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<!DOCTYPE html>

<head>

<title>Red Black Tree</title>

window.dataLayer = window.dataLayer || [];

function gtag() { dataLayer.push(arguments); }

gtag('js', new Date());

gtag('config', 'G-HCERBDV76D');

</script>

</head>

<body>

<nav>

Python Tutorial

</a>

</div>

</div>

</div>

<li>

Home

</a>

</li>

<li>

Projects

</a>

</li>

<li>

Free Course

</a>

</li>

<li>

DSA

</a>

</li>

</ul>

</div>

</nav>

</div>

<h3>Page Index</h3>

<ul>

<li><a href="/dsa.html#data-structure-1" title="Data Structures (I)">Data Structures

(I)</a></li>

<li><a href="/dsa.html#data-structure-2" title="Data Structures (II)">Data Structures

(II)</a></li>

<li><a href="/dsa.html#tree-1" title="Tree based DSA (I)">Tree based DSA (I)</a></li>

<li><a href="/dsa.html#tree-2" title="Tree based DSA (II)">Tree based DSA (II)</a></li>

<li><a href="/dsa.html#graph" title="Graph Data Structures and Algorithm">Graph based

DSA</a></li>

<li><a href="/dsa.html#sorting-searching" title="Sorting and Searching">Sorting and

Searching</a></li>

<li><a href="/dsa.html#greedy-algorithm" title="Greedy Algorithms">Greedy Algorithms</a>

</li>

<li><a href="/dsa.html#dynamic-programming" title="Dynamic Programming">Dynamic

Programming</a></li>

<li><a href="/dsa.html#other-algorithms" title="Other Algorithms">Other Algorithms</a>

</li>

</ul>

</div>

<h1>Red-Black Tree</h1>

In this tutorial, you will learn what a red-black tree is. Also, you will find working examples of various operations performed on a red-black tree in C, C++, Java and Python.

Red-Black tree is a self-balancing binary search tree in which each node contains an extra bit for denoting the color of the node, either red or black.

A red-black tree satisfies the following properties:

<ol><li>Red/Black Property: Every node is colored, either red or black.</li>

<li>Root Property: The root is black.</li>

<li>Leaf Property: Every leaf (NIL) is black.</li>

<li>Red Property: If a red node has children then, the children are always black.</li>

<li>Depth Property: For each node, any simple path from this node to any of its descendant leaf has the same black-depth (the number of black nodes).</li>

</ol>An example of a red-black tree is:

<figure><img alt="red-black tree" src="//cdn.programiz.com/sites/tutorial2program/files/red-black-tree_0.png" title="red-black tree" width="500" height="358"><figcaption>Red Black Tree</figcaption></figure>Each node has the following attributes:

<ul><li>color</li>

<li>leftChild</li>

<li>rightChild</li>

<li>parent (except root node)</li>

</ul><hr>How the red-black tree maintains the property of self-balancing?

The red-black color is meant for balancing the tree.

The limitations put on the node colors ensure that any simple path from the root to a leaf is not more than twice as long as any other such path. It helps in maintaining the self-balancing property of the red-black tree.

<hr><h2>Operations on a Red-Black Tree</h2>

Various operations that can be performed on a red-black tree are:

<h3 id="rotation">Rotating the subtrees in a Red-Black Tree</h3>

In rotation operation, the positions of the nodes of a subtree are interchanged.

Rotation operation is used for maintaining the properties of a red-black tree when they are violated by other operations such as insertion and deletion.

There are two types of rotations:

<hr><h3>Left Rotate</h3>

In left-rotation, the arrangement of the nodes on the right is transformed into the arrangements on the left node.

Algorithm

<ol><li>Let the initial tree be:

<figure><img alt="left-rotate" src="//cdn.programiz.com/sites/tutorial2program/files/leftrotate-1_0.png" title="Initial Tree" width="150" height="177"><figcaption>Initial tree</figcaption></figure></li>

<li>If <var>y</var> has a left subtree, assign <var>x</var> as the parent of the left subtree of <var>y</var>.

