/*
* RBInsert and RBDelete modify the tree which may result in a violation of the
* red-black poperties. In order to fix this we may need to "move around" some of
* the nodes as well as their colors. LeftRotate and RightRotate help us do this.
* */
private Node LeftRotate(Node x)
{
Node y = x.right;
x.right = y.left;
if (y.left != NIL.Instance())
{
y.left.parent = x;
}
y.parent = x.parent;
if (x.parent == NIL.Instance())
{
root = y;
}
else if (x == x.parent.left)
{
x.parent.left = y;
}
else
{
x.parent.right = y;
}
y.left = x;
x.parent = y;
return(x);
}
private void LeftRotate(Node nodeToRotate)
{ // setting node which will come in place of nodeToRotate
Node nodeToReplace = nodeToRotate.Right;
//turn nodeToReplace's left subtree into nodeToRotate's right subtree
nodeToRotate.Right = nodeToReplace.Left;
if (nodeToReplace.Left != NIL.Instance())
{ // if left subtree exists make it's parent nodeToRotate
nodeToReplace.Left.Parent = nodeToRotate;
}
if (nodeToReplace != NIL.Instance())
{ // link nodeToRotate parent to nodeToReplace
nodeToReplace.Parent = nodeToRotate.Parent;
}
if (nodeToRotate.Parent == NIL.Instance())
{ // if nodeToRotate is the root, make nodeToReplace as new root
Root = nodeToReplace;
}
if (nodeToRotate == nodeToRotate.Parent.Left)
{ // if nodeToRotate is a left child, nodeToReplace has to become left child of nodeToRotate's parent
nodeToRotate.Parent.Left = nodeToReplace;
}
else
{ // if nodeToRotate is a right child, nodeToReplace has to become right child of nodeToRotate's parent
nodeToRotate.Parent.Right = nodeToReplace;
}
// put nodeToRotate on nodeToReplace's left
nodeToReplace.Left = nodeToRotate;
// if nodeToRotate is not nil, make it's parent nodeToReplace
if (nodeToRotate != NIL.Instance())
{
nodeToRotate.Parent = nodeToReplace;
}
}
/*
* To find the maximum of the three from node n (including
* the root) we just keep going down the right braches until there
* are no more nodes.
* */
private Node RBTreeMaximum(Node x)
{
while (x.right != NIL.Instance())
{
x = x.right;
}
return(x);
}
/*
* To find the minimum of the tree from node n (including
* the root) we just keep going down the left branches until there
* are no more nodes.
* */
private Node RBTreeMinimum(Node x)
{
while (x.left != NIL.Instance())
{
x = x.left;
}
return(x);
}
/// <summary>
/// passing through the tree by InOrderTraversal
/// </summary>
/// <param name="root"> root of a subtree to be passed </param>
private void InOrderDisplay(Node root)
{
if (root != NIL.Instance())
{
InOrderDisplay(root.Left);
Console.Write("Key is {0} and Value is {1} ", root.Key, root.Value);
InOrderDisplay(root.Right);
}
}
/// <summary>
/// to restore the red-black properties
/// </summary>
/// <param name="NewAddedNode"> node which was inserted </param>
private void RBT_InsertFixUp(Node NewAddedNode)
{
while (NewAddedNode != Root && NewAddedNode.Parent.color == COLOR.Red)
{ // if parent of new added node is a left child
if (NewAddedNode.Parent == NewAddedNode.Parent.Parent.Left)
{ // uncle of newAddedNode
Node uncle = NewAddedNode.Parent.Parent.Right;
if (uncle != NIL.Instance() && uncle.color == COLOR.Red)
{
NewAddedNode.Parent.color = COLOR.Black;
uncle.color = COLOR.Black;
NewAddedNode.Parent.Parent.color = COLOR.Red;
// make newNode's grandparent as the new newNode and repeat the steps
NewAddedNode = NewAddedNode.Parent.Parent;
} // if uncle is black and parent of newNode is not black there are 2 cases
