List<V> list = new List<V>();
AddToList(_root, list);
return list;
}
#endregion
#region Private Methods (BST)
/// <summary>
/// Adds all values that are children of or contained within <paramref name="node"/> into <paramref name="list"/>, in Key Order.
/// </summary>
/// <param name="node">The node to search for values within</param>
/// <param name="list">The list to add values to</param>
private void AddToList(IntervalTreeNode<K, V> node, List<V> list)
{
if (node == null)
{
return;
}
AddToList(node.Left, list);
list.Add(node.Value);
AddToList(node.Right, list);
}
/// <summary>
/// Retrieve the node reference whose key is <paramref name="key"/>, or null if no such node exists.
/// </summary>
/// <param name="key">Key of the node to get</param>
/// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
/// <returns>Node reference in the tree</returns>
private IntervalTreeNode<K, V> GetNode(K key)
{
if (key == null)
{
throw new ArgumentNullException(nameof(key));
}
IntervalTreeNode<K, V> node = _root;
while (node != null)
{
int cmp = key.CompareTo(node.Start);
if (cmp < 0)
{
node = node.Left;
}
else if (cmp > 0)
{
node = node.Right;
}
else
{
return node;
}
}
return null;
}
/// <summary>
/// Retrieve all keys that overlap the given start and end keys.
/// </summary>
/// <param name="start">Start of the range</param>
/// <param name="end">End of the range</param>
/// <param name="overlaps">Overlaps array to place results in</param>
/// <param name="overlapCount">Overlaps count to update</param>
private void GetKeys(IntervalTreeNode<K, V> node, K start, K end, ref K[] overlaps, ref int overlapCount)
{
if (node == null || start.CompareTo(node.Max) >= 0)
{
return;
}
GetKeys(node.Left, start, end, ref overlaps, ref overlapCount);
bool endsOnRight = end.CompareTo(node.Start) > 0;
if (endsOnRight)
{
if (start.CompareTo(node.End) < 0)
{
if (overlaps.Length >= overlapCount)
{
Array.Resize(ref overlaps, overlapCount + ArrayGrowthSize);
}
overlaps[overlapCount++] = node.Start;
}
GetKeys(node.Right, start, end, ref overlaps, ref overlapCount);
}
}
/// <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);
}
/// <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;
}
/// <summary>
/// Removes the value from the dictionary after searching for it with <paramref name="key"/>.
/// </summary>
/// <param name="key">Key to search for</param>
/// <returns>Number of deleted values</returns>
private int Delete(K key)
{
IntervalTreeNode<K, V> nodeToDelete = GetNode(key);
if (nodeToDelete == null)
{
return 0;
}
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);
}
return 1;
}
/// <summary>
/// Returns the node with the largest key where <paramref name="node"/> is considered the root node.
/// </summary>
/// <param name="node">Root Node</param>
/// <returns>Node with the maximum key in the tree of <paramref name="node"/></returns>
private static IntervalTreeNode<K, V> Maximum(IntervalTreeNode<K, V> node)
{
IntervalTreeNode<K, V> tmp = node;
while (tmp.Right != null)
{
tmp = tmp.Right;
}
return tmp;
}
/// <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;
}
#endregion
#region Private Methods (RBL)
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);
}
private void RestoreBalanceAfterInsertion(IntervalTreeNode<K, V> balanceNode)
{
SetColor(balanceNode, Red);
while (balanceNode != null && balanceNode != _root && ColorOf(ParentOf(balanceNode)) == Red)
{
if (ParentOf(balanceNode) == LeftOf(ParentOf(ParentOf(balanceNode))))
{
IntervalTreeNode<K, V> sibling = RightOf(ParentOf(ParentOf(balanceNode)));
if (ColorOf(sibling) == Red)
{
SetColor(ParentOf(balanceNode), Black);
SetColor(sibling, Black);
SetColor(ParentOf(ParentOf(balanceNode)), Red);
