/*************************************************************************************************/
/// <summary>
/// Insert data item to tree
/// </summary>
public override void Insert(TKey key, TValue value)
{
var newNode = new RedBlackTreeMapNode <TKey, TValue>(key, value);
// Invoke the super BST insert node method.
// This insert node recursively starting from the root and checks for success status (related to allowDuplicates flag).
// The functions increments count on its own.
var success = base._insertNode(newNode);
if (success == false && _allowDuplicates == false)
{
throw new InvalidOperationException("Tree does not allow inserting duplicate elements.");
}
// Adjust Red-Black Tree rules
if (!newNode.IsEqualTo(Root))
{
if (newNode.Parent.Color != RedBlackTreeColors.Black) // Case 0: Parent is not black and we have to restructure tree
{
_adjustTreeAfterInsertion(newNode);
}
}
// Always color root as black
Root.Color = RedBlackTreeColors.Black;
}
protected virtual RedBlackTreeColors _safeGetColor(RedBlackTreeMapNode <TKey, TValue> node)
{
if (node == null)
{
return(RedBlackTreeColors.Black);
}
return(node.Color);
}
protected RedBlackTreeMapNode <TKey, TValue> _safeGetRightChild(RedBlackTreeMapNode <TKey, TValue> node)
{
if (node == null)
{
return(null);
}
return(node.RightChild);
}
protected RedBlackTreeMapNode <TKey, TValue> _safeGetSibling(RedBlackTreeMapNode <TKey, TValue> node)
{
if (node == null || node.Parent == null)
{
return(null);
}
return(node.Sibling);
}
/*************************************************************************************************/
/***
* Safety Checks/Getters/Setters.
*
* The following are helper methods for safely checking, getting and updating possibly-null objects.
* These helpers make the algorithms of adjusting the tree after insertion and removal more readable.
*/
protected RedBlackTreeMapNode <TKey, TValue> _safeGetGrandParent(RedBlackTreeMapNode <TKey, TValue> node)
{
if (node == null || node.Parent == null)
{
return(null);
}
return(node.GrandParent);
}
protected virtual void _safeUpdateColor(RedBlackTreeMapNode <TKey, TValue> node, RedBlackTreeColors color)
{
if (node == null)
{
return;
}
node.Color = color;
}
/// <summary>
/// Rotates a node to the right in the Red-Black Tree.
/// </summary>
protected virtual void _rotateRightAt(RedBlackTreeMapNode <TKey, TValue> currentNode)
{
// We check the right child because it's going to be a pivot node for the rotation
if (currentNode == null || currentNode.HasLeftChild == false)
{
return;
}
// Pivot on *left* child
var pivotNode = currentNode.LeftChild;
// Parent of currentNode
var parent = currentNode.Parent;
// Check if currentNode is it's parent's left child.
bool isLeftChild = currentNode.IsLeftChild;
// Check if currentNode is the Root
bool isRootNode = (currentNode == this.Root);
// Perform the rotation
currentNode.LeftChild = pivotNode.RightChild;
pivotNode.RightChild = currentNode;
// Update parents references
currentNode.Parent = pivotNode;
pivotNode.Parent = parent;
if (currentNode.HasLeftChild)
{
currentNode.LeftChild.Parent = currentNode;
}
// Update the entire tree's Root if necessary
if (isRootNode)
{
this.Root = pivotNode;
}
// Update the original parent's child node
if (isLeftChild)
{
parent.LeftChild = pivotNode;
}
else if (parent != null)
{
parent.RightChild = pivotNode;
}
}
/// <summary>
/// The internal remove helper.
/// Separated from the overriden version to avoid casting the objects from BSTMapNode to RedBlackTreeMapNode.
/// This is called from the overriden _remove(BSTMapNode nodeToDelete) helper.
/// </summary>
protected bool _remove(RedBlackTreeMapNode <TKey, TValue> nodeToDelete)
{
if (nodeToDelete == null)
{
return(false);
}
// Temporary nodes
RedBlackTreeMapNode <TKey, TValue> node1, node2;
// If nodeToDelete has either one child or no children at all
if (!nodeToDelete.HasLeftChild || !nodeToDelete.HasRightChild)
{
node1 = nodeToDelete;
}
else
{
// nodeToDelete has two children
node1 = (RedBlackTreeMapNode <TKey, TValue>)base._findNextLarger(nodeToDelete);
}
// Left child case
if (node1.HasLeftChild)
{
node2 = node1.LeftChild;
}
else
{
node2 = node1.RightChild;
}
// If node2 is not null, copy parent references
if (node2 != null)
{
node2.Parent = node1.Parent;
}
if (node1.Parent != null)
{
if (node1.IsLeftChild)
{
node1.Parent.LeftChild = node2;
}
else
{
node1.Parent.RightChild = node2;
}
}
else
{
Root = node2;
Root.Parent = null;
}
// Swap values
if (!node1.IsEqualTo(nodeToDelete))
{
nodeToDelete.Key = node1.Key;
nodeToDelete.Value = node1.Value;
}
// Adjust the Red-Black Tree rules
if (node1.Color == RedBlackTreeColors.Black && node2 != null)
{
_adjustTreeAfterRemoval(node2);
Root.Color = RedBlackTreeColors.Black;
}
// Decrement the count
base._count--;
return(true);
}
/// <summary>
/// After removal tree-adjustement helper.
