Ryujinx/Ryujinx.Common/Collections/TreeDictionary.cs
riperiperi db97b1d7d2
Implement and use an Interval Tree for the MultiRangeList (#2641)
* Implement and use an Interval Tree for the MultiRangeList

* Feedback

* Address Feedback

* Missed this somehow
2021-09-19 14:55:07 +02:00

987 lines
32 KiB
C#

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;
namespace Ryujinx.Common.Collections
{
/// <summary>
/// Dictionary that provides the ability for O(logN) Lookups for keys that exist in the Dictionary, and O(logN) lookups for keys immediately greater than or less than a specified key.
/// </summary>
/// <typeparam name="K">Key</typeparam>
/// <typeparam name="V">Value</typeparam>
public class TreeDictionary<K, V> : IDictionary<K, V> where K : IComparable<K>
{
private const bool Black = true;
private const bool Red = false;
private Node<K, V> _root = null;
private int _count = 0;
public TreeDictionary() { }
#region Public Methods
/// <summary>
/// Returns the value of the node whose key is <paramref name="key"/>, or the default value if no such node exists.
/// </summary>
/// <param name="key">Key of the node value to get</param>
/// <returns>Value associated w/ <paramref name="key"/></returns>
/// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
public V Get(K key)
{
if (key == null)
{
throw new ArgumentNullException(nameof(key));
}
Node<K, V> node = GetNode(key);
if (node == null)
{
return default;
}
return node.Value;
}
/// <summary>
/// Adds a new node into the tree whose key is <paramref name="key"/> key and value is <paramref name="value"/>.
/// <br></br>
/// <b>Note:</b> Adding the same key multiple times will cause the value for that key to be overwritten.
/// </summary>
/// <param name="key">Key of the node to add</param>
/// <param name="value">Value of the node to add</param>
/// <exception cref="ArgumentNullException"><paramref name="key"/> or <paramref name="value"/> are null</exception>
public void Add(K key, V value)
{
if (key == null)
{
throw new ArgumentNullException(nameof(key));
}
if (null == value)
{
throw new ArgumentNullException(nameof(value));
}
Insert(key, value);
}
/// <summary>
/// Removes the node whose key is <paramref name="key"/> from the tree.
/// </summary>
/// <param name="key">Key of the node to remove</param>
/// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
public void Remove(K key)
{
if (key == null)
{
throw new ArgumentNullException(nameof(key));
}
if (Delete(key) != null)
{
_count--;
}
}
/// <summary>
/// Returns the value whose key is equal to or immediately less than <paramref name="key"/>.
/// </summary>
/// <param name="key">Key for which to find the floor value of</param>
/// <returns>Key of node immediately less than <paramref name="key"/></returns>
/// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
public K Floor(K key)
{
Node<K, V> node = FloorNode(key);
if (node != null)
{
return node.Key;
}
return default;
}
/// <summary>
/// Returns the node whose key is equal to or immediately greater than <paramref name="key"/>.
/// </summary>
/// <param name="key">Key for which to find the ceiling node of</param>
/// <returns>Key of node immediately greater than <paramref name="key"/></returns>
/// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
public K Ceiling(K key)
{
Node<K, V> node = CeilingNode(key);
if (node != null)
{
return node.Key;
}
return default;
}
/// <summary>
/// Finds the value whose key is immediately greater than <paramref name="key"/>.
/// </summary>
/// <param name="key">Key to find the successor of</param>
/// <returns>Value</returns>
public K SuccessorOf(K key)
{
Node<K, V> node = GetNode(key);
if (node != null)
{
Node<K, V> successor = SuccessorOf(node);
return successor != null ? successor.Key : default;
}
return default;
}
/// <summary>
/// Finds the value whose key is immediately less than <paramref name="key"/>.
/// </summary>
/// <param name="key">Key to find the predecessor of</param>
/// <returns>Value</returns>
public K PredecessorOf(K key)
{
Node<K, V> node = GetNode(key);
if (node != null)
{
Node<K, V> predecessor = PredecessorOf(node);
return predecessor != null ? predecessor.Key : default;
}
return default;
}
/// <summary>
/// Adds all the nodes in the dictionary as key/value pairs into <paramref name="list"/>.
/// <br></br>
/// The key/value pairs will be added in Level Order.