<figure><img alt="left-rotate" src="//cdn.programiz.com/sites/tutorial2program/files/leftrotate-2_0.png" title="Assign x as the parent of the left subtree of y" width="150" height="136"><figcaption>Assign x as the parent of the left subtree of y</figcaption></figure></li>

<li>If the parent of <var>x</var> is <code>NULL</code>, make <var>y</var> as the root of the tree.</li>

<li>Else if <var>x</var> is the left child of <var>p</var>, make <var>y</var> as the left child of <var>p</var>.</li>

<li>Else assign <var>y</var> as the right child of <var>p</var>.

<figure><img alt="left-rotate" src="//cdn.programiz.com/sites/tutorial2program/files/leftrotate-3_0.png" title="change the parent of x to that of y" width="150" height="117"><figcaption>Change the parent of x to that of y</figcaption></figure></li>

<li>Make <var>y</var> as the parent of <var>x</var>.

<figure><img alt="left-rotate" src="//cdn.programiz.com/sites/tutorial2program/files/leftrotate-4_0.png" title="Assign y as the parent of x." width="150" height="167"><figcaption>Assign y as the parent of x.</figcaption></figure></li>

</ol><hr><h3>Right Rotate</h3>

In right-rotation, the arrangement of the nodes on the left is transformed into the arrangements on the right node.

<ol><li>Let the initial tree be:

<figure><img alt="right-rotate" src="//cdn.programiz.com/sites/tutorial2program/files/rightrotate-1_0.png" title="initial tree" width="150" height="168"><figcaption>Initial Tree</figcaption></figure></li>

<li>If <var>x</var> has a right subtree, assign y as the parent of the right subtree of <var>x</var>.

<figure><img alt="right-rotate" src="//cdn.programiz.com/sites/tutorial2program/files/rightrotate-2_0.png" title="assign y as the parent of the right subtree of x." width="150" height="140"><figcaption>Assign y as the parent of the right subtree of x</figcaption></figure></li>

<li>If the parent of <var>y</var> is <code>NULL</code>, make <var>x</var> as the root of the tree.</li>

<li>Else if <var>y</var> is the right child of its parent <var>p</var>, make <var>x</var> as the right child of <var>p</var>.</li>

<li>Else assign <var>x</var> as the left child of <var>p</var>.

<figure><img alt="right-rotate" src="//cdn.programiz.com/sites/tutorial2program/files/rightrotate-3_0.png" title="Assign the parent of y as the parent of x." width="150" height="121"><figcaption>Assign the parent of y as the parent of x</figcaption></figure></li>

<li>Make <var>x</var> as the parent of <var>y</var>.

<figure><img alt="right-rotate" src="//cdn.programiz.com/sites/tutorial2program/files/rightrotate-4_0.png" title="assign x as the parent of y" width="150" height="168"><figcaption>Assign x as the parent of y</figcaption></figure></li>

</ol><hr><h3>Left-Right and Right-Left Rotate</h3>

In left-right rotation, the arrangements are first shifted to the left and then to the right.

<ol><li>Do left rotation on x-y.

<figure><img alt="left-right rotate" src="//cdn.programiz.com/sites/tutorial2program/files/leftright-rotate-1_0.png" title="left rotate x-y" width="375" height="205"><figcaption>Left rotate x-y</figcaption></figure></li>

<li>Do right rotation on y-z.

<figure><img alt="left-right rotate" src="//cdn.programiz.com/sites/tutorial2program/files/leftright-rotate-2_0.png" title="right rotate z-y" width="375" height="194"><figcaption>Right rotate z-y</figcaption></figure></li>

</ol><div class="clearfix"></div>In right-left rotation, the arrangements are first shifted to the right and then to the left.

<ol><li>Do right rotation on x-y.

<figure><img alt="right-left rotate" src="//cdn.programiz.com/sites/tutorial2program/files/rightleft-rotate-1_0.png" title="right rotate x-y" width="375" height="200"><figcaption>Right rotate x-y</figcaption></figure></li>

<li>Do left rotation on z-y.

