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RedBlackBST.cs
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RedBlackBST.cs
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// http://algs4.cs.princeton.edu/33balanced/RedBlackLiteBST.java.html
// http://algs4.cs.princeton.edu/33balanced/RedBlackBST.java.html
namespace SedgewickWayne.Algorithms
{
using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics.Contracts;
using System.Linq;
/// <summary>
/// A symbol table implemented using a left-leaning red-black BST. This is the 2-3 version.
/// </summary>
/// <typeparam name="Key"></typeparam>
/// <typeparam name="Value"></typeparam>
/// <remarks>
/// The class represents an ordered symbol table of generic key-value pairs.
/// Construction takes constant time.
/// Uses the convention that values cannot be null—setting the value associated with a key to null is equivalent to deleting the key from the symbol table.
/// The put, contains, remove, minimum, maximum, ceiling, and floor operations each take logarithmic time in the worst case, if the tree becomes unbalanced.
/// The size, and is-empty operations take constant time.
/// </remarks>
public class RedBlackBST<Key, Value>
: TreeSTBase<Key, Value>
where Key : IComparable<Key>, IEquatable<Key>
where Value : IEquatable<Value>
{
/// <summary>
/// Initializes an empty symbol table.
/// </summary>
public RedBlackBST()
{
root = null;
}
internal RedBlackNode<Key, Value> Root => root as RedBlackNode<Key, Value>;
/// <summary>
/// Standard BST search.
/// </summary>
/// <param name="x"></param>
/// <param name="key"></param>
/// <returns>TODO: refactor?</returns>
internal override Value GetKey(BaseNode<Key, Value> x, Key key)
{
while (x != null)
{
int cmp = key.CompareTo(x.key);
if (cmp < 0) x = x.left;
else if (cmp > 0) x = x.right;
else return x.val;
}
return default(Value);
}
/// <summary>
/// insert the key-value pair in the subtree rooted at h.
/// Red-black tree insertion
/// </summary>
/// <param name="h"></param>
/// <param name="key"></param>
/// <param name="val"></param>
/// <returns></returns>
internal override BaseNode<Key, Value> PutKey(BaseNode<Key, Value> h, Key key, Value val)
{
if (h == null) return new RedBlackNode<Key, Value>(key, val, NodeColor.RED, 1);
int cmp = key.CompareTo(h.key);
if (cmp < 0) h.left = PutKey(h.left, key, val);
else if (cmp > 0) h.right = PutKey(h.right, key, val);
else h.val = val;
if (h is RedBlackNode<Key, Value> hh)
{
// fix-up any right-leaning links
if (IsRed(hh.right) && !IsRed(hh.left)) h = RotateLeft(hh);
if (IsRed(hh.left) && IsRed(hh.left.left)) h = RotateRight(hh);
if (IsRed(hh.left) && IsRed(hh.right)) FlipColors(hh);
hh.UpdateSize();
return h;
}
else throw new TypeLoadException(h.GetType().FullName);
}
public override void Put(Key key, Value val)
{
base.Put(key, val);
Root.color = NodeColor.BLACK;
}
private bool IsRed(BaseNode<Key, Value> x) => (x != null) && (x is RedBlackNode<Key,Value> y) && y.IsRed;
private bool IsBlack(BaseNode<Key, Value> x) => (x != null) && (x is RedBlackNode<Key, Value> y) && y.IsBlack;
/// <summary>
/// make a right-leaning link lean to the left
/// </summary>
/// <param name="h"></param>
/// <returns></returns>
private RedBlackNode<Key, Value> RotateLeft(RedBlackNode<Key, Value> h)
{
Contract.Assert((h != null) && IsRed(h.right));
var x = h.Right;
h.right = x.left;
x.left = h;
x.color = x.Left.color;
x.Left.color = NodeColor.RED;
x.SetSize (h.Size);
h.UpdateSize();
return x;
}
/// <summary>
/// make a left-leaning link lean to the right
/// </summary>
/// <param name="h"></param>
