[英]Is there a .NET data structure with the following characteristics of a Binary Search Tree?
我知道SortedDictionary是一個二叉搜索樹（它幾乎可以完成我需要做的事情！），但是我不知道如何以正確的復雜度完成我需要做的一切。
所以這是約束（以及我所知道的數據結構）
O(log n)插入和刪除（SortedDictionary） O(log n) （SortedDictionary和SortedList） O(log n) + O(m)迭代（其中m是中間的元素數） （SortedList） 如您所見，我不知道如何獲取SortedDictionary來執行數字3。基本上，我需要做的是獲取具有范圍的所有元素而不迭代集合。
如果我的問題不清楚，請告訴我。
我認為框架中沒有一個集合可以執行您描述的內容，盡管我可能是錯的。
您正在尋找的是一個用二叉樹建立索引的鏈表。 這將為您提供
使用二叉樹進行O(log n)插入，刪除和搜索，使用O(m)遍歷
鏈表。
您可能想看看C5通用館藏庫 。 盡管似乎沒有一個適合您描述的集合，但是您可以將它們的TreeSet<T>和LinkedList<T>對象結合在一起，創建一個新的SortedLinkedList<T>對象。
這似乎完美地描述了B +樹： http : //en.wikipedia.org/wiki/B%2B_tree ：
這里似乎存在AC＃實現： http : //bplusdotnet.sourceforge.net/
一些建議非常好，但是我決定自己實施該集合（聽起來很有趣）。 我從SortedDictionary的.NET實現開始，並對其進行了大量修改以實現所需的功能
正是這樣，其他人才能從我的工作中受益，這是課程：
internal delegate void TreeWalkAction<Key, Value>(BinaryTreeSearch<Key, Value>.Node node);
internal delegate bool TreeWalkTerminationPredicate<Key, Value>(BinaryTreeSearch<Key, Value>.Node node);
internal class BinaryTreeSearch<Key, Value>
{
// Fields
private IComparer<Key> comparer;
private int count;
private Node root;
private int version;
// Methods
public BinaryTreeSearch(IComparer<Key> comparer)
{
if (comparer == null)
{
this.comparer = Comparer<Key>.Default;
}
else
{
this.comparer = comparer;
}
}
private Node First
{
get
{
if (root == null) return null;
Node n = root;
while (n.Left != null)
{
n = n.Left;
}
return n;
}
}
public Key Min
{
get
{
Node first = First;
return first == null ? default(Key) : first.Key;
}
}
public Key Max
{
get
{
if (root == null) return default(Key);
Node n = root;
while (n.Right != null)
{
n = n.Right;
}
return n.Key;
}
}
public List<Value> this[Key key]
{
get
{
Node n = FindNode(key);
return n == null ? new List<Value>() : n.Values;
}
}
public List<Value> GetRange(Key start, Key end)
{
Node node = FindNextNode(start);
List<Value> ret = new List<Value>();
InOrderTreeWalk(node,
aNode => ret.AddRange(aNode.Values),
aNode => comparer.Compare(end, aNode.Key) < 0);
return ret;
}
public void Add(Key key, Value value)
{
if (this.root == null)
{
this.root = new Node(null, key, value, false);
this.count = 1;
}
else
{
Node root = this.root;
Node node = null;
Node grandParent = null;
Node greatGrandParent = null;
int num = 0;
while (root != null)
{
num = this.comparer.Compare(key, root.Key);
if (num == 0)
{
root.Values.Add(value);
count++;
return;
}
if (Is4Node(root))
{
Split4Node(root);
if (IsRed(node))
{
this.InsertionBalance(root, ref node, grandParent, greatGrandParent);
}
}
greatGrandParent = grandParent;
grandParent = node;
node = root;
root = (num < 0) ? root.Left : root.Right;
}
Node current = new Node(node, key, value);
if (num > 0)
{
node.Right = current;
}
else
{
node.Left = current;
}
if (node.IsRed)
{
this.InsertionBalance(current, ref node, grandParent, greatGrandParent);
}
this.root.IsRed = false;
this.count++;
this.version++;
}
}
public void Clear()
{
this.root = null;
this.count = 0;
this.version++;
}
public bool Contains(Key key)
{
return (this.FindNode(key) != null);
}
internal Node FindNode(Key item)
{
int num;
for (Node node = this.root; node != null; node = (num < 0) ? node.Left : node.Right)
{
num = this.comparer.Compare(item, node.Key);
if (num == 0)
{
return node;
}
}
return null;
}
internal Node FindNextNode(Key key)
{
int num;
Node node = root;
while (true)
{
num = comparer.Compare(key, node.Key);
if (num == 0)
{
return node;
}
else if (num < 0)
{
if (node.Left == null) return node;
node = node.Left;
}
else
{
node = node.Right;
}
}
}
private static Node GetSibling(Node node, Node parent)
{
if (parent.Left == node)
{
return parent.Right;
}
return parent.Left;
}
