public void Insert(int data)
{
RBTreeNode newNode;
RBTreeNode y = null;
RBTreeNode x;
if (Root == null) // Empty tree
{
Root = new RBTreeNode(data, red: false);
return;
}
newNode = new RBTreeNode(data); // Instantiate as Red node
x = Root;
// Traverse until y is a leaf in a location where x doesn’t violate
// the tree’s ordering
while (x != null)
{
y = x;
if (newNode < x)
{
x = x.Left();
}
else
{
x = x.Right();
}
}
// Make newNode child of y
newNode.SetParent(y);
if (newNode < y)
{
y.SetLeft(newNode);
}
else
{
y.SetRight(newNode);
}
RebalancePostInsertion(newNode);
}
private void RotateLeft(RBTreeNode x)
{
/**
* Make right subtree left subtree */
// setup x & y
RBTreeNode y = x.Right();
x.SetRight(y.Left());
// if y has a left child, make x the parent of the left child of y.
if (y.Left() != null)
{
y.Left().SetParent(x);
}
y.SetParent(x.Parent());
// if x has no parent, make y the root of the tree.
if (x.Parent() == null)
{
Root = y;
}
// else if x is the left child of p, make y the left child of p.
else if (x == x.Parent().Left())
{
x.Parent().SetLeft(y);
}
// else make y the right child of p
else
{
x.Parent().SetRight(y);
}
// make y the parent of x
y.SetLeft(x);
x.SetParent(y);
}
private void RotateRight(RBTreeNode y)
{
/**
* Make left subtree right subtree */
// setup x & y
RBTreeNode x = y.Left();
y.SetLeft(x.Right());
// if x has a right child, make y the parent of the right child of x.
if (x.Right() != null)
{
x.Right().SetParent(y);
}
x.SetParent(y.Parent());
// if y has no parent, make x the root of the tree.
if (y.Parent() == null)
{
Root = x;
}
// else if y is the right child of its parent p, make x the right child of p.
else if (y == y.Parent().Right())
{
y.Parent().SetRight(x);
}
// else assign x as the left child of p.
else
{
y.Parent().SetLeft(x);
}
// make x the parent of y.
x.SetRight(y);
y.SetParent(x);
}
private void Transplant(RBTreeNode oldNode, RBTreeNode newNode)
{
// Replace oldNode with newNode
RBTreeNode parent = oldNode.Parent();
if (parent == null)
{
Root = newNode;
}
else if (oldNode == parent.Left())
{
parent.SetLeft(newNode);
}
else
{
parent.SetRight(newNode);
}
// Null check for when newNode is null
if (newNode != null)
{
newNode.SetParent(parent);
}
}
public void SetRight(RBTreeNode rightChild)
{
RightChild = rightChild;
}
public void SetLeft(RBTreeNode leftChild)
{
LeftChild = leftChild;
}
public void SetParent(RBTreeNode parent)
{
ParentNode = parent;
}
public string VisualizeTree(RBTreeNode node, int verticalSpacing,
int indentPerLevel, bool print = true,
bool safeChars = true)
{
/**
* Parameters:
* node: RBTree node treated as the root in the visualization
* verticalSpacing: number of lines between each displayed node
* indentPerLevel: width of the line separating each level of the tree
* print: if true, write output to console
* safeChars: if true, use standard dash '-' character for horizontal lines.
* else, use the special full-width horizontal bar character
* which seems to occasionally break StringBuilder
*
* Note: functionality inspired by the following Baeldung article:
* https://www.baeldung.com/java-print-binary-tree-diagram */
string pointerChars;
if (safeChars)
{
pointerChars = new string('-', indentPerLevel);
}
else
{
pointerChars = new string('─', indentPerLevel);
}
string oneChildPointer = "└" + pointerChars;
string twoChildrenPointer = "├" + pointerChars;
string paddingChars = new string(' ', indentPerLevel + 1);
string twoChildrenIndent = "│" + paddingChars;
string whiteSpaceIndent = " " + paddingChars;
void Traverse(StringBuilder sb, String padding, String pointer,
RBTreeNode node, bool hasRightSibling)
{
if (node == null || node.IsEmpty())
{
return;
}
// Append vertical line spacing
for (int i = 0; i < verticalSpacing; i++)
{
sb.Append("\n" + padding);
if (pointer == whiteSpaceIndent)
{
sb.Append('|');
}
else
{
sb.Append("| ");
}
}
// Append line rows with values
sb.Append($"\n{padding}{pointer} {node.VisualizerString()}");
// Calculate and append padding next row
StringBuilder paddingSB = new StringBuilder(padding);
if (hasRightSibling)
{
paddingSB.Append(twoChildrenIndent);
}
else
{
paddingSB.Append(whiteSpaceIndent);
}
string newPadding = paddingSB.ToString();
// Determine pointer for next row
string pointerLeft =
(node.Right() != null) ? twoChildrenPointer : oneChildPointer;
// Recurse
Traverse(sb, newPadding, pointerLeft, node.Left(), node.Right() != null);
Traverse(sb, newPadding, oneChildPointer, node.Right(), false);
}
string TraversePreOrder(RBTreeNode root)
{
// Handle root
if (root == null)
{
return("Empty binary tree.");
}
StringBuilder sb = new StringBuilder();
sb.Append(root.GetData() + " (B)");
// Determine initial pointer
string pointerLeft =
(root.Right() != null) ? twoChildrenPointer : oneChildPointer;
Traverse(sb, "", pointerLeft, root.Left(), root.Right() != null);
Traverse(sb, "", oneChildPointer, root.Right(), false);
return(sb.ToString());
}
string prettyBinaryTree = TraversePreOrder(node);
if (print)
{
Console.WriteLine(prettyBinaryTree);
}
return(prettyBinaryTree);
}
public string PrintTreeTraversalOrder(int order, RBTreeNode treeRoot)
{
/**
* Output to console & return as string.