/// <returns></returns>
private RedBlackNode<Key, Value> RotateRight(RedBlackNode<Key, Value> h)
{
Contract.Assert((h != null) && IsRed(h.left));
var x = h.Left;
h.left = x.right;
x.right = h;
x.color = x.Right.color;
x.Right.color = NodeColor.RED;
x.SetSize(h.Size);
h.UpdateSize();
return x;
}
/// <summary>
/// flip the colors of a node and its two children
/// </summary>
/// <param name="h"></param>
private void FlipColors(RedBlackNode<Key, Value> h)
{
// h must have opposite color of its two children
Contract.Assert ((h != null) && (h.left != null) && (h.right != null));
Contract.Assert((IsBlack(h) && IsRed(h.left) && IsRed(h.right)) || (IsRed(h) && IsBlack(h.left) && IsBlack(h.right)));
h.FlipColor();
h.Left.FlipColor();
h.Right.FlipColor();
}
void SetColor(BaseNode<Key, Value> node, NodeColor color) => (node as RedBlackNode<Key, Value>).color = color;
#region Red-black tree deletion
public override void Delete(Key key)
{
KeyArgumentNull(key, nameof(Delete));
if (!Contains(key)) return;
// if both children of root are black, set root to red
if (IsBlack(root.left) && IsBlack(root.right)) SetColor(root, NodeColor.RED);
root = DeleteKey(Root, key);
if (!IsEmpty) SetColor(root, NodeColor.BLACK);
// assert check();
}
/// <summary>
/// delete the key-value pair with the given key rooted at h
/// </summary>
/// <param name="h"></param>
/// <param name="key"></param>
/// <returns></returns>
private RedBlackNode<Key, Value> DeleteKey(RedBlackNode<Key, Value> h, Key key)
{
// Contract.Assert(!Get(h, key).Equals(default(Value)));
if (key.CompareTo(h.key) < 0)
{
if (!IsRed(h.left) && !IsRed(h.left.left))
h = moveRedLeft(h);
h.left = DeleteKey(h.Left, key);
}
else
{
if (IsRed(h.left))
h = RotateRight(h);
if (key.CompareTo(h.key) == 0 && (h.right == null))
return null;
if (!IsRed(h.right) && !IsRed(h.right.left))
h = moveRedRight(h);
if (key.CompareTo(h.key) == 0)
{
var x = MinimumNode(h.Right);
h.key = x.key;
h.val = x.val;
// h.val = get(h.right, min(h.right).key);
// h.key = min(h.right).key;
h.right = DeleteMin(h.Right);
}
else h.right = DeleteKey(h.Right, key);
}
return balance(h);
}
public override void DeleteMax() => CommonDeleteLimit(DeleteMax);
private RedBlackNode<Key, Value> DeleteMax(RedBlackNode<Key, Value> h)
{
if (IsRed(h.left)) h = RotateRight(h);
if (h.right == null) return null;
if (IsBlack(h.right) && IsBlack(h.right.left)) h = moveRedRight(h);
h.right = DeleteMax(h.Right);
return balance(h);
}
public override void DeleteMin() => CommonDeleteLimit(DeleteMin);
private RedBlackNode<Key, Value> DeleteMin(RedBlackNode<Key, Value> h)
{
if (h.left == null) return null;
if (IsBlack(h.left) && IsBlack(h.left.left)) h = moveRedLeft(h);
h.left = DeleteMin(h.Left);
return balance(h);
}
private void CommonDeleteLimit(Func<RedBlackNode<Key, Value>, RedBlackNode<Key, Value>> f)
{
SymbolTableUnderflow();
// if both children of root are black, set root to red
if (IsBlack(root.left) && IsBlack(root.right))
SetColor(root, NodeColor.RED);
root = f(Root);
if (!IsEmpty)
SetColor(root, NodeColor.BLACK);
// assert check();
}
/// <summary>
/// restore red-black tree invariant
/// </summary>
/// <param name="h"></param>
/// <returns></returns>
private RedBlackNode<Key, Value> balance(RedBlackNode<Key, Value> h)
{
Contract.Assert (h != null);
if (IsRed(h.right)) h = RotateLeft(h);
if (IsRed(h.left) && IsRed(h.left.left)) h = RotateRight(h);
if (IsRed(h.left) && IsRed(h.right)) FlipColors(h);
h.UpdateSize();
return h;
}
/// <summary>
/// Assuming that h is red and both h.right and h.right.left are black, make h.right or one of its children red.