<figure><img alt="right-left rotate" src="//cdn.programiz.com/sites/tutorial2program/files/rightleft-rotate-2_0.png" title="left rotate z-y" width="375" height="196"><figcaption>Left rotate z-y</figcaption></figure></li>

</ol><hr><h3 id="insertion">Inserting an element into a Red-Black Tree</h3>

While inserting a new node, the new node is always inserted as a RED node. After insertion of a new node, if the tree is violating the properties of the red-black tree then, we do the following operations.

<ol><li>Recolor</li>

<li>Rotation</li>

</ol><hr><h3>Algorithm to insert a node</h3>

Following steps are followed for inserting a new element into a red-black tree:

<li>Check if the tree is empty (ie. whether <var>x</var> is <code>NIL</code>). If yes, insert <var>newNode</var> as a root node and color it black.</li>

<li>Else, repeat steps following steps until leaf (<code>NIL</code>) is reached.

<ol type="a"><li>Compare <var>newKey</var> with <var>rootKey</var>.</li>

<li>If <var>newKey</var> is greater than rootKey, traverse through the right subtree.</li>

<li>Else traverse through the left subtree.</li>

</ol></li>

<li>Assign the parent of the leaf as a parent of <var>newNode</var>.</li>

<li>If <var>leafKey</var> is greater than <var>newKey</var>, make <var>newNode</var> as <var>rightChild</var>.</li>

<li>Else, make <var>newNode</var> as <var>leftChild</var>.</li>

<li>Assign <code>NULL</code> to the left and <var>rightChild</var> of <var>newNode</var>.</li>

<li>Assign RED color to <var>newNode</var>.</li>

<li>Call InsertFix-algorithm to maintain the property of red-black tree if violated.</li>

</ol><hr>Why newly inserted nodes are always red in a red-black tree?

This is because inserting a red node does not violate the depth property of a red-black tree.

If you attach a red node to a red node, then the rule is violated but it is easier to fix this problem than the problem introduced by violating the depth property.

<hr><h3>Algorithm to maintain red-black property after insertion</h3>

This algorithm is used for maintaining the property of a red-black tree if the insertion of a newNode violates this property.

<ol><li>Do the following while the parent of <var>newNode</var> <var>p</var> is RED.</li>

<li>If <var>p</var> is the left child of <var>grandParent</var> <var>gP</var> of <var>z</var>, do the following. Case-I:

<ol type="a"><li>If the color of the right child of <var>gP</var> of <var>z</var> is RED, set the color of both the children of <var>gP</var> as BLACK and the color of <var>gP</var> as RED.</li>

<li>Assign <var>gP</var> to <var>newNode</var>. Case-II:</li>

<li>Else if <var>newNode</var> is the right child of <var>p</var> then, assign <var>p</var> to <var>newNode</var>.</li>

<li>Left-Rotate <var>newNode</var>. Case-III:</li>

<li>Set color of <var>p</var> as BLACK and color of <var>gP</var> as RED.</li>

<li>Right-Rotate <var>gP</var>.</li>

</ol></li>

<li>Else, do the following.

<ol type="a"><li>If the color of the left child of <var>gP</var> of <var>z</var> is RED, set the color of both the children of <var>gP</var> as BLACK and the color of <var>gP</var> as RED.</li>

<li>Assign <var>gP</var> to <var>newNode</var>.</li>

<li>Else if newNode is the left child of <var>p</var> then, assign <var>p</var> to <var>newNode</var> and Right-Rotate <var>newNode</var>.</li>

<li>Set color of <var>p</var> as BLACK and color of <var>gP</var> as RED.</li>

<li>Left-Rotate <var>gP</var>.</li>

</ol></li>

<li>Set the root of the tree as BLACK.</li>

</ol><hr><h3 id="deletion">Deleting an element from a Red-Black Tree</h3>

This operation removes a node from the tree. After deleting a node, the red-black property is maintained again.