internal void InOrderTreeWalk(Node start, TreeWalkAction<Key, Value> action, TreeWalkTerminationPredicate<Key, Value> terminationPredicate)
{
Node node = start;
while (node != null && !terminationPredicate(node))
{
action(node);
node = node.Next;
}
}
private void InsertionBalance(Node current, ref Node parent, Node grandParent, Node greatGrandParent)
{
Node node;
bool flag = grandParent.Right == parent;
bool flag2 = parent.Right == current;
if (flag == flag2)
{
node = flag2 ? RotateLeft(grandParent) : RotateRight(grandParent);
}
else
{
node = flag2 ? RotateLeftRight(grandParent) : RotateRightLeft(grandParent);
parent = greatGrandParent;
}
grandParent.IsRed = true;
node.IsRed = false;
this.ReplaceChildOfNodeOrRoot(greatGrandParent, grandParent, node);
}
private static bool Is2Node(Node node)
{
return ((IsBlack(node) && IsNullOrBlack(node.Left)) && IsNullOrBlack(node.Right));
}
private static bool Is4Node(Node node)
{
return (IsRed(node.Left) && IsRed(node.Right));
}
private static bool IsBlack(Node node)
{
return ((node != null) && !node.IsRed);
}
private static bool IsNullOrBlack(Node node)
{
if (node != null)
{
return !node.IsRed;
}
return true;
}
private static bool IsRed(Node node)
{
return ((node != null) && node.IsRed);
}
private static void Merge2Nodes(Node parent, Node child1, Node child2)
{
parent.IsRed = false;
child1.IsRed = true;
child2.IsRed = true;
}
public bool Remove(Key key, Value value)
{
if (this.root == null)
{
return false;
}
Node root = this.root;
Node parent = null;
Node node3 = null;
Node match = null;
Node parentOfMatch = null;
bool flag = false;
while (root != null)
{
if (Is2Node(root))
{
if (parent == null)
{
root.IsRed = true;
}
else
{
Node sibling = GetSibling(root, parent);
if (sibling.IsRed)
{
if (parent.Right == sibling)
{
RotateLeft(parent);
}
else
{
RotateRight(parent);
}
parent.IsRed = true;
sibling.IsRed = false;
this.ReplaceChildOfNodeOrRoot(node3, parent, sibling);
node3 = sibling;
if (parent == match)
{
parentOfMatch = sibling;
}
sibling = (parent.Left == root) ? parent.Right : parent.Left;
}
if (Is2Node(sibling))
{
Merge2Nodes(parent, root, sibling);
}
else
{
TreeRotation rotation = RotationNeeded(parent, root, sibling);
Node newChild = null;
switch (rotation)
{
case TreeRotation.LeftRotation:
sibling.Right.IsRed = false;
newChild = RotateLeft(parent);
break;
case TreeRotation.RightRotation:
sibling.Left.IsRed = false;
newChild = RotateRight(parent);
break;
case TreeRotation.RightLeftRotation:
newChild = RotateRightLeft(parent);
break;
case TreeRotation.LeftRightRotation:
newChild = RotateLeftRight(parent);
break;
}
newChild.IsRed = parent.IsRed;
parent.IsRed = false;
root.IsRed = true;
this.ReplaceChildOfNodeOrRoot(node3, parent, newChild);
if (parent == match)
{
parentOfMatch = newChild;
}
node3 = newChild;
}
}
}
int num = flag ? -1 : this.comparer.Compare(key, root.Key);
if (num == 0)
{
flag = true;
match = root;
parentOfMatch = parent;
}
node3 = parent;
parent = root;
if (num < 0)
{
root = root.Left;
}
else
{
root = root.Right;
}
}
if (match != null)
{
if (match.Values.Remove(value))
{
this.count--;
}
if (match.Values.Count == 0)
{
this.ReplaceNode(match, parentOfMatch, parent, node3);
}
}
if (this.root != null)
{
this.root.IsRed = false;
}
this.version++;
return flag;
}
private void ReplaceChildOfNodeOrRoot(Node parent, Node child, Node newChild)
{
if (parent != null)
{
if (parent.Left == child)
{
parent.Left = newChild;
}
else
{
parent.Right = newChild;
}
if (newChild != null) newChild.Parent = parent;
}
else
{
this.root = newChild;
}
}
private void ReplaceNode(Node match, Node parentOfMatch, Node succesor, Node parentOfSuccesor)
{
if (succesor == match)
{