/// </summary>
/// <param name="h"></param>
/// <returns></returns>
private RedBlackNode<Key, Value> moveRedRight(RedBlackNode<Key, Value> h)
{
Contract.Assert (h != null);
Contract.Assert (IsRed(h) && !IsRed(h.right) && !IsRed(h.right.left));
FlipColors(h);
if (IsRed(h.left.left))
{
h = RotateRight(h);
FlipColors(h);
}
return h;
}
/// <summary>
/// Assuming that h is red and both h.left and h.left.left are black, make h.left or one of its children red.
/// </summary>
/// <param name="h"></param>
/// <returns></returns>
private RedBlackNode<Key, Value> moveRedLeft(RedBlackNode<Key, Value> h)
{
Contract.Assert(h != null);
Contract.Assert (IsRed(h) && !IsRed(h.left) && !IsRed(h.left.left));
FlipColors(h);
if (IsRed(h.right.left))
{
h.right = RotateRight(h.Right);
h = RotateLeft(h);
FlipColors(h);
}
return h;
}
#endregion
internal override BaseNode<Key, Value> MaximumNode(BaseNode<Key, Value> x) => (x.right == null) ? x : MaximumNode(x.right);
internal override BaseNode<Key, Value> MinimumNode(BaseNode<Key, Value> x) => (x.left == null) ? x : MinimumNode(x.left);
#region ordered
/// <summary>
/// Returns the smallest key in the symbol table greater than or equal to <paramref name="key"/>
/// </summary>
/// <param name="key">the key</param>
/// <returns></returns>
public override Key Ceiling(Key key) => CommonFloorCeiling(key, ceiling);
/// <summary>
/// the smallest key in the subtree rooted at x greater than or equal to the given key
/// </summary>
/// <param name="x"></param>
/// <param name="key"></param>
/// <returns></returns>
private RedBlackNode<Key, Value> ceiling(RedBlackNode<Key, Value> x, Key key)
{
if (x == null) return null;
int cmp = key.CompareTo(x.key);
if (cmp == 0) return x;
if (cmp > 0) return ceiling(x.Right, key);
var t = ceiling(x.Left, key);
return t ?? x;
}
public override Key Floor(Key key) => CommonFloorCeiling(key, floor);
private RedBlackNode<Key, Value> floor(RedBlackNode<Key, Value> x, Key key)
{
if (x == null) return null;
int cmp = key.CompareTo(x.key);
if (cmp == 0) return x;
if (cmp < 0) return floor(x.Left, key);
var t = floor(x.Right, key);
if (t != null) return t;
else return x;
}
private Key CommonFloorCeiling(Key key, Func<RedBlackNode<Key, Value>, Key, RedBlackNode<Key, Value>> f)
{
KeyArgumentNull(key, nameof(CommonFloorCeiling));
SymbolTableUnderflow();
var x = f(Root, key);
return (x == null) ? default(Key) : x.key;
}
#endregion
#region enumerable
public override IEnumerator<Key> GetEnumerator() => Keys().GetEnumerator();
/// <summary>
/// Returns all keys in the symbol table
/// </summary>
/// <returns></returns>
IEnumerable<Key> Keys() => IsEmpty ? Enumerable.Empty<Key>() : Keys(Min, Max);
private IEnumerable<Key> Keys(Key lo, Key hi)
{
KeyArgumentNull(lo, nameof(Keys));
KeyArgumentNull(hi, nameof(Keys));
var queue = new Queue<Key>();
keys(Root, queue, lo, hi);
return queue;
}
/// <summary>
/// add the keys between <paramref name="lo"/> and <paramref name="hi"/>
/// in the subtree rooted at <paramref name="x"/> to the queue <paramref name="q"/>
/// </summary>
/// <param name="x"></param>
/// <param name="q"></param>
/// <param name="lo"></param>
/// <param name="hi"></param>
private void keys(RedBlackNode<Key, Value> x, Queue<Key> q, Key lo, Key hi)
{
if (x == null) return;
int cmplo = lo.CompareTo(x.key);
int cmphi = hi.CompareTo(x.key);
if (cmplo < 0) keys(x.Left, q, lo, hi);
if (cmplo <= 0 && cmphi >= 0) q.Enqueue(x.key);
if (cmphi > 0) keys(x.Right, q, lo, hi);
}
#endregion
/// <summary>
/// TODO
/// </summary>
internal override void CheckBstDataStructure()
{
}
}
}