/// </summary>
/// <param name="list">List to add the tree pairs into</param>
public List<KeyValuePair<K, V>> AsLevelOrderList()
{
List<KeyValuePair<K, V>> list = new List<KeyValuePair<K, V>>();
Queue<Node<K, V>> nodes = new Queue<Node<K, V>>();
if (this._root != null)
{
nodes.Enqueue(this._root);
}
while (nodes.Count > 0)
{
Node<K, V> node = nodes.Dequeue();
list.Add(new KeyValuePair<K, V>(node.Key, node.Value));
if (node.Left != null)
{
nodes.Enqueue(node.Left);
}
if (node.Right != null)
{
nodes.Enqueue(node.Right);
}
}
return list;
}
/// <summary>
/// Adds all the nodes in the dictionary into <paramref name="list"/>.
/// </summary>
/// <returns>A list of all KeyValuePairs sorted by Key Order</returns>
public List<KeyValuePair<K, V>> AsList()
{
List<KeyValuePair<K, V>> list = new List<KeyValuePair<K, V>>();
AddToList(_root, list);
return list;
}
#endregion
#region Private Methods (BST)
/// <summary>
/// Adds all nodes 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 nodes within</param>
/// <param name="list">The list to add node to</param>
private void AddToList(Node<K, V> node, List<KeyValuePair<K, V>> list)
{
if (node == null)
{
return;
}
AddToList(node.Left, list);
list.Add(new KeyValuePair<K, V>(node.Key, 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>
/// <returns>Node reference in the tree</returns>
/// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
private Node<K, V> GetNode(K key)
{
if (key == null)
{
throw new ArgumentNullException(nameof(key));
}
Node<K, V> node = _root;
while (node != null)
{
int cmp = key.CompareTo(node.Key);
if (cmp < 0)
{
node = node.Left;
}
else if (cmp > 0)
{
node = node.Right;
}
else
{
return node;
}
}
return null;
}
/// <summary>
/// Inserts a new node into the tree whose key is <paramref name="key"/> and value is <paramref name="value"/>.
/// <br></br>
/// Adding the same key multiple times will overwrite the previous value.
/// </summary>
/// <param name="key">Key of the node to insert</param>
/// <param name="value">Value of the node to insert</param>
private void Insert(K key, V value)
{
Node<K, V> newNode = BSTInsert(key, value);
RestoreBalanceAfterInsertion(newNode);
}
/// <summary>
/// Insertion Mechanism for a Binary Search Tree (BST).
/// <br></br>
/// Iterates the tree starting from the root and inserts a new node where all children in the left subtree are less than <paramref name="key"/>, and all children in the right subtree are greater than <paramref name="key"/>.
/// <br></br>
/// <b>Note: </b> If a node whose key is <paramref name="key"/> already exists, it's value will be overwritten.
/// </summary>
/// <param name="key">Key of the node to insert</param>
/// <param name="value">Value of the node to insert</param>
/// <returns>The inserted Node</returns>
private Node<K, V> BSTInsert(K key, V value)
{
Node<K, V> parent = null;
Node<K, V> node = _root;
while (node != null)
{
parent = node;
int cmp = key.CompareTo(node.Key);
if (cmp < 0)
{
node = node.Left;
}
else if (cmp > 0)
{
node = node.Right;
}
else
{
node.Value = value;
return node;
}
}
Node<K, V> newNode = new Node<K, V>(key, value, parent);
if (newNode.Parent == null)
{
_root = newNode;
}
else if (key.CompareTo(parent.Key) < 0)
{
parent.Left = newNode;
}
else
{
parent.Right = newNode;
}
_count++;
return newNode;
}
/// <summary>
/// Removes <paramref name="key"/> from the dictionary, if it exists.
/// </summary>
/// <param name="key">Key of the node to delete</param>
/// <returns>The deleted Node</returns>
private Node<K, V> Delete(K key)
{
// O(1) Retrieval
Node<K, V> nodeToDelete = GetNode(key);
if (nodeToDelete == null) return null;
Node<K, V> replacementNode;
if (LeftOf(nodeToDelete) == null || RightOf(nodeToDelete) == null)
{
replacementNode = nodeToDelete;
}
else
{
replacementNode = PredecessorOf(nodeToDelete);
}
Node<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.Key = replacementNode.Key;
nodeToDelete.Value = replacementNode.Value;
}
if (tmp != null && ColorOf(replacementNode) == Black)
{
RestoreBalanceAfterRemoval(tmp);
}
return replacementNode;
}
/// <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 Node<K, V> Maximum(Node<K, V> node)
{
Node<K, V> tmp = node;
while (tmp.Right != null)
{
tmp = tmp.Right;
}
return tmp;
}
/// <summary>
/// Returns the node with the smallest key where <paramref name="node"/> is considered the root node.