<hr><h3>Algorithm to delete a node</h3>

<ol><li>Save the color of <var>nodeToBeDeleted</var> in <var>origrinalColor</var>.</li>

<li>If the left child of <var>nodeToBeDeleted</var> is <code>NULL</code>

<ol type="a"><li>Assign the right child of <var>nodeToBeDeleted</var> to x.</li>

<li>Transplant <var>nodeToBeDeleted</var> with <var>x</var>.</li>

</ol></li>

<li>Else if the right child of <var>nodeToBeDeleted</var> is <code>NULL</code>

<ol type="a"><li>Assign the left child of <var>nodeToBeDeleted</var> into <var>x</var>.</li>

<li>Transplant <var>nodeToBeDeleted</var> with <var>x</var>.</li>

</ol></li>

<li>Else

<ol type="a"><li>Assign the minimum of right subtree of <var>noteToBeDeleted</var> into <var>y</var>.</li>

<li>Save the color of <var>y</var> in <var>originalColor</var>.</li>

<li>Assign the <var>rightChild</var> of <var>y</var> into <var>x</var>.</li>

<li>If <var>y</var> is a child of <var>nodeToBeDeleted</var>, then set the parent of <var>x</var> as <var>y</var>.</li>

<li>Else, transplant <var>y</var> with <var>rightChild</var> of <var>y</var>.</li>

<li>Transplant <var>nodeToBeDeleted</var> with <var>y</var>.</li>

<li>Set the color of y with originalColor.</li>

</ol></li>

<li>If the <var>originalColor</var> is BLACK, call DeleteFix(x).</li>

</ol><hr><h3>Algorithm to maintain Red-Black property after deletion</h3>

This algorithm is implemented when a black node is deleted because it violates the black depth property of the red-black tree.

This violation is corrected by assuming that node <var>x</var> (which is occupying <var>y</var>'s original position) has an extra black. This makes node <var>x</var> neither red nor black. It is either doubly black or black-and-red. This violates the red-black properties.

However, the color attribute of <var>x</var> is not changed rather the extra black is represented in <var>x</var>'s pointing to the node.

The extra black can be removed if

<ol><li>It reaches the root node.</li>

<li>If <var>x</var> points to a red-black node. In this case, <var>x</var> is colored black.</li>

<li>Suitable rotations and recoloring are performed.</li>

</ol>The following algorithm retains the properties of a red-black tree.

<ol><li>Do the following until the <var>x</var> is not the root of the tree and the color of <var>x</var> is BLACK</li>

<li>If <var>x</var> is the left child of its parent then,

<ol type="a"><li>Assign w to the sibling of x.</li>

<li>If the right child of parent of <var>x</var> is RED, Case-I:

<ol type="i"><li>Set the color of the right child of the parent of <var>x</var> as BLACK.</li>

<li>Set the color of the parent of <var>x</var> as RED.</li>

<li>Left-Rotate the parent of <var>x</var>.</li>

<li>Assign the <var>rightChild</var> of the parent of <var>x</var> to <var>w</var>.</li>

</ol></li>

<li>If the color of both the right and the <var>leftChild</var> of <var>w</var> is BLACK, Case-II:

<ol type="i"><li>Set the color of <var>w</var> as RED</li>

<li>Assign the parent of <var>x</var> to <var>x</var>.</li>

</ol></li>

<li>Else if the color of the <var>rightChild</var> of <var>w</var> is BLACK Case-III:

<ol type="i"><li>Set the color of the <var>leftChild</var> of <var>w</var> as BLACK</li>

<li>Set the color of <var>w</var> as RED</li>

<li>Right-Rotate <var>w</var>.</li>

<li>Assign the <var>rightChild</var> of the parent of <var>x</var> to <var>w.</var></li>

</ol></li>

<li>If any of the above cases do not occur, then do the following. Case-IV:

<ol type="i"><li>Set the color of <var>w</var> as the color of the parent of <var>x</var>.</li>

<li>Set the color of the parent of <var>x</var> as BLACK.</li>

<li>Set the color of the right child of <var>w</var> as BLACK.</li>

<li>Left-Rotate the parent of <var>x</var>.</li>

</ol></li>

<li>Else the same as above with right changed to left and vice versa.</li>

<li>Set the color of <var>x</var> as BLACK.</li>

</ol><hr>Please refer to <a href="/dsa/insertion-in-a-red-black-tree.html">insertion</a> and <a href="/deletion-from-a-red-black-tree.html">deletion</a> operations for more explanation with examples.

