Red-Black Trees | Top-Down Insertion
Last Updated :
18 Mar, 2024
In Bottom-Up insertion of Red-Black Trees, “simple” Binary Search Tree insertion is used, followed by correction of the RB-Tree Violations on the way back up to the root. This can be done easily with the help of recursion. While in Top-Down Insertion, the corrections are done while traversing down the tree to the insertion point. When the actual insertion is done, no further corrections are needed, so no need to traverse back up the tree.
Therefore, the goal of Top-Down insertion is to traverse from the root to the insertion point in such a way that RB properties are maintained. This iterative approach thus makes Top-Down insertion faster than Bottom-Up insertion.
The two basic operations to perform for fixing violations and balancing are-
Following is the detailed Algorithm
The main goal of this algorithm is to create an insertion point at which the parent of the new node is Black, or the uncle of the new node is black.
Let N be the new node to be inserted.
- If Y and Z are Black:
- If X’s Parent is Black:
- X’s Parent P is Red, Grandparent is Black and X and P are both left OR right children of Grandparent G:
- Recolor X, Y, Z
- Rotate P around G
- Color P black
- Color G red
- X’s Parent is Red, Grandparent is Black and X and P are opposite children of Grandparent G
- Recolor X, Y, Z
- Rotate X around P
- Rotate X around G
- Recolor X and G
Below the implementation of the following approach:
C++
#include<bits/stdc++.h>
using namespace std;
// Class for representing a node of the tree
class TreeNode {
public:
string data, color;
TreeNode* children[2];
TreeNode(string data) {
this->data = data;
this->color = "R";
children[0] = NULL;
children[1] = NULL;
}
};
// Class for performing RBTree operations
class RbTree {
public:
TreeNode* Root = NULL;
// Function to calculate the height of the tree
int HeightT(TreeNode* Root) {
int lefth = 0, righth = 0;
if (Root == NULL || (Root->children[0] == NULL && Root->children[1] == NULL)) {
return 0;
}
lefth = HeightT(Root->children[0]);
righth = HeightT(Root->children[1]);
return (max(lefth, righth) + 1);
}
// Function to check if dir is equal to 0
static int check(int dir) {
return dir == 0 ? 1 : 0;
}
// Function to check if a node's color is red or not
static bool isRed(TreeNode* Node) {
return Node != NULL && Node->color == "R";
}
// Function to perform single rotation
TreeNode* SingleRotate(TreeNode* Node, int dir) {
TreeNode* temp = Node->children[check(dir)];
Node->children[check(dir)] = temp->children[dir];
temp->children[dir] = Node;
Root->color = "R";
temp->color = "B";
return temp;
}
// Function to perform double rotation
TreeNode* DoubleRotate(TreeNode* Node, int dir) {
Node->children[check(dir)] = SingleRotate(Node->children[check(dir)], check(dir));
return SingleRotate(Node, dir);
}
// Function to insert a new node with given data
TreeNode* Insert(RbTree* tree, string data) {
if (tree->Root == NULL) {
tree->Root = new TreeNode(data);
if (tree->Root == NULL)
return NULL;
}
else {
// A temporary root
TreeNode* temp = new TreeNode("");
// Grandparent and Parent
TreeNode *g, *t;
TreeNode *p, *q;
int dir = 0, last = 0;
t = temp;
g = p = NULL;
t->children[1] = tree->Root;
q = t->children[1];
while (true) {
if (q == NULL) {
// Inserting root node
q = new TreeNode(data);
p->children[dir] = q;
}
// Sibling is red
else if (isRed(q->children[0]) && isRed(q->children[1])) {
// Recoloring if both children are red
q->color = "R";
q->children[0]->color = "B";
q->children[1]->color = "B";
}
if (isRed(q) && isRed(p)) {
// Resolving red-red violation
int dir2;
if (t->children[1] == g) {
dir2 = 1;
}
else {
dir2 = 0;
}
// If children and parent are left-left or right-right of grand-parent
if (q == p->children[last]) {
t->children[dir2] = SingleRotate(g, last == 0 ? 1 : 0);
}
// If they are opposite childs i.e left-right or right-left
else {
t->children[dir2] = DoubleRotate(g, last == 0 ? 1 : 0);
}
}
// Checking for correct position of node
if (q->data == data) {
break;
}
last = dir;
// Finding the path to traverse [Either left or right]
dir = q->data < data ? 1 : 0;
if (g != NULL) {
t = g;
}
// Rearranging pointers
g = p;
p = q;
q = q->children[dir];
}
tree->Root = temp->children[1];
}