*
* Parameters:
* order: 1 -> Inorder
* 2 -> Preorder
* 3 -> Postorder
* treeRoot: the root node of the Red-Black tree to traverse */
// Helpers:
void PrintInOrder(RBTreeNode currRoot)
{
if (currRoot == null)
{
return;
}
PrintInOrder(currRoot.Left());
Console.Write($"{currRoot.GetData()}, ");
PrintInOrder(currRoot.Right());
}
void PrintPreOrder(RBTreeNode currRoot)
{
if (currRoot == null)
{
return;
}
Console.Write($"{currRoot.GetData()}, ");
PrintPreOrder(currRoot.Left());
PrintPreOrder(currRoot.Right());
}
void PrintPostOrder(RBTreeNode currRoot)
{
if (currRoot == null)
{
return;
}
PrintPostOrder(currRoot.Left());
PrintPostOrder(currRoot.Right());
Console.Write($"{currRoot.GetData()}, ");
}
// Write to string using console:
StringWriter sw = new StringWriter();
Console.SetOut(sw);
if (order == 1)
{
Console.Write("Inorder traversal: ");
PrintInOrder(treeRoot);
}
else if (order == 2)
{
Console.Write("Preorder traversal: ");
PrintPreOrder(treeRoot);
}
else if (order == 3)
{
Console.Write("Postorder traversal: ");
PrintPostOrder(treeRoot);
}
else
{
throw new Exception(
$"Invalid order parameter {order} when calling traverse.");
}
// store string & remove trailing comma & space
String output = sw.ToString();
output = output.Remove(output.Length - 2, 2);
// close StringWriter, reset standard out, print, and return
sw.Close();
var standardOutput = new StreamWriter(Console.OpenStandardOutput());
standardOutput.AutoFlush = true;
Console.SetOut(standardOutput);
Console.WriteLine(output);
return(output);
}
private void RebalancePostInsertion(RBTreeNode newNode)
{
/**
* Insert function places newNode as an appropriate leaf for a regular BST but
* not necessarily a Red-black tree. Check if newNode's parent is RED (ie. if it
* breaks a only red-black tree condition). If so, use the RED and BLACK labels
* of newNode's parent, grandparent, and/or pibling (aunt/uncle) to balance.
*
* Note on conceptualizing this process:
* At this point, newNode is a RED leaf whose addition may cause the tree to
* not meet the required RED-BLACK conditions (noted in class description)
* such that it is imbalanced beyond the red-black tree threshold. In order
* to correct for this, we re-balance and/or recolor the subtree rooted at
* newNode's grandparent. We perform this process iteratively, reassigning
* newNode to its decendants (parents/grandparents), until we reach the root.
* At no point do we consider ancestors of newNode.
*
* See this page for a more detailed overview of the process:
* https://www.geeksforgeeks.org/red-black-tree-set-2-insert/ */
if (newNode.GrandParent() == null)
{
return;
}
RBTreeNode u; // Will represent pibling (aunt/uncle) or parent of newNode.
// ie. given newNode's grandparent (gP), u can be either gP's
// left or right child
while (newNode.Parent().IsRed())
{
// Case: p is the RIGHT child of gP:
if (newNode.Parent() == newNode.GrandParent().Right())
{
// Set u as the (LEFT) pibling of newNode
u = newNode.GrandParent().Left();
// Case: u exists and is RED: set both u & p to BLACK, set gP to RED,
// assign newNode = gP
if (u != null && u.IsRed())
{
u.SetBlack();
newNode.Parent().SetBlack();
newNode.GrandParent().SetRed();
newNode = newNode.GrandParent();
}
else // Case: the (LEFT) pibling of newNode is BLACK
// Case: newNode is the left child of p: assign newNode = p and
// right rotate newNode
{
if (newNode == newNode.Parent().Left())
{
newNode = newNode.Parent();
RotateRight(newNode);
}
// Set p to BLACK and gP to RED. Then left rotate gP.
newNode.Parent().SetBlack();
newNode.GrandParent().SetRed();
RotateLeft(newNode.GrandParent());
}
}
else // Case: p is the LEFT child of gP:
// Assign u as the (RIGHT) pibling of newNode
{
u = newNode.GrandParent().Right();
// Case: u is RED: set the color of both children of gP to BLACK, set
// gp to RED. Assign gP = newNode.
if (u != null && u.IsRed())
{
u.SetBlack();
newNode.Parent().SetBlack();
newNode.GrandParent().SetRed();
newNode = newNode.GrandParent();
}
else
{
// Case: newNode is the right child of p then: set p = newNode.