<hr><h2 id="examples">Python, Java and C/C++ Examples</h2>

<div id="py1" onclick="changepy()" class="tabbed-editor__node tabbed-editor__node--active"><a href="#python-code">Python</a></div>

</div>

<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"># Implementing Red-Black Tree in Python

import sys

# Node creation

class Node():

def __init__(self, item):

self.item = item

self.parent = None

self.left = None

self.right = None

self.color = 1

class RedBlackTree():

def __init__(self):

self.TNULL = Node(0)

self.TNULL.color = 0

self.TNULL.left = None

self.TNULL.right = None

self.root = self.TNULL

# Preorder

def pre_order_helper(self, node):

if node != TNULL:

sys.stdout.write(node.item + " ")

self.pre_order_helper(node.left)

self.pre_order_helper(node.right)

# Inorder

def in_order_helper(self, node):

if node != TNULL:

self.in_order_helper(node.left)

sys.stdout.write(node.item + " ")

self.in_order_helper(node.right)

# Postorder

def post_order_helper(self, node):

if node != TNULL:

self.post_order_helper(node.left)

self.post_order_helper(node.right)

sys.stdout.write(node.item + " ")

# Search the tree

def search_tree_helper(self, node, key):

if node == TNULL or key == node.item:

return node

if key < node.item:

return self.search_tree_helper(node.left, key)

return self.search_tree_helper(node.right, key)

# Balancing the tree after deletion

def delete_fix(self, x):

while x != self.root and x.color == 0:

if x == x.parent.left:

s = x.parent.right

if s.color == 1:

s.color = 0

x.parent.color = 1

self.left_rotate(x.parent)

s = x.parent.right

if s.left.color == 0 and s.right.color == 0:

s.color = 1

x = x.parent

else:

if s.right.color == 0:

s.left.color = 0

s.color = 1

self.right_rotate(s)

s = x.parent.right

s.color = x.parent.color

x.parent.color = 0

s.right.color = 0

self.left_rotate(x.parent)

x = self.root

else:

s = x.parent.left

if s.color == 1:

s.color = 0

x.parent.color = 1

self.right_rotate(x.parent)

s = x.parent.left

if s.right.color == 0 and s.right.color == 0:

s.color = 1

x = x.parent

else:

if s.left.color == 0:

s.right.color = 0

s.color = 1

self.left_rotate(s)

s = x.parent.left

s.color = x.parent.color

x.parent.color = 0

s.left.color = 0

self.right_rotate(x.parent)

x = self.root

x.color = 0

def __rb_transplant(self, u, v):

if u.parent == None:

self.root = v

elif u == u.parent.left:

u.parent.left = v

else:

u.parent.right = v

v.parent = u.parent

# Node deletion

def delete_node_helper(self, node, key):

z = self.TNULL

while node != self.TNULL:

if node.item == key:

z = node

if node.item <= key:

node = node.right

else:

node = node.left

if z == self.TNULL:

print("Cannot find key in the tree")

return

y = z

y_original_color = y.color

if z.left == self.TNULL:

x = z.right

self.__rb_transplant(z, z.right)

elif (z.right == self.TNULL):

x = z.left

self.__rb_transplant(z, z.left)

else:

y = self.minimum(z.right)

y_original_color = y.color

x = y.right

if y.parent == z:

x.parent = y

else:

self.__rb_transplant(y, y.right)

y.right = z.right

y.right.parent = y

self.__rb_transplant(z, y)

y.left = z.left

y.left.parent = y

y.color = z.color

if y_original_color == 0:

self.delete_fix(x)

# Balance the tree after insertion

def fix_insert(self, k):

while k.parent.color == 1:

if k.parent == k.parent.parent.right:

u = k.parent.parent.left

if u.color == 1:

u.color = 0

k.parent.color = 0

k.parent.parent.color = 1

k = k.parent.parent

else:

if k == k.parent.left:

k = k.parent

self.right_rotate(k)

k.parent.color = 0

k.parent.parent.color = 1

self.left_rotate(k.parent.parent)

else:

u = k.parent.parent.right

if u.color == 1:

u.color = 0

k.parent.color = 0

k.parent.parent.color = 1

k = k.parent.parent

else:

if k == k.parent.right:

k = k.parent

self.left_rotate(k)

k.parent.color = 0

k.parent.parent.color = 1

self.right_rotate(k.parent.parent)

if k == self.root:

break

self.root.color = 0

# Printing the tree

def __print_helper(self, node, indent, last):

if node != self.TNULL:

sys.stdout.write(indent)

if last:

sys.stdout.write("R----")

indent += " "

else:

sys.stdout.write("L----")

indent += "| "

s_color = "RED" if node.color == 1 else "BLACK"

print(str(node.item) + "(" + s_color + ")")

self.__print_helper(node.left, indent, False)

self.__print_helper(node.right, indent, True)

def preorder(self):

self.pre_order_helper(self.root)

def inorder(self):

self.in_order_helper(self.root)

def postorder(self):

self.post_order_helper(self.root)

def searchTree(self, k):

return self.search_tree_helper(self.root, k)

def minimum(self, node):

while node.left != self.TNULL:

node = node.left

return node

def maximum(self, node):

while node.right != self.TNULL:

node = node.right

return node

def successor(self, x):

if x.right != self.TNULL:

return self.minimum(x.right)

y = x.parent

while y != self.TNULL and x == y.right:

x = y

y = y.parent

return y

def predecessor(self, x):

if (x.left != self.TNULL):

return self.maximum(x.left)

y = x.parent

while y != self.TNULL and x == y.left:

x = y

y = y.parent

return y

def left_rotate(self, x):

y = x.right

x.right = y.left

if y.left != self.TNULL:

y.left.parent = x

y.parent = x.parent

if x.parent == None:

self.root = y

elif x == x.parent.left:

x.parent.left = y

else:

x.parent.right = y

y.left = x

x.parent = y

def right_rotate(self, x):

y = x.left

x.left = y.right

if y.right != self.TNULL:

y.right.parent = x

y.parent = x.parent

if x.parent == None:

self.root = y

elif x == x.parent.right:

x.parent.right = y

else:

x.parent.left = y

y.right = x

x.parent = y

def insert(self, key):

node = Node(key)

node.parent = None

node.item = key

node.left = self.TNULL

node.right = self.TNULL

node.color = 1

y = None

x = self.root

while x != self.TNULL:

y = x

if node.item < x.item:

x = x.left

else:

x = x.right

node.parent = y

if y == None:

self.root = node

elif node.item < y.item:

y.left = node

else:

y.right = node

if node.parent == None:

node.color = 0

return

if node.parent.parent == None:

return

self.fix_insert(node)

def get_root(self):

return self.root

def delete_node(self, item):

self.delete_node_helper(self.root, item)

def print_tree(self):

self.__print_helper(self.root, "", True)

if __name__ == "__main__":

bst = RedBlackTree()

bst.insert(55)

bst.insert(40)

bst.insert(65)

bst.insert(60)

bst.insert(75)

bst.insert(57)

bst.print_tree()

print("\nAfter deleting an element")

bst.delete_node(40)

bst.print_tree()

</code></pre></div>

</div>

<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs">// Implementing Red-Black Tree in Java

class Node {

int data;

Node parent;

Node left;

Node right;

int color;

}

public class RedBlackTree {

private Node root;

private Node TNULL;

// Preorder

private void preOrderHelper(Node node) {

if (node != TNULL) {

System.out.print(node.data + " ");

preOrderHelper(node.left);

preOrderHelper(node.right);

}

// Inorder

private void inOrderHelper(Node node) {

if (node != TNULL) {

inOrderHelper(node.left);

System.out.print(node.data + " ");

inOrderHelper(node.right);

}

// Post order

private void postOrderHelper(Node node) {

if (node != TNULL) {

postOrderHelper(node.left);

postOrderHelper(node.right);

System.out.print(node.data + " ");

}

// Search the tree

private Node searchTreeHelper(Node node, int key) {

if (node == TNULL || key == node.data) {

return node;

}

if (key < node.data) {

return searchTreeHelper(node.left, key);

}

return searchTreeHelper(node.right, key);