// Assign black color to the root node
tree->Root->color = "B";
return tree->Root;
}
// Print nodes at each level in level order traversal
void PrintLevel(TreeNode* root, int i) {
if (root == NULL) {
return;
}
if (i == 1) {
cout << "| " << root->data << " | " << root->color << " |";
if (root->children[0] != NULL) {
cout << " " << root->children[0]->data << " |";
}
else {
cout << " " << "NULL" << " |";
}
if (root->children[1] != NULL) {
cout << " " << root->children[1]->data << " |";
}
else {
cout << " " << "NULL" << " |";
}
cout << " ";
return;
}
PrintLevel(root->children[0], i - 1);
PrintLevel(root->children[1], i - 1);
}
// Utility Function to perform level order traversal
void LevelOrder(TreeNode* root) {
int i;
for (i = 1; i < HeightT(root) + 1; i++) {
PrintLevel(root, i);
cout << "\n\n";
}
}
};
// Driver Code
int main() {
// Tree Node Representation
// -------------------------------------------
// DATA | COLOR | LEFT CHILD | RIGHT CHILD |
// -------------------------------------------
RbTree* Tree = new RbTree();
string Sentence, Word;
Sentence = "old is gold";
vector<string> Word_Array;
stringstream ss(Sentence);
while (ss >> Word) {
Word_Array.push_back(Word);
}
for (int i = 0; i < Word_Array.size(); i++) {
Tree->Root = Tree->Insert(Tree, Word_Array[i]);
}
// Print Level Order Traversal
cout << "The Level Order Traversal of the tree is:\n";
Tree->LevelOrder(Tree->Root);
cout << "\nInserting a word in the tree:\n";
Word = "forever";
Tree->Root = Tree->Insert(Tree, Word);
cout << "\n";
Tree->LevelOrder(Tree->Root);
return 0;
}
// Java implementation for Top-Down
// Red-Black Tree Insertion creating
// a red black tree and storing an
// English sentence into it using Top
// down insertion approach
import static java.lang.Integer.max;
// Class for performing
// RBTree operations
public class RbTree {
TreeNode Root = null;
// Function to calculate
// the height of the tree
int HeightT(TreeNode Root)
{
int lefth, righth;
if (Root == null
|| (Root.children == null
&& Root.children[1] == null)) {
return 0;
}
lefth = HeightT(Root.children[0]);
righth = HeightT(Root.children[1]);
return (max(lefth, righth) + 1);
}
// Function to check if
// dir is equal to 0
int check(int dir)
{
return dir == 0 ? 1 : 0;
}
// Function to check if a
// node's color is red or not
boolean isRed(TreeNode Node)
{
return Node != null
&& Node.color.equals("R");
}
// Function to perform
// single rotation
TreeNode SingleRotate(TreeNode Node,
int dir)
{
TreeNode temp
= Node.children[check(dir)];
Node.children[check(dir)]
= temp.children[dir];
temp.children[dir] = Node;
Root.color = "R";
temp.color = "B";
return temp;
}
// Function to perform double rotation
TreeNode DoubleRotate(TreeNode Node,
int dir)
{
Node.children[check(dir)]
= SingleRotate(Node.children[check(dir)],
check(dir));
return SingleRotate(Node, dir);
}
// Function to insert a new
// node with given data
TreeNode Insert(RbTree tree,
String data)
{
if (tree.Root == null) {
tree.Root
= new TreeNode(data);
if (tree.Root == null)
return null;
}
else {
// A temporary root
TreeNode temp = new TreeNode("");
// Grandparent and Parent
TreeNode g, t;
TreeNode p, q;
int dir = 0, last = 0;
t = temp;
g = p = null;
t.children[1] = tree.Root;
q = t.children[1];
while (true) {
if (q == null) {
// Inserting root node
q = new TreeNode(data);
p.children[dir] = q;
}
// Sibling is red
else if (isRed(q.children[0])
&& isRed(q.children[1])) {
// Recoloring if both
// children are red
q.color = "R";
q.children[0].color = "B";
q.children[1].color = "B";
}
if (isRed(q) && isRed(p)) {
// Resolving red-red
// violation
int dir2;
if (t.children[1] == g) {
dir2 = 1;
}
else {
dir2 = 0;
}
// If children and parent
// are left-left or
// right-right of grand-parent
if (q == p.children[last]) {
t.children[dir2]
= SingleRotate(g,
last == 0
? 1
: 0);
}
// If they are opposite
// childs i.e left-right
// or right-left
else {
t.children[dir2]
= DoubleRotate(g,
last == 0
? 1
: 0);
}
}
// Checking for correct
// position of node
if (q.data.equals(data)) {
break;
}
last = dir;
// Finding the path to
// traverse [Either left
// or right ]
dir = q.data.compareTo(data) < 0
? 1
: 0;
if (g != null) {
t = g;
}
// Rearranging pointers
g = p;
p = q;
q = q.children[dir];
}
tree.Root = temp.children[1];
}