balanceNode = ParentOf(ParentOf(balanceNode));
}
else
{
if (balanceNode == RightOf(ParentOf(balanceNode)))
{
balanceNode = ParentOf(balanceNode);
RotateLeft(balanceNode);
}
SetColor(ParentOf(balanceNode), Black);
SetColor(ParentOf(ParentOf(balanceNode)), Red);
RotateRight(ParentOf(ParentOf(balanceNode)));
}
}
else
{
IntervalTreeNode<K, V> sibling = LeftOf(ParentOf(ParentOf(balanceNode)));
if (ColorOf(sibling) == Red)
{
SetColor(ParentOf(balanceNode), Black);
SetColor(sibling, Black);
SetColor(ParentOf(ParentOf(balanceNode)), Red);
balanceNode = ParentOf(ParentOf(balanceNode));
}
else
{
if (balanceNode == LeftOf(ParentOf(balanceNode)))
{
balanceNode = ParentOf(balanceNode);
RotateRight(balanceNode);
}
SetColor(ParentOf(balanceNode), Black);
SetColor(ParentOf(ParentOf(balanceNode)), Red);
RotateLeft(ParentOf(ParentOf(balanceNode)));
}
}
}
SetColor(_root, Black);
}
private void RotateLeft(IntervalTreeNode<K, V> node)
{
if (node != null)
{
IntervalTreeNode<K, V> right = RightOf(node);
node.Right = LeftOf(right);
if (node.Right != null)
{
node.Right.Parent = node;
}
IntervalTreeNode<K, V> nodeParent = ParentOf(node);
right.Parent = nodeParent;
if (nodeParent == null)
{
_root = right;
}
else if (node == LeftOf(nodeParent))
{
nodeParent.Left = right;
}
else
{
nodeParent.Right = right;
}
right.Left = node;
node.Parent = right;
PropagateFull(node);
}
}
private void RotateRight(IntervalTreeNode<K, V> node)
{
if (node != null)
{
IntervalTreeNode<K, V> left = LeftOf(node);
node.Left = RightOf(left);
if (node.Left != null)
{
node.Left.Parent = node;
}
IntervalTreeNode<K, V> nodeParent = ParentOf(node);
left.Parent = nodeParent;
if (nodeParent == null)
{
_root = left;
}
else if (node == RightOf(nodeParent))
{
nodeParent.Right = left;
}
else
{
nodeParent.Left = left;
}
left.Right = node;
node.Parent = left;
PropagateFull(node);
}
}
#endregion
#region Safety-Methods
// 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;
}
/// <summary>
/// Sets the color of <paramref name="node"/> node to <paramref name="color"/>.
/// <br></br>
/// This method does nothing if <paramref name="node"/> is null.
/// </summary>
/// <param name="node">Node to set the color of</param>
/// <param name="color">Color (Boolean)</param>
private static void SetColor(IntervalTreeNode<K, V> node, bool color)
{
if (node != null)
{
node.Color = color;
}
}
/// <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;
}
/// <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>
/// 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;
}
#endregion
public bool ContainsKey(K key)
{
return GetNode(key) != null;
}
public void Clear()
{
_root = null;
_count = 0;
}
}
/// <summary>
/// Represents a node in the IntervalTree which contains start and end keys of type K, and a value of generic type V.
/// </summary>
/// <typeparam name="K">Key type of the node</typeparam>
/// <typeparam name="V">Value type of the node</typeparam>
class IntervalTreeNode<K, V>
{
public bool Color = true;
public IntervalTreeNode<K, V> Left = null;
public IntervalTreeNode<K, V> Right = null;
public IntervalTreeNode<K, V> Parent = null;
/// <summary>
/// The start of the range.
/// </summary>
public K Start;
/// <summary>
/// The end of the range.
/// </summary>
public K End;
/// <summary>
/// The maximum end value of this node and all its children.
/// </summary>
public K Max;
/// <summary>
/// Value stored on this node.
/// </summary>
public V Value;
public IntervalTreeNode(K start, K end, V value, IntervalTreeNode<K, V> parent)
{
Start = start;
End = end;
Max = end;
Value = value;
Parent = parent;
}
}
}
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