public TKey GetMaxKey()
{
RedBlackNode <TKey, TValue> workNode = _treeBaseNode;
if (workNode == null || workNode == SentinelNode)
{
throw (new RedBlackException(Properties.Resources.ExceptionTreeIsEmpty));
}
// traverse to the extreme right to find the largest key
while (workNode.Right != SentinelNode)
{
workNode = workNode.Right;
}
_lastNodeFound = workNode;
return(workNode.Key);
}
///<summary>
/// Balance Tree After Insert
/// Additions to red-black trees usually destroy the red-black
/// properties. Examine the tree and restore. Rotations are normally
/// required to restore it
///</summary>
private void BalanceTreeAfterInsert(RedBlackNode <TKey, TValue> insertedNode)
{
// x and y are used as variable names for brevity, in a more formal
// implementation, you should probably change the names
// maintain red-black tree properties after adding newNode
while (insertedNode != _treeBaseNode && insertedNode.Parent.Color == RedBlackNodeType.Red)
{
// Parent node is .Colored red;
RedBlackNode <TKey, TValue> workNode;
if (insertedNode.Parent == insertedNode.Parent.Parent.Left) // determine traversal path
{ // is it on the Left or Right subtree?
workNode = insertedNode.Parent.Parent.Right; // get uncle
if (workNode != null && workNode.Color == RedBlackNodeType.Red)
{ // uncle is red; change x's Parent and uncle to black
insertedNode.Parent.Color = RedBlackNodeType.Black;
workNode.Color = RedBlackNodeType.Black;
// grandparent must be red. Why? Every red node that is not
// a leaf has only black children
insertedNode.Parent.Parent.Color = RedBlackNodeType.Red;
insertedNode = insertedNode.Parent.Parent; // continue loop with grandparent
}
else
{
// uncle is black; determine if newNode is greater than Parent
if (insertedNode == insertedNode.Parent.Right)
{ // yes, newNode is greater than Parent; rotate Left
// make newNode a Left child
insertedNode = insertedNode.Parent;
RotateLeft(insertedNode);
}
// no, newNode is less than Parent
insertedNode.Parent.Color = RedBlackNodeType.Black; // make Parent black
insertedNode.Parent.Parent.Color = RedBlackNodeType.Red; // make grandparent black
RotateRight(insertedNode.Parent.Parent); // rotate right
}
}
else
{ // newNode's Parent is on the Right subtree
// this code is the same as above with "Left" and "Right" swapped
workNode = insertedNode.Parent.Parent.Left;
if (workNode != null && workNode.Color == RedBlackNodeType.Red)
{
insertedNode.Parent.Color = RedBlackNodeType.Black;
workNode.Color = RedBlackNodeType.Black;
insertedNode.Parent.Parent.Color = RedBlackNodeType.Red;
insertedNode = insertedNode.Parent.Parent;
}
else
{
if (insertedNode == insertedNode.Parent.Left)
{
insertedNode = insertedNode.Parent;
RotateRight(insertedNode);
}
insertedNode.Parent.Color = RedBlackNodeType.Black;
insertedNode.Parent.Parent.Color = RedBlackNodeType.Red;
RotateLeft(insertedNode.Parent.Parent);
}
}
}
_treeBaseNode.Color = RedBlackNodeType.Black; // rbTree should always be black
}
///<summary>
/// BalanceTreeAfterDelete
/// Deletions from red-black trees may destroy the red-black
/// properties. Examine the tree and restore. Rotations are normally
/// required to restore it
///</summary>
private void BalanceTreeAfterDelete(RedBlackNode <TKey, TValue> linkedNode)
{
// maintain Red-Black tree balance after deleting node
while (linkedNode != _treeBaseNode && linkedNode.Color == RedBlackNodeType.Black)
{
RedBlackNode <TKey, TValue> workNode;
// determine sub tree from parent
if (linkedNode == linkedNode.Parent.Left)
{
// y is x's sibling
workNode = linkedNode.Parent.Right;
if (workNode.Color == RedBlackNodeType.Red)
{
// x is black, y is red - make both black and rotate
linkedNode.Parent.Color = RedBlackNodeType.Red;
workNode.Color = RedBlackNodeType.Black;
RotateLeft(linkedNode.Parent);
workNode = linkedNode.Parent.Right;
}