// 1 case (left right case)
else if (NewAddedNode == NewAddedNode.Parent.Right)
{
NewAddedNode = NewAddedNode.Parent;
LeftRotate(NewAddedNode);
}
else
{// case 2 (left left case)
NewAddedNode.Parent.color = COLOR.Black;
NewAddedNode.Parent.Parent.color = COLOR.Red;
RightRotate(NewAddedNode.Parent.Parent);
}
}
else
{ // if parent of a new added node is right child
Node y = NewAddedNode.Parent.Parent.Left; // uncle of newNode
if (y != NIL.Instance() && y.color == COLOR.Red)
{
NewAddedNode.Parent.color = COLOR.Black;
y.color = COLOR.Black;
NewAddedNode.Parent.Parent.color = COLOR.Red;
NewAddedNode = NewAddedNode.Parent.Parent;
} // case 1 (right left)
else if (NewAddedNode == NewAddedNode.Parent.Left)
{
NewAddedNode = NewAddedNode.Parent;
RightRotate(NewAddedNode);
}
else
{ //case 2(right right)
NewAddedNode.Parent.color = COLOR.Black;
NewAddedNode.Parent.Parent.color = COLOR.Red;
LeftRotate(NewAddedNode.Parent.Parent);
}
}
Root.color = COLOR.Black;
}
}
/*
*
* */
public void RBInsert(Key kz, Value vz)
{
//Only add a new node if the key does not already exist
Node newNode = new Node();
newNode.key = kz;
newNode.val = vz;
newNode.left = NIL.Instance();
newNode.right = NIL.Instance();
RBInsert(newNode);
}
/// <summary>
/// displaying tree
/// </summary>
public void Display()
{
if (Root != NIL.Instance())
{
InOrderDisplay(Root);
}
else
{
throw new Exception("No tree");
}
}
/// <summary>
/// to delete node from the tree
/// </summary>
/// <param name="nodeToDelete"> node to be deleted </param>
private void RBT_Delete(Node nodeToDelete)
{
Node node = nodeToDelete;
/*
* We have to store nodeToDelete's original color, because when we move a node
* into it's postion and the color of nodeToDelete is black we must call DeleteFixup
*/
COLOR originalColor = node.color;
Node x;
// when nodeToDelete has one child we just need to replace nodeToDelete with the child
if (nodeToDelete.Left == NIL.Instance())
{
x = nodeToDelete.Right;
RBTransplant(nodeToDelete, nodeToDelete.Right);
}
else if (nodeToDelete.Right == NIL.Instance())
{
x = nodeToDelete.Left;
RBTransplant(nodeToDelete, nodeToDelete.Left);
}
else
{
/* if nodeToDelete has two children we have to find the successor (the smallest key
* that is larger than nodeToDelete) and move it into nodeToDelete's position */
node = RBTreeMinimum(nodeToDelete.Right);
originalColor = node.color;
x = node.Right;
// if successor is right child
if (node.Parent == nodeToDelete)
{
x.Parent = node;
}
else
{ // succesor will move into nodeToDelete's position
RBTransplant(node, node.Right);
node.Right = nodeToDelete.Right;
node.Right.Parent = node;
}
RBTransplant(nodeToDelete, node);
node.Left = nodeToDelete.Left;
node.Left.Parent = node;
node.color = nodeToDelete.color;
}
// if node which was deleted is black, we restore red-black tree properties
if (originalColor == COLOR.Black)
{
RBT_DeleteFixup(x);
}
}
/*
* Used to "replace" u with v. Used when deleting a node and we need to replace
* the deleted node with an other node from the tree.
* */
private void RBTransplant(Node u, Node v)
{
if (u.parent == NIL.Instance())
{
root = v;
}
else if (u == u.parent.left)
{
u.parent.left = v;
}
else
{
u.parent.right = v;
}
v.parent = u.parent;
}
/*
* This is similar to insert for a binary search tree with a few differences. We use NIL.Instance()
* instead of null.
* After inserting we call RBInsertFixup incase we've violated one of the red-black properties.
