private void SwapColor(KStatisticRBNode a, KStatisticRBNode b)
{
var tmp = a.Color;
a.Color = b.Color;
b.Color = tmp;
}
private void RotateRight(KStatisticRBNode node)
{
var nodeLeft = node.Left;
node.Left = nodeLeft.Right;
if (node.Left != null)
{
node.Left.Parent = node;
}
nodeLeft.Parent = node.Parent;
if (node.Parent == null)
{
Root = node;
}
else if (node == node.Parent.Left)
{
node.Parent.Left = nodeLeft;
}
else
{
node.Parent.Right = nodeLeft;
}
nodeLeft.Right = node;
node.Parent = nodeLeft;
}
private void InOrderDisplay(KStatisticRBNode current)
{
if (current != null)
{
InOrderDisplay(current.Left);
Console.Write("({0}) ", current.Data);
InOrderDisplay(current.Right);
}
}
public void DisplayTree(KStatisticRBNode root)
{
if (root == null)
{
Console.WriteLine("Nothing in the tree!");
return;
}
InOrderDisplay(root);
}
public void Insert(int data)
{
var node = new KStatisticRBNode(data);
// Do a normal BST insert
Root = BSTInsert(Root, node);
// fix Red Black Tree violations
FixViolation(node);
}
private KStatisticRBNode Minimum(KStatisticRBNode node)
{
while (node.Left.Left != null)
{
node = node.Left;
}
if (node.Left.Right != null)
{
node = node.Left.Right;
}
return(node);
}
private KStatisticRBNode TreeSuccessor(KStatisticRBNode node)
{
if (node.Left != null)
{
return(Minimum(node));
}
var parentNode = node.Parent;
while (parentNode != null && node == parentNode.Right)
{
node = parentNode;
parentNode = parentNode.Parent;
}
return(parentNode);
}
private KStatisticRBNode GetStatistic(KStatisticRBNode node, int k)
{
var r = (node.Left?.Size ?? 0) + 1;
if (k == r)
{
return(node);
}
if (k < r)
{
return(GetStatistic(node.Left, k));
}
return(GetStatistic(node.Right, k - r));
}
public void Delete(KStatisticRBNode root, int key)
{
//first find the node in the tree to delete and assign to item pointer/reference
var item = Search(root, key);
KStatisticRBNode itemNode;
if (item == null)
{
Console.WriteLine("Nothing to delete!");
return;
}
if (item.Left == null || item.Right == null)
{
itemNode = item;
}
else
{
itemNode = TreeSuccessor(item);
}
var childNode = itemNode.Left ?? itemNode.Right;
if (childNode != null)
{
childNode.Parent = itemNode;
}
if (itemNode.Parent == null)
{
root = childNode;
}
else if (itemNode == itemNode.Parent.Left)
{
itemNode.Parent.Left = childNode;
}
else
{
itemNode.Parent.Left = childNode;
}
if (itemNode != item)
{
item.Data = itemNode.Data;
}
if (itemNode.Color == Color.Black)
{
DeleteFixUp(root, childNode);
}
}
public KStatisticRBNode Search(KStatisticRBNode root, int key)
{
var isFound = false;
var temp = root;
KStatisticRBNode item = null;
while (!isFound)
{
if (temp == null)
{
break;
}
if (key < temp.Data)
{
temp = temp.Left;
if (temp == null)
{
return(null);
}
}
if (key > temp.Data)
{
temp = temp.Right;
if (temp == null)
{
return(null);
}
}
if (key == temp.Data)
{
isFound = true;
item = temp;
}
}
if (isFound)
{
Console.WriteLine("{0} was found", key);
return(temp);
}
Console.WriteLine("{0} not found", key);
return(null);
}
/* A utility function to insert a new node with given key
* in BST */
KStatisticRBNode BSTInsert(KStatisticRBNode root, KStatisticRBNode node)
{
/* If the tree is empty, return a new node */
if (root == null)
{
return(node);
}
/* Otherwise, recur down the tree */
if (node.Data < root.Data)
{
root.Left = BSTInsert(root.Left, node);
root.Left.Parent = root;
}
else if (node.Data > root.Data)
{
root.Right = BSTInsert(root.Right, node);
root.Right.Parent = root;
}
/* return the (unchanged) node pointer */