if (workNode.Left.Color == RedBlackNodeType.Black &&
workNode.Right.Color == RedBlackNodeType.Black)
{
// children are both black
// change parent to red
workNode.Color = RedBlackNodeType.Red;
// move up the tree
linkedNode = linkedNode.Parent;
}
else
{
if (workNode.Right.Color == RedBlackNodeType.Black)
{
workNode.Left.Color = RedBlackNodeType.Black;
workNode.Color = RedBlackNodeType.Red;
RotateRight(workNode);
workNode = linkedNode.Parent.Right;
}
linkedNode.Parent.Color = RedBlackNodeType.Black;
workNode.Color = linkedNode.Parent.Color;
workNode.Right.Color = RedBlackNodeType.Black;
RotateLeft(linkedNode.Parent);
linkedNode = _treeBaseNode;
}
}
else
{ // right subtree - same as code above with right and left swapped
workNode = linkedNode.Parent.Left;
if (workNode.Color == RedBlackNodeType.Red)
{
linkedNode.Parent.Color = RedBlackNodeType.Red;
workNode.Color = RedBlackNodeType.Black;
RotateRight(linkedNode.Parent);
workNode = linkedNode.Parent.Left;
}
if (workNode.Right.Color == RedBlackNodeType.Black &&
workNode.Left.Color == RedBlackNodeType.Black)
{
workNode.Color = RedBlackNodeType.Red;
linkedNode = linkedNode.Parent;
}
else
{
if (workNode.Left.Color == RedBlackNodeType.Black)
{
workNode.Right.Color = RedBlackNodeType.Black;
workNode.Color = RedBlackNodeType.Red;
RotateLeft(workNode);
workNode = linkedNode.Parent.Left;
}
workNode.Color = linkedNode.Parent.Color;
linkedNode.Parent.Color = RedBlackNodeType.Black;
workNode.Left.Color = RedBlackNodeType.Black;
RotateRight(linkedNode.Parent);
linkedNode = _treeBaseNode;
}
}
}
linkedNode.Color = RedBlackNodeType.Black;
}
///<summary>
/// Delete
/// Delete a node from the tree and restore red black properties
///</summary>
private void Delete(RedBlackNode <TKey, TValue> deleteNode)
{
// A node to be deleted will be:
// 1. a leaf with no children
// 2. have one child
// 3. have two children
// If the deleted node is red, the red black properties still hold.
// If the deleted node is black, the tree needs rebalancing
// work node
RedBlackNode <TKey, TValue> workNode;
// find the replacement node (the successor to x) - the node one with
// at *most* one child.
if (deleteNode.Left == SentinelNode || deleteNode.Right == SentinelNode)
{
// node has sentinel as a child
workNode = deleteNode;
}
else
{
// z has two children, find replacement node which will
// be the leftmost node greater than z
// traverse right subtree
workNode = deleteNode.Right;
// to find next node in sequence
while (workNode.Left != SentinelNode)
{
workNode = workNode.Left;
}
}
// at this point, y contains the replacement node. it's content will be copied
// to the valules in the node to be deleted
// x (y's only child) is the node that will be linked to y's old parent.
RedBlackNode <TKey, TValue> linkedNode = workNode.Left != SentinelNode
? workNode.Left
: workNode.Right;
// replace x's parent with y's parent and
// link x to proper subtree in parent
// this removes y from the chain
linkedNode.Parent = workNode.Parent;
if (workNode.Parent != null)
{
if (workNode == workNode.Parent.Left)
{
workNode.Parent.Left = linkedNode;
}
else
{
workNode.Parent.Right = linkedNode;
}
}
else
{
// make x the root node
_treeBaseNode = linkedNode;
}
// copy the values from y (the replacement node) to the node being deleted.
// note: this effectively deletes the node.
if (workNode != deleteNode)
{
deleteNode.Key = workNode.Key;
deleteNode.Data = workNode.Data;
}
if (workNode.Color == RedBlackNodeType.Black)
{
BalanceTreeAfterDelete(linkedNode);
}
_lastNodeFound = SentinelNode;
Interlocked.Decrement(ref _count);
InvokeOnRemove(new RedBlackEventArgs <TKey, TValue> {
Item = deleteNode.Data, Key = deleteNode.Key
});
}
///<summary>
/// Clear
/// Empties or clears the tree
///</summary>
public void Clear()
{
_treeBaseNode = SentinelNode;
_count = 0;
InvokeOnClear(new EventArgs());
}