succesor = match.Left;
}
else
{
if (succesor.Right != null)
{
succesor.Right.IsRed = false;
}
if (parentOfSuccesor != match)
{
parentOfSuccesor.Left = succesor.Right; if (succesor.Right != null) succesor.Right.Parent = parentOfSuccesor;
succesor.Right = match.Right; if (match.Right != null) match.Right.Parent = succesor;
}
succesor.Left = match.Left; if (match.Left != null) match.Left.Parent = succesor;
}
if (succesor != null)
{
succesor.IsRed = match.IsRed;
}
this.ReplaceChildOfNodeOrRoot(parentOfMatch, match, succesor);
}
private static Node RotateLeft(Node node)
{
Node right = node.Right;
node.Right = right.Left; if (right.Left != null) right.Left.Parent = node;
right.Left = node; if (node != null) node.Parent = right;
return right;
}
private static Node RotateLeftRight(Node node)
{
Node left = node.Left;
Node right = left.Right;
node.Left = right.Right; if (right.Right != null) right.Right.Parent = node;
right.Right = node; if (node != null) node.Parent = right;
left.Right = right.Left; if (right.Left != null) right.Left.Parent = left;
right.Left = left; if (left != null) left.Parent = right;
return right;
}
private static Node RotateRight(Node node)
{
Node left = node.Left;
node.Left = left.Right; if (left.Right != null) left.Right.Parent = node;
left.Right = node; if (node != null) node.Parent = left;
return left;
}
private static Node RotateRightLeft(Node node)
{
Node right = node.Right;
Node left = right.Left;
node.Right = left.Left; if (left.Left != null) left.Left.Parent = node;
left.Left = node; if (node != null) node.Parent = left;
right.Left = left.Right; if (left.Right != null) left.Right.Parent = right;
left.Right = right; if (right != null) right.Parent = left;
return left;
}
private static TreeRotation RotationNeeded(Node parent, Node current, Node sibling)
{
if (IsRed(sibling.Left))
{
if (parent.Left == current)
{
return TreeRotation.RightLeftRotation;
}
return TreeRotation.RightRotation;
}
if (parent.Left == current)
{
return TreeRotation.LeftRotation;
}
return TreeRotation.LeftRightRotation;
}
private static void Split4Node(Node node)
{
node.IsRed = true;
node.Left.IsRed = false;
node.Right.IsRed = false;
}
// Properties
public IComparer<Key> Comparer
{
get
{
return this.comparer;
}
}
public int Count
{
get
{
return this.count;
}
}
internal class Node
{
// Fields
private bool isRed;
private Node left, right, parent;
private Key key;
private List<Value> values;
// Methods
public Node(Node parent, Key item, Value value) : this(parent, item, value, true)
{
}
public Node(Node parent, Key key, Value value, bool isRed)
{
this.key = key;
this.parent = parent;
this.values = new List<Value>(new Value[] { value });
this.isRed = isRed;
}
// Properties
public bool IsRed
{
get
{
return this.isRed;
}
set
{
this.isRed = value;
}
}
public Key Key
{
get
{
return this.key;
}
set
{
this.key = value;
}
}
public List<Value> Values { get { return values; } }
public Node Left
{
get
{
return this.left;
}
set
{
this.left = value;
}
}
public Node Right
{
get
{
return this.right;
}
set
{
this.right = value;
}
}
public Node Parent
{
get
{
return this.parent;
}
set
{
this.parent = value;
}
}
public Node Next
{
get
{
if (right == null)
{
if (parent == null)
{
return null; // this puppy must be lonely
}
else if (parent.Left == this) // this is a left child
{
return parent;
}
else
{
//this is a right child, we need to go up the tree
//until we find a left child. Then the parent will be the next
Node n = this;
do
{
n = n.parent;
if (n.parent == null)
{
return null; // this must have been a node along the right edge of the tree
}
} while (n.parent.right == n);
return n.parent;
}
}
else // there is a right child.
