private Node TreeSuccessor(Node x)
{
if (x.Left != null)
{
return Minimum(x);
}
Node y = x.Parent;
while (y != null && x == y.Right)
{
x = y;
y = y.Parent;
}
return y;
}
/// <summary>
/// Deletes a specified value from the tree
/// </summary>
/// <param name="key"></param>
public void Delete(int key)
{
//first find the node in the tree to delete and assign to item pointer/reference
Node item = Find(key);
Node x;
Node y;
if (item == null)
{
Console.WriteLine("Nothing to delete!");
return;
}
if (item.Left == null || item.Right == null)
{
y = item;
}
else
{
y = TreeSuccessor(item);
}
x = y.Left ?? y.Right;
if (x != null)
{
x.Parent = y;
}
if (y.Parent == null)
{
_root = x;
}
else if (y == y.Parent.Left)
{
y.Parent.Left = x;
}
else
{
y.Parent.Left = x;
}
if (y != item)
{
item.Data = y.Data;
}
if (y.Colour == Color.Black)
{
DeleteFixUp(x);
}
}
private Node Minimum(Node x)
{
while (x.Left.Left != null)
{
x = x.Left;
}
if (x.Left.Right != null)
{
x = x.Left.Right;
}
return x;
}
/// <summary>
/// Rotate Right
/// </summary>
/// <param name="y"></param>
/// <returns>void</returns>
private void RightRotate(Node y)
{
// right rotate is simply mirror code from left rotate
Node x = y.Left;
y.Left = x.Right;
if (x.Right != null)
{
x.Right.Parent = y;
}
if (x != null)
{
x.Parent = y.Parent;
}
if (y.Parent == null)
{
_root = x;
}
if (y.Parent != null && y == y.Parent.Right)
{
y.Parent.Right = x;
}
if (y.Parent != null && y == y.Parent.Left)
{
y.Parent.Left = x;
}
x.Right = y;//put Y on X's right
y.Parent = x;
}
/// <summary>
/// Left Rotate
/// </summary>
/// <param name="x"></param>
/// <returns>void</returns>
private void LeftRotate(Node x)
{
Node y = x.Right; // set Y
x.Right = y.Left;//turn Y's left subtree into X's right subtree
if (y.Left != null)
{
y.Left.Parent = x;
}
if (y != null)
{
y.Parent = x.Parent;//link X's parent to Y
}
if (x.Parent == null)
{
_root = y;
}
if (x.Parent != null && x == x.Parent.Left)
{
x.Parent.Left = y;
}
else
{
if (x.Parent != null) x.Parent.Right = y;
}
y.Left = x; //put X on Y's left
x.Parent = y;
}
private void InsertFixUp(Node item)
{
//Checks Red-Black Tree properties
while (item != _root && item.Parent.Colour == Color.Red)
{
/*We have a violation*/
if (item.Parent == item.Parent.Parent.Left)
{
Node y = item.Parent.Parent.Right;
if (y != null && y.Colour == Color.Red)//Case 1: uncle is red
{
item.Parent.Colour = Color.Black;
y.Colour = Color.Black;
item.Parent.Parent.Colour = Color.Red;
item = item.Parent.Parent;
}
else //Case 2: uncle is black
{
if (item == item.Parent.Right)
{
item = item.Parent;
LeftRotate(item);
}
//Case 3: recolour & rotate
item.Parent.Colour = Color.Black;
item.Parent.Parent.Colour = Color.Red;
RightRotate(item.Parent.Parent);
}
}
else
{
//mirror image of code above
Node x;
x = item.Parent.Parent.Left;
if (x != null && x.Colour == Color.Black)//Case 1
{
item.Parent.Colour = Color.Red;
x.Colour = Color.Red;
item.Parent.Parent.Colour = Color.Black;
item = item.Parent.Parent;
}
else //Case 2
{
if (item == item.Parent.Left)
{
item = item.Parent;
RightRotate(item);
}
//Case 3: recolour & rotate
item.Parent.Colour = Color.Black;
item.Parent.Parent.Colour = Color.Red;
LeftRotate(item.Parent.Parent);
}
}
_root.Colour = Color.Black;//re-colour the root black as necessary
}
}
private void InOrderDisplay(Node current)
{
if (current != null)
{
InOrderDisplay(current.Left);
Console.Write("({0}) ", current.Data);
InOrderDisplay(current.Right);
}
}
/// <summary>
/// Checks the tree for any violations after deletion and performs a fix
/// </summary>
/// <param name="x"></param>
private void DeleteFixUp(Node x)
{
while (x != null && x != _root && x.Colour == Color.Black)
{
if (x == x.Parent.Left)
{
Node w = x.Parent.Right;
if (w.Colour == Color.Red)
{
w.Colour = Color.Black; //case 1
x.Parent.Colour = Color.Red; //case 1
LeftRotate(x.Parent); //case 1
w = x.Parent.Right; //case 1
}
if (w.Left.Colour == Color.Black && w.Right.Colour == Color.Black)
{
w.Colour = Color.Red; //case 2
x = x.Parent; //case 2
}
else if (w.Right.Colour == Color.Black)
{
w.Left.Colour = Color.Black; //case 3
w.Colour = Color.Red; //case 3
RightRotate(w); //case 3
w = x.Parent.Right; //case 3
}
w.Colour = x.Parent.Colour; //case 4
x.Parent.Colour = Color.Black; //case 4
w.Right.Colour = Color.Black; //case 4
LeftRotate(x.Parent); //case 4
x = _root; //case 4
}
else //mirror code from above with "right" & "left" exchanged
{
Node w = x.Parent.Left;
if (w.Colour == Color.Red)
{
w.Colour = Color.Black;
x.Parent.Colour = Color.Red;
RightRotate(x.Parent);
w = x.Parent.Left;
}
if (w.Right.Colour == Color.Black && w.Left.Colour == Color.Black)
{
w.Colour = Color.Black;
x = x.Parent;
}
else if (w.Left.Colour == Color.Black)
{
w.Right.Colour = Color.Black;
w.Colour = Color.Red;
LeftRotate(w);
w = x.Parent.Left;
}
w.Colour = x.Parent.Colour;
x.Parent.Colour = Color.Black;
w.Left.Colour = Color.Black;
RightRotate(x.Parent);
x = _root;
}
}
if (x != null)
x.Colour = Color.Black;
}
/// <summary>
/// Insert a new object into the RB Tree
/// </summary>
/// <param name="item"></param>
public void Insert(int item)
{
Node newItem = new Node(item);
if (_root == null)
{
_root = newItem;
_root.Colour = Color.Black;
return;
}
Node y = null;
Node x = _root;
while (x != null)
{
y = x;
x = newItem.Data < x.Data ? x.Left : x.Right;
}
newItem.Parent = y;
if (y == null)
{
_root = newItem;
}
else if (newItem.Data < y.Data)
{
y.Left = newItem;
}
else
{
y.Right = newItem;
}
newItem.Left = null;
newItem.Right = null;
newItem.Colour = Color.Red;//colour the new node red
InsertFixUp(newItem);//call method to check for violations and fix
}