// Then left rotate newNode.
if (newNode == newNode.Parent().Right())
{
newNode = newNode.Parent();
RotateLeft(newNode);
}
// Set color of p as BLACK and color of gP as RED. Then right
// rotate gP.
newNode.Parent().SetBlack();
newNode.GrandParent().SetRed();
RotateRight(newNode.GrandParent());
}
}
if (newNode == Root)
{
break;
}
}
Root.SetBlack();
}
public void Delete(RBTreeNode node, int value)
{
// Traverse until we find nodeToDelete
RBTreeNode nodeToDelete = null;
while (node != null)
{
if (node.GetData() == value)
{
nodeToDelete = node;
break;
}
node = (value < node.GetData()) ? node.Left() : node.Right();
}
if (nodeToDelete == null)
{
throw new Exception("Cannot find node to delete with " +
$"value {value} in Red Black Tree");
}
RBTreeNode x, y;
// Save the color of nodeToDelete
bool originallyRed = nodeToDelete.IsRed();
// If nodeToDelete only has left children, replace with its left subtree
if (nodeToDelete.Left() == null || nodeToDelete.Left().IsEmpty())
{
x = nodeToDelete.Right();
if (x == null)
{
x = Leaf;
}
Transplant(nodeToDelete, x);
// If nodeToDelete only has right children, replace with its right subtree
}
else if (nodeToDelete.Right() == null || nodeToDelete.Right().IsEmpty())
{
x = nodeToDelete.Left();
if (x == null)
{
x = Leaf;
}
Transplant(nodeToDelete, x);
}
else // nodeToDelete either has two children or is a leaf
// y = smallest node whose value is greater than that of nodeToDelete
// will replace nodeToDelete
{
y = Minimum(nodeToDelete.Right());
originallyRed = y.IsRed();
// x = subtree root with values greater than y
x = y.Right();
if (x == null)
{
x = Leaf;
}
// if y is a child of nodeToDelete, x is already stored in the right place
if (y.Parent() == nodeToDelete)
{
x.SetParent(y);
}
else // else replace y with its right subtree and update attributes
{
Transplant(y, y.Right());
y.SetRight(nodeToDelete.Right());
y.Right().SetParent(y);
}
// replace nodeToDelete with y and update attributes
Transplant(nodeToDelete, y);
y.SetLeft(nodeToDelete.Left());
y.Left().SetParent(y);
// y will replace nodeToDelete's location in tree, update its color
if (originallyRed)
{
y.SetRed();
}
else
{
y.SetBlack();
}
}
if (!(originallyRed))
{
RebalancePostDeletion(x);
}
}
private void RebalancePostDeletion(RBTreeNode node)
{
// Very similar to RebalancePostInsertion function
// node is the node in the location of/closest to the node just deleted
RBTreeNode s; // represents sibbling of node
while (node != Root && node.IsBlack())
{
if (node == node.Parent().Left())
{
s = node.Parent().Right();
if (s.IsRed()) // case 1
{
s.SetBlack();
node.Parent().SetRed();
RotateLeft(node.Parent());
s = node.Parent().Right();
}
if (s.Left().IsBlack() && s.Right().IsBlack()) // case 2
{
s.SetRed();
node = node.Parent();
}
else
{
if (s.Right().IsBlack()) // case 3
{
s.Left().SetBlack();
s.SetRed();
RotateRight(s);
s = node.Parent().Right();
}
if (s.Parent().IsRed())
{
s.SetRed();
}
else
{
s.SetBlack();
}
node.Parent().SetBlack();
s.Right().SetBlack();
RotateLeft(s.Parent());
node = Root;
}
}
else
{
s = node.Parent().Left();
if (s.IsRed())
{
s.SetBlack();
node.Parent().SetRed();
RotateRight(node.Parent());
s = node.Parent().Left();
}
if (s.Right() == null)
{
s.SetRight(Leaf);
}
if (s.Left() == null)
{
s.SetLeft(Leaf);
}
if (s.Right().IsBlack() && s.Left().IsBlack())
{
s.SetRed();
node = node.Parent();
}
else
{
if (s.Left().IsBlack())
{
s.Right().SetBlack();
s.SetRed();
RotateLeft(s);
s = node.Parent().Left();
}
if (s.Parent().IsRed())
{
s.SetRed();
}
else
{
s.SetBlack();
}
node.Parent().SetBlack();
s.Left().SetBlack();
RotateRight(node.Parent());
node = Root;
}
}
}
node.SetBlack();
}