{
Node go = right;
while (go.left != null)
{
go = go.left;
}
return go;
}
}
}
public override string ToString()
{
return key.ToString() + " - [" + string.Join(", ", new List<string>(values.Select<Value, string>(o => o.ToString())).ToArray()) + "]";
}
}
internal enum TreeRotation
{
LeftRightRotation = 4,
LeftRotation = 1,
RightLeftRotation = 3,
RightRotation = 2
}
}
和快速的單元測試（實際上並沒有涵蓋所有代碼，因此可能仍然存在一些錯誤）：
[TestFixture]
public class BTSTest
{
private class iC : IComparer<int>{public int Compare(int x, int y){return x.CompareTo(y);}}
[Test]
public void Test()
{
BinaryTreeSearch<int, int> bts = new BinaryTreeSearch<int, int>(new iC());
bts.Add(5, 1);
bts.Add(5, 2);
bts.Add(6, 2);
bts.Add(2, 3);
bts.Add(8, 2);
bts.Add(10, 11);
bts.Add(9, 4);
bts.Add(3, 32);
bts.Add(12, 32);
bts.Add(8, 32);
bts.Add(9, 32);
Assert.AreEqual(11, bts.Count);
Assert.AreEqual(2, bts.Min);
Assert.AreEqual(12, bts.Max);
List<int> val = bts[5];
Assert.AreEqual(2, val.Count);
Assert.IsTrue(val.Contains(1));
Assert.IsTrue(val.Contains(2));
val = bts[6];
Assert.AreEqual(1, val.Count);
Assert.IsTrue(val.Contains(2));
Assert.IsTrue(bts.Contains(5));
Assert.IsFalse(bts.Contains(-1));
val = bts.GetRange(5, 8);
Assert.AreEqual(5, val.Count);
Assert.IsTrue(val.Contains(1));
Assert.IsTrue(val.Contains(32));
Assert.AreEqual(3, val.Count<int>(num => num == 2));
bts.Remove(8, 32);
bts.Remove(5, 2);
Assert.AreEqual(9, bts.Count);
val = bts.GetRange(5, 8);
Assert.AreEqual(3, val.Count);
Assert.IsTrue(val.Contains(1));
Assert.AreEqual(2, val.Count<int>(num => num == 2));
bts.Remove(2, 3);
Assert.IsNull(bts.FindNode(2));
bts.Remove(12, 32);
Assert.IsNull(bts.FindNode(12));
Assert.AreEqual(3, bts.Min);
Assert.AreEqual(10, bts.Max);
bts.Remove(9, 4);
bts.Remove(5, 1);
bts.Remove(6, 2);
}
}
System.Collections.ObjectModel.KeyedCollection<TKey, TItem>出System.Collections.ObjectModel.KeyedCollection<TKey, TItem> -它可能不符合您的要求，但看起來很合適，因為它提供了一個內部查找字典，該字典允許O（1）通過索引檢索項目並接近O （1）按鍵。
需要注意的是，它旨在存儲將鍵定義為對象屬性的對象，因此，除非您可以混搭輸入數據以適合它，否則不合適。
我將提供有關您打算存儲哪些數據和卷的更多信息，因為這可能有助於提供替代方法。
如何在二叉搜索樹數據結構中存儲類型及其子類型信息？
[英]How to store types, their subtype information all together in binary search tree data structure?
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