/// </summary>
/// <param name="node">Root Node</param>
/// <returns>Node with the minimum key in the tree of <paramref name="node"/></returns>
///<exception cref="ArgumentNullException"><paramref name="node"/> is null</exception>
private static Node<K, V> Minimum(Node<K, V> node)
{
if (node == null)
{
throw new ArgumentNullException(nameof(node));
}
Node<K, V> tmp = node;
while (tmp.Left != null)
{
tmp = tmp.Left;
}
return tmp;
}
/// <summary>
/// Returns the node whose key immediately less than or equal to <paramref name="key"/>.
/// </summary>
/// <param name="key">Key for which to find the floor node of</param>
/// <returns>Node whose key is immediately less than or equal to <paramref name="key"/>, or null if no such node is found.</returns>
/// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
private Node<K, V> FloorNode(K key)
{
if (key == null)
{
throw new ArgumentNullException(nameof(key));
}
Node<K, V> tmp = _root;
while (tmp != null)
{
int cmp = key.CompareTo(tmp.Key);
if (cmp > 0)
{
if (tmp.Right != null)
{
tmp = tmp.Right;
}
else
{
return tmp;
}
}
else if (cmp < 0)
{
if (tmp.Left != null)
{
tmp = tmp.Left;
}
else
{
Node<K, V> parent = tmp.Parent;
Node<K, V> ptr = tmp;
while (parent != null && ptr == parent.Left)
{
ptr = parent;
parent = parent.Parent;
}
return parent;
}
}
else
{
return tmp;
}
}
return null;
}
/// <summary>
/// Returns the node whose key is immediately greater than or equal to than <paramref name="key"/>.
/// </summary>
/// <param name="key">Key for which to find the ceiling node of</param>
/// <returns>Node whose key is immediately greater than or equal to <paramref name="key"/>, or null if no such node is found.</returns>
/// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
private Node<K, V> CeilingNode(K key)
{
if (key == null)
{
throw new ArgumentNullException(nameof(key));
}
Node<K, V> tmp = _root;
while (tmp != null)
{
int cmp = key.CompareTo(tmp.Key);
if (cmp < 0)
{
if (tmp.Left != null)
{
tmp = tmp.Left;
}
else
{
return tmp;
}
}
else if (cmp > 0)
{
if (tmp.Right != null)
{
tmp = tmp.Right;
}
else
{
Node<K, V> parent = tmp.Parent;
Node<K, V> ptr = tmp;
while (parent != null && ptr == parent.Right)
{
ptr = parent;
parent = parent.Parent;
}
return parent;
}
}
else
{
return tmp;
}
}
return null;
}
/// <summary>
/// Finds the node with the key is immediately greater than <paramref name="node"/>.
/// </summary>
/// <param name="node">Node to find the successor of</param>
/// <returns>Successor of <paramref name="node"/></returns>
private static Node<K, V> SuccessorOf(Node<K, V> node)
{
if (node.Right != null)
{
return Minimum(node.Right);
}
Node<K, V> parent = node.Parent;
while (parent != null && node == parent.Right)
{
node = parent;
parent = parent.Parent;
}
return parent;
}
/// <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 Node<K, V> PredecessorOf(Node<K, V> node)
{
if (node.Left != null)
{
return Maximum(node.Left);
}
Node<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(Node<K, V> balanceNode)
{
Node<K, V> ptr = balanceNode;
while (ptr != _root && ColorOf(ptr) == Black)
{
if (ptr == LeftOf(ParentOf(ptr)))
{
Node<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
{
Node<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(Node<K, V> balanceNode)
{
SetColor(balanceNode, Red);
while (balanceNode != null && balanceNode != _root && ColorOf(ParentOf(balanceNode)) == Red)
{
if (ParentOf(balanceNode) == LeftOf(ParentOf(ParentOf(balanceNode))))
{
Node<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
{
Node<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(Node<K, V> node)
{
if (node != null)
{
Node<K, V> right = RightOf(node);
node.Right = LeftOf(right);
if (LeftOf(right) != null)
{
LeftOf(right).Parent = node;
}
right.Parent = ParentOf(node);
if (ParentOf(node) == null)
{
_root = right;
}
else if (node == LeftOf(ParentOf(node)))
{
ParentOf(node).Left = right;
}
else
{
ParentOf(node).Right = right;
}
right.Left = node;
node.Parent = right;
}
}
private void RotateRight(Node<K, V> node)
{
if (node != null)
{
Node<K, V> left = LeftOf(node);
node.Left = RightOf(left);
if (RightOf(left) != null)
{
RightOf(left).Parent = node;
}
left.Parent = node.Parent;
if (ParentOf(node) == null)
{
_root = left;
}
else if (node == RightOf(ParentOf(node)))
{
ParentOf(node).Right = left;
}
else
{
ParentOf(node).Left = left;
}
left.Right = node;
node.Parent = left;
}
}
#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(Node<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(Node<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 Node<K, V> LeftOf(Node<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 Node<K, V> RightOf(Node<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 Node<K, V> ParentOf(Node<K, V> node)
{
return node?.Parent;
}
#endregion
#region Interface Implementations
// Method descriptions are not provided as they are already included as part of the interface.