return(root);
}
private void DeleteFixUp(KStatisticRBNode root, KStatisticRBNode node)
{
while (node != null && node != root && node.Color == Color.Black)
{
if (node == node.Parent.Left)
{
var parentRight = node.Parent.Right;
if (parentRight.Color == Color.Red)
{
parentRight.Color = Color.Black; //case 1
node.Parent.Color = Color.Red; //case 1
RotateLeft(node.Parent); //case 1
parentRight = node.Parent.Right; //case 1
}
if (parentRight.Left.Color == Color.Black && parentRight.Right.Color == Color.Black)
{
parentRight.Color = Color.Red; //case 2
node = node.Parent; //case 2
}
else if (parentRight.Right.Color == Color.Black)
{
parentRight.Left.Color = Color.Black; //case 3
parentRight.Color = Color.Red; //case 3
RotateRight(parentRight); //case 3
parentRight = node.Parent.Right; //case 3
}
parentRight.Color = node.Parent.Color; //case 4
node.Parent.Color = Color.Black; //case 4
parentRight.Right.Color = Color.Black; //case 4
RotateLeft(node.Parent); //case 4
node = root; //case 4
}
else //mirror code from above with "right" & "left" exchanged
{
var parentLeft = node.Parent.Left;
if (parentLeft.Color == Color.Red)
{
parentLeft.Color = Color.Black;
node.Parent.Color = Color.Red;
RotateRight(node.Parent);
parentLeft = node.Parent.Left;
}
if (parentLeft.Right.Color == Color.Black && parentLeft.Left.Color == Color.Black)
{
parentLeft.Color = Color.Black;
node = node.Parent;
}
else if (parentLeft.Left.Color == Color.Black)
{
parentLeft.Right.Color = Color.Black;
parentLeft.Color = Color.Red;
RotateLeft(parentLeft);
parentLeft = node.Parent.Left;
}
parentLeft.Color = node.Parent.Color;
node.Parent.Color = Color.Black;
parentLeft.Left.Color = Color.Black;
RotateRight(node.Parent);
node = root;
}
}
if (node != null)
{
node.Color = Color.Black;
}
}
private void FixViolation(KStatisticRBNode node)
{
while (node != Root && (node.Color != Color.Black) &&
(node.Parent.Color == Color.Red))
{
var parentNode = node.Parent;
var grandParentNode = node.Parent.Parent;
/* Case : A
* Parent of pt is left child of Grand-parent of pt */
if (parentNode == grandParentNode.Left)
{
var uncleNode = grandParentNode.Right;
/* Case : 1
* The uncle of pt is also red
* Only Recoloring required */
if (uncleNode != null && uncleNode.Color == Color.Red)
{
grandParentNode.Color = Color.Red;
parentNode.Color = Color.Black;
uncleNode.Color = Color.Black;
node = grandParentNode;
}
else
{
/* Case : 2
* pt is right child of its parent
* Left-rotation required */
if (node == parentNode.Right)
{
RotateLeft(parentNode);
node = parentNode;
parentNode = node.Parent;
}
/* Case : 3
* pt is left child of its parent
* Right-rotation required */
RotateRight(grandParentNode);
SwapColor(parentNode, grandParentNode);
node = parentNode;
}
}
/* Case : B
* Parent of pt is right child of Grand-parent of pt */
else
{
var uncleNode = grandParentNode.Left;
/* Case : 1
* The uncle of pt is also red
* Only Recoloring required */
if ((uncleNode != null) && (uncleNode.Color == Color.Red))
{
grandParentNode.Color = Color.Red;
parentNode.Color = Color.Black;
uncleNode.Color = Color.Black;
node = grandParentNode;
}
else
{
/* Case : 2
* pt is left child of its parent
* Right-rotation required */
if (node == parentNode.Left)
{
RotateRight(parentNode);
node = parentNode;
parentNode = node.Parent;
}
/* Case : 3
* pt is right child of its parent
* Left-rotation required */
RotateLeft(grandParentNode);
SwapColor(parentNode, grandParentNode);
node = parentNode;
}
}
}
Root.Color = Color.Black;
}