* */
private void RBInsert(Node z)
{
Node y = NIL.Instance();
Node x = root;
int cmp;
while (x != NIL.Instance())
{
y = x;
cmp = z.key.CompareTo(x.key);
if (cmp < 0)
{
x = x.left;
}
else if (cmp > 0)
{
x = x.right;
}
else if (cmp == 0) //This key already exists, exit without adding it
{
return;
}
}
z.parent = y;
cmp = z.key.CompareTo(y.key);
if (y == NIL.Instance())
{
root = z;
}
else if (cmp < 0)
{
y.left = z;
}
else if (cmp > 0)
{
y.right = z;
}
else if (cmp == 0)//This key already exists, exit without adding it
{
return;
}
z.left = NIL.Instance();
z.right = NIL.Instance();
z.color = RBColor.RED;
z = RBInsertFixup(z);
}
/// <summary>
/// replaces the subtree rooted at node u with the subtree rooted at v
/// </summary>
/// <param name="u"> node to be replaced </param>
/// <param name="v"> node which subtree will come into the place of u node's subtree </param>
private void RBTransplant(Node x, Node y)
{ // if u is a root make v as a root
if (x.Parent == NIL.Instance())
{
Root = y;
}
else if (x == x.Parent.Left)
{
x.Parent.Left = y;
}
else
{
x.Parent.Right = y;
}
// even if u.Parent is NIL we can assign it
y.Parent = x.Parent;
}
/// <summary>
/// Insert a given node
/// </summary>
/// <param name="newNode"> node to be inserted into the tree </param>
private void Insert(Node newNode)
{ // if tree is empty, make NewNode as the root
if (Root == NIL.Instance())
{
Root = newNode;
Root.color = COLOR.Black;
return;
}
Node parentOfNewNode = NIL.Instance();
Node a = Root;
while (a != NIL.Instance())
{ // finding the right subtree to insert the newNode
parentOfNewNode = a;
if (newNode.Key.CompareTo(a.Key) < 0)
{
a = a.Left;
}
else
{
a = a.Right;
}
}
newNode.Parent = parentOfNewNode;
if (parentOfNewNode == NIL.Instance())
{
Root = newNode;
}
// finding in which subtree of b newNode have to be inserted
else if (newNode.Key.CompareTo(parentOfNewNode.Key) >= 0)
{
parentOfNewNode.Right = newNode;
}
else
{
parentOfNewNode.Left = newNode;
}
// making inserted node's left and right children NIL and it's color RED
newNode.Left = NIL.Instance();
newNode.Right = NIL.Instance();
newNode.color = COLOR.Red;
// because coloring red may cause a violation of one of the red-black properties we must guarantee that the red-black properties are preserved
RBT_InsertFixUp(newNode);
}
// Adds an element with given key and value
public void Add(TKey key, TValue value)
{
if (ContainsKey(key) == false)
{
Node NewNode = new Node
{
Key = key,
Value = value,
Left = NIL.Instance(),
Right = NIL.Instance(),
Parent = NIL.Instance()
};
Keys_List.Add(key);
Key_Values.Add(value);
Insert(NewNode);
listForNodes.Add(new KeyValuePair <TKey, TValue>(key, value));
}
else
{
throw new Exception("Key is already inserted");
}
}
/*
* Delete node z and replace it with y. If z has only one child we just replace z with
* that child. If z has two children then y should be z's successor.
* */
private void RBDelete(Node z)
{
Node x;
//First, set y equal to z
Node y = z;
/*
* We want to store z's original color so when we move a node
* into z's postion and the value of yOriginalColor is black then we call
* RBDeleteFixup.
*/
RBColor yOriginalColor = y.color;
/*
* The first two if statements cover when z just has one child. If
* so, just replace z with the child
*/
if (z.left == NIL.Instance())
{
x = z.right;
RBTransplant(z, z.right);
}
else if (z.right == NIL.Instance())
{
x = z.left;
RBTransplant(z, z.left);
}
else
{
/*
* z has two children. First find the successor (the smallest key
* that is larger than z. Move it into z's position by setting it's
* parent to z and re-assign child nodes.
*/
y = RBTreeMinimum(z.right);
yOriginalColor = y.color;
x = y.right;
if (y.parent == z)
{
x.parent = y;
}
else
{
RBTransplant(y, y.right);
y.right = z.right;
y.right.parent = y;
}
RBTransplant(z, y);
y.left = z.left;
y.left.parent = y;
y.color = z.color;
}
/*
* If node y was black, several problems may arise which RBDeleteFixup will fix.
* */
if (yOriginalColor == RBColor.BLACK)
{
RBDeleteFixup(x);
}
}
/// <summary>
/// Removes all items from the tree
/// </summary>
public void Clear()
{
Root = NIL.Instance();
}