/// </summary>
protected virtual void _adjustTreeAfterRemoval(RedBlackTreeMapNode <TKey, TValue> currentNode)
{
while (currentNode != null && currentNode != Root && currentNode.IsBlack)
{
if (currentNode.IsLeftChild)
{
// Get sibling of currentNode
// Safe equivalent of currentNode.Sibling or currentNode.Parent.RightChild
var sibling = _safeGetRightChild(_safeGetParent(currentNode));
// Safely check sibling.IsRed property
if (_safeCheckIsRed(sibling))
{
// Color currentNode.Sibling as black
_safeUpdateColor(sibling, RedBlackTreeColors.Black);
// Color currentNode.Parent as red
_safeUpdateColor(_safeGetParent(currentNode), RedBlackTreeColors.Red);
// Left Rotate on currentNode's parent
_rotateLeftAt(_safeGetParent(currentNode));
// Update sibling reference
// Might end be being set to null
sibling = _safeGetRightChild(_safeGetParent(currentNode));
}
// Check if the left and right children of the sibling node are black
// Use the safe methods to check for: (sibling.LeftChild.IsBlack && sibling.RightChild.IsBlack)
if (_safeCheckIsBlack(_safeGetLeftChild(sibling)) && _safeCheckIsBlack(_safeGetRightChild(sibling)))
{
// Color currentNode.Sibling as red
_safeUpdateColor(sibling, RedBlackTreeColors.Red);
// Assign currentNode.Parent to currentNode
currentNode = _safeGetParent(currentNode);
}
else
{
if (_safeCheckIsBlack(_safeGetRightChild(sibling)))
{
// Color currentNode.Sibling.LeftChild as black
_safeUpdateColor(_safeGetLeftChild(sibling), RedBlackTreeColors.Black);
// Color currentNode.Sibling as red
_safeUpdateColor(sibling, RedBlackTreeColors.Red);
// Right Rotate on sibling
_rotateRightAt(sibling);
// Update sibling reference
// Might end be being set to null
sibling = _safeGetRightChild(_safeGetParent(currentNode));
}
// Color the Sibling node as currentNode.Parent.Color
_safeUpdateColor(sibling, _safeGetColor(_safeGetParent(currentNode)));
// Color currentNode.Parent as black
_safeUpdateColor(_safeGetParent(currentNode), RedBlackTreeColors.Black);
// Color Sibling.RightChild as black
_safeUpdateColor(_safeGetRightChild(sibling), RedBlackTreeColors.Black);
// Rotate on currentNode's parent
_rotateLeftAt(_safeGetParent(currentNode));
currentNode = Root;
}
}
else
{
// Get sibling of currentNode
// Safe equivalent of currentNode.Sibling or currentNode.Parent.LeftChild
var sibling = _safeGetLeftChild(_safeGetParent(currentNode));
if (_safeCheckIsRed(sibling))
{
// Color currentNode.Sibling as black
_safeUpdateColor(sibling, RedBlackTreeColors.Black);
// Color currentNode.Parent as red
_safeUpdateColor(_safeGetParent(currentNode), RedBlackTreeColors.Red);
// Right Rotate tree around the parent of currentNode
_rotateRightAt(_safeGetParent(currentNode));
// Update sibling reference
// Might end be being set to null
sibling = _safeGetLeftChild(_safeGetParent(currentNode));
}
// Check if the left and right children of the sibling node are black
// Use the safe methods to check for: (sibling.LeftChild.IsBlack && sibling.RightChild.IsBlack)
if (_safeCheckIsBlack(_safeGetLeftChild(sibling)) && _safeCheckIsBlack(_safeGetRightChild(sibling)))
{
_safeUpdateColor(sibling, RedBlackTreeColors.Red);
// Assign currentNode.Parent to currentNode
currentNode = _safeGetParent(currentNode);
}
else
{
// Check if sibling.LeftChild.IsBlack == true
if (_safeCheckIsBlack(_safeGetLeftChild(sibling)))
{
// Color currentNode.Sibling.RightChild as black
_safeUpdateColor(_safeGetRightChild(sibling), RedBlackTreeColors.Black);
// Color currentNode.Sibling as red
_safeUpdateColor(sibling, RedBlackTreeColors.Red);
// Left rotate on sibling
_rotateLeftAt(sibling);
// Update sibling reference
// Might end be being set to null
sibling = _safeGetLeftChild(_safeGetParent(currentNode));
}
// Color the Sibling node as currentNode.Parent.Color
_safeUpdateColor(sibling, _safeGetColor(_safeGetParent(currentNode)));
// Color currentNode.Parent as black
_safeUpdateColor(_safeGetParent(currentNode), RedBlackTreeColors.Black);
// Color Sibling.RightChild as black
_safeUpdateColor(_safeGetLeftChild(sibling), RedBlackTreeColors.Black);
// Right rotate on the parent of currentNode
_rotateRightAt(_safeGetParent(currentNode));
currentNode = Root;
}
}
}
// Color currentNode as black
_safeUpdateColor(currentNode, RedBlackTreeColors.Black);
}
/// <summary>
/// After insertion tree-adjustement helper.