}

// Balance the tree after deletion of a node

private void fixDelete(Node x) {

Node s;

while (x != root && x.color == 0) {

if (x == x.parent.left) {

s = x.parent.right;

if (s.color == 1) {

s.color = 0;

x.parent.color = 1;

leftRotate(x.parent);

s = x.parent.right;

}

if (s.left.color == 0 && s.right.color == 0) {

s.color = 1;

x = x.parent;

} else {

if (s.right.color == 0) {

s.left.color = 0;

s.color = 1;

rightRotate(s);

s = x.parent.right;

}

s.color = x.parent.color;

x.parent.color = 0;

s.right.color = 0;

leftRotate(x.parent);

x = root;

}

} else {

s = x.parent.left;

if (s.color == 1) {

s.color = 0;

x.parent.color = 1;

rightRotate(x.parent);

s = x.parent.left;

}

if (s.right.color == 0 && s.right.color == 0) {

s.color = 1;

x = x.parent;

} else {

if (s.left.color == 0) {

s.right.color = 0;

s.color = 1;

leftRotate(s);

s = x.parent.left;

}

s.color = x.parent.color;

x.parent.color = 0;

s.left.color = 0;

rightRotate(x.parent);

x = root;

}

x.color = 0;

}

private void rbTransplant(Node u, Node v) {

if (u.parent == null) {

root = v;

} else if (u == u.parent.left) {

u.parent.left = v;

} else {

u.parent.right = v;

}

v.parent = u.parent;

}

private void deleteNodeHelper(Node node, int key) {

Node z = TNULL;

Node x, y;

while (node != TNULL) {

if (node.data == key) {

z = node;

}

if (node.data <= key) {

node = node.right;

} else {

node = node.left;

}

if (z == TNULL) {

System.out.println("Couldn't find key in the tree");

return;

}

y = z;

int yOriginalColor = y.color;

if (z.left == TNULL) {

x = z.right;

rbTransplant(z, z.right);

} else if (z.right == TNULL) {

x = z.left;

rbTransplant(z, z.left);

} else {

y = minimum(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 (yOriginalColor == 0) {

fixDelete(x);

}

// Balance the node after insertion

private void fixInsert(Node k) {

Node u;

while (k.parent.color == 1) {

if (k.parent == k.parent.parent.right) {

u = k.parent.parent.left;

if (u.color == 1) {

u.color = 0;

k.parent.color = 0;

k.parent.parent.color = 1;

k = k.parent.parent;

} else {

if (k == k.parent.left) {

k = k.parent;

rightRotate(k);

}

k.parent.color = 0;

k.parent.parent.color = 1;

leftRotate(k.parent.parent);

}

} else {

u = k.parent.parent.right;

if (u.color == 1) {

u.color = 0;

k.parent.color = 0;

k.parent.parent.color = 1;

k = k.parent.parent;

} else {

if (k == k.parent.right) {

k = k.parent;

leftRotate(k);

}

k.parent.color = 0;

k.parent.parent.color = 1;

rightRotate(k.parent.parent);

}

if (k == root) {

break;

}

root.color = 0;

}

private void printHelper(Node root, String indent, boolean last) {

if (root != TNULL) {

System.out.print(indent);

if (last) {

System.out.print("R----");

indent += " ";

} else {

System.out.print("L----");

indent += "| ";

}

String sColor = root.color == 1 ? "RED" : "BLACK";

System.out.println(root.data + "(" + sColor + ")");

printHelper(root.left, indent, false);

printHelper(root.right, indent, true);

}

public RedBlackTree() {

TNULL = new Node();

TNULL.color = 0;

TNULL.left = null;

TNULL.right = null;

root = TNULL;

}

public void preorder() {

preOrderHelper(this.root);

}

public void inorder() {

inOrderHelper(this.root);

}

public void postorder() {

postOrderHelper(this.root);

}

public Node searchTree(int k) {

return searchTreeHelper(this.root, k);

}

public Node minimum(Node node) {

while (node.left != TNULL) {

node = node.left;

}

return node;

}

public Node maximum(Node node) {

while (node.right != TNULL) {

node = node.right;

}

return node;

}

public Node successor(Node x) {

if (x.right != TNULL) {

return minimum(x.right);

}

Node y = x.parent;

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