public bool ContainsKey(K key)
{
if (key == null)
{
throw new ArgumentNullException(nameof(key));
}
return GetNode(key) != null;
}
bool IDictionary<K, V>.Remove(K key)
{
int count = _count;
Remove(key);
return count > _count;
}
public bool TryGetValue(K key, [MaybeNullWhen(false)] out V value)
{
if (null == key)
{
throw new ArgumentNullException(nameof(key));
}
Node<K, V> node = GetNode(key);
value = node != null ? node.Value : default;
return node != null;
}
public void Add(KeyValuePair<K, V> item)
{
if (item.Key == null)
{
throw new ArgumentNullException(nameof(item.Key));
}
Add(item.Key, item.Value);
}
public void Clear()
{
_root = null;
_count = 0;
}
public bool Contains(KeyValuePair<K, V> item)
{
if (item.Key == null)
{
return false;
}
Node<K, V> node = GetNode(item.Key);
if (node != null)
{
return node.Key.Equals(item.Key) && node.Value.Equals(item.Value);
}
return false;
}
public void CopyTo(KeyValuePair<K, V>[] array, int arrayIndex)
{
if (arrayIndex < 0 || array.Length - arrayIndex < this.Count)
{
throw new ArgumentOutOfRangeException(nameof(arrayIndex));
}
SortedList<K, V> list = GetKeyValues();
int offset = 0;
for (int i = arrayIndex; i < array.Length && offset < list.Count; i++)
{
array[i] = new KeyValuePair<K, V>(list.Keys[i], list.Values[i]);
offset++;
}
}
public bool Remove(KeyValuePair<K, V> item)
{
Node<K, V> node = GetNode(item.Key);
if (node == null)
{
return false;
}
if (node.Value.Equals(item.Value))
{
int count = _count;
Remove(item.Key);
return count > _count;
}
return false;
}
public IEnumerator<KeyValuePair<K, V>> GetEnumerator()
{
return GetKeyValues().GetEnumerator();
}
IEnumerator IEnumerable.GetEnumerator()
{
return GetKeyValues().GetEnumerator();
}
public int Count => _count;
public ICollection<K> Keys => GetKeyValues().Keys;
public ICollection<V> Values => GetKeyValues().Values;
public bool IsReadOnly => false;
public V this[K key]
{
get => Get(key);
set => Add(key, value);
}
#endregion
#region Private Interface Helper Methods
/// <summary>
/// Returns a sorted list of all the node keys / values in the tree.
/// </summary>
/// <returns>List of node keys</returns>
private SortedList<K, V> GetKeyValues()
{
SortedList<K, V> set = new SortedList<K, V>();
Queue<Node<K, V>> queue = new Queue<Node<K, V>>();
if (_root != null)
{
queue.Enqueue(_root);
}
while (queue.Count > 0)
{
Node<K, V> node = queue.Dequeue();
set.Add(node.Key, node.Value);
if (null != node.Left)
{
queue.Enqueue(node.Left);
}
if (null != node.Right)
{
queue.Enqueue(node.Right);
}
}
return set;
}
#endregion
}
/// <summary>
/// Represents a node in the TreeDictionary which contains a key and value of generic type K and V, respectively.
/// </summary>
/// <typeparam name="K">Key of the node</typeparam>
/// <typeparam name="V">Value of the node</typeparam>
internal class Node<K, V>
{
internal bool Color = true;
internal Node<K, V> Left = null;
internal Node<K, V> Right = null;
internal Node<K, V> Parent = null;
internal K Key;
internal V Value;
public Node(K key, V value, Node<K, V> parent)
{
this.Key = key;
this.Value = value;
this.Parent = parent;
}
}
}