/// </summary>
protected virtual void _adjustTreeAfterInsertion(RedBlackTreeMapNode <TKey, TValue> currentNode)
{
//
// STEP 1:
// Color the currentNode as red
_safeUpdateColor(currentNode, RedBlackTreeColors.Red);
//
// STEP 2:
// Fix the double red-consecutive-nodes problems, if there exists any.
if (currentNode != null && currentNode != Root && _safeCheckIsRed(_safeGetParent(currentNode)))
{
//
// STEP 2.A:
// This is the simplest step: Basically recolor, and bubble up to see if more work is needed.
if (_safeCheckIsRed(_safeGetSibling(currentNode.Parent)))
{
// If it has a sibling and it is red, then then it has a parent
currentNode.Parent.Color = RedBlackTreeColors.Red;
// Color sibling of parent as black
_safeUpdateColor(_safeGetSibling(currentNode.Parent), RedBlackTreeColors.Black);
// Color grandparent as red
_safeUpdateColor(_safeGetGrandParent(currentNode), RedBlackTreeColors.Red);
// Adjust on the grandparent of currentNode
_adjustTreeAfterInsertion(_safeGetGrandParent(currentNode));
}
//
// STEP 2.B:
// Restructure the tree if the parent of currentNode is a left child to the grandparent of currentNode
// (parent is a left child to its own parent).
// If currentNode is also a left child, then do a single right rotation; otherwise, a left-right rotation.
//
// using the safe methods to check: currentNode.Parent.IsLeftChild == true
else if (_safeGetParent(currentNode) == _safeGetLeftChild(_safeGetGrandParent(currentNode)))
{
if (currentNode.IsRightChild)
{
currentNode = _safeGetParent(currentNode);
_rotateLeftAt(currentNode);
}
// Color parent as black
_safeUpdateColor(_safeGetParent(currentNode), RedBlackTreeColors.Black);
// Color grandparent as red
_safeUpdateColor(_safeGetGrandParent(currentNode), RedBlackTreeColors.Red);
// Right Rotate tree around the currentNode's grand parent
_rotateRightAt(_safeGetGrandParent(currentNode));
}
//
// STEP 2.C:
// Restructure the tree if the parent of currentNode is a right child to the grandparent of currentNode
// (parent is a right child to its own parent).
// If currentNode is a right-child in it's parent, then do a single left rotation; otherwise a right-left rotation.
//
// using the safe methods to check: currentNode.Parent.IsRightChild == true
else if (_safeGetParent(currentNode) == _safeGetRightChild(_safeGetGrandParent(currentNode)))
{
if (currentNode.IsLeftChild)
{
currentNode = _safeGetParent(currentNode);
_rotateRightAt(currentNode);
}
// Color parent as black
_safeUpdateColor(_safeGetParent(currentNode), RedBlackTreeColors.Black);
// Color grandparent as red
_safeUpdateColor(_safeGetGrandParent(currentNode), RedBlackTreeColors.Red);
// Left Rotate tree around the currentNode's grand parent
_rotateLeftAt(_safeGetGrandParent(currentNode));
}
}
// STEP 3:
// Color the root node as black
_safeUpdateColor(Root, RedBlackTreeColors.Black);
}
protected virtual bool _safeCheckIsRed(RedBlackTreeMapNode <TKey, TValue> node)
{
return(node != null && node.IsRed);
}