// Assign black color
// to the root node
tree.Root.color = "B";
return tree.Root;
}
// Print nodes at each
// level in level order
// traversal
void PrintLevel(TreeNode root, int i)
{
if (root == null) {
return;
}
if (i == 1) {
System.out.print("| "
+ root.data
+ " | "
+ root.color
+ " |");
if (root.children[0] != null) {
System.out.print(" "
+ root.children[0].data
+ " |");
}
else {
System.out.print(" "
+ "NULL"
+ " |");
}
if (root.children[1] != null) {
System.out.print(" "
+ root.children[1].data
+ " |");
}
else {
System.out.print(" "
+ "NULL"
+ " |");
}
System.out.print(" ");
return;
}
PrintLevel(root.children[0],
i - 1);
PrintLevel(root.children[1],
i - 1);
}
// Utility Function to
// perform level order
// traversal
void LevelOrder(TreeNode root)
{
int i;
for (i = 1;
i < HeightT(root) + 1;
i++) {
PrintLevel(root, i);
System.out.print("\n\n");
}
}
}
// Class for representing
// a node of the tree
class TreeNode {
// Class variables
String data, color;
TreeNode children[];
public TreeNode(String data)
{
// Color R- Red
// and B - Black
this.data = data;
this.color = "R";
children
= new TreeNode[2];
children[0] = null;
children[1] = null;
}
}
// Driver Code
class Driver {
public static void main(String[] args)
{
// Tree Node Representation
// -------------------------------------------
// DATA | COLOR | LEFT CHILD | RIGHT CHILD |
// -------------------------------------------
RbTree Tree = new RbTree();
String Sentence, Word;
Sentence = "old is gold";
String Word_Array[]
= Sentence.split(" ");
for (int i = 0;
i < Word_Array.length;
i++) {
Tree.Root
= Tree.Insert(Tree,
Word_Array[i]);
}
// Print Level Order Traversal
System.out.println("The Level"
+ "Order Traversal"
+ "of the tree is:");
Tree.LevelOrder(Tree.Root);
System.out.println("\nInserting a"
+ " word in the tree:");
Word = "forever";
Tree.Root = Tree.Insert(Tree,
Word);
System.out.println("");
Tree.LevelOrder(Tree.Root);
}
}
// C# implementation for Top-Down
// Red-Black Tree Insertion creating
// a red black tree and storing an
// English sentence into it using Top
// down insertion approach
using System;
// Class for performing
// RBTree operations
class RbTree
{
public TreeNode Root = null;
// Function to calculate
// the height of the tree
public int HeightT(TreeNode Root)
{
int lefth, righth;
if (Root == null ||
(Root.children == null &&
Root.children[1] == null))
{
return 0;
}
lefth = HeightT(Root.children[0]);
righth = HeightT(Root.children[1]);
return (Math.Max(lefth, righth) + 1);
}
// Function to check if
// dir is equal to 0
public int check(int dir)
{
return dir == 0 ? 1 : 0;
}
// Function to check if a
// node's color is red or not
public bool isRed(TreeNode Node)
{
return Node != null &&
Node.color.Equals("R");
}
// Function to perform
// single rotation
public TreeNode SingleRotate(TreeNode Node, int dir)
{
TreeNode temp = Node.children[check(dir)];
Node.children[check(dir)] = temp.children[dir];
temp.children[dir] = Node;
Root.color = "R";
temp.color = "B";
return temp;
}
// Function to perform double rotation
public TreeNode DoubleRotate(TreeNode Node, int dir)
{
Node.children[check(dir)] =
SingleRotate(Node.children[check(dir)],
check(dir));
return SingleRotate(Node, dir);
}
// Function to insert a new
// node with given data
public TreeNode Insert(RbTree tree,
String data)
{
if (tree.Root == null)
{
tree.Root = new TreeNode(data);
if (tree.Root == null)
return null;
}
else
{
// A temporary root
TreeNode temp = new TreeNode("");
// Grandparent and Parent
TreeNode g, t;
TreeNode p, q;
int dir = 0, last = 0;
t = temp;
g = p = null;
t.children[1] = tree.Root;
q = t.children[1];
while (true)
{
if (q == null)
{
// Inserting root node
q = new TreeNode(data);
p.children[dir] = q;
}
// Sibling is red
else if (isRed(q.children[0]) &&
isRed(q.children[1]))
{
// Recoloring if both
// children are red
q.color = "R";
q.children[0].color = "B";
q.children[1].color = "B";
}
if (isRed(q) && isRed(p))
{
// Resolving red-red
// violation
int dir2;
if (t.children[1] == g)
{
dir2 = 1;
}
else
{
dir2 = 0;
}
// If children and parent
// are left-left or
// right-right of grand-parent
if (q == p.children[last])
{
t.children[dir2] =
SingleRotate(g, last == 0 ? 1 : 0);
}
// If they are opposite
// childs i.e left-right
// or right-left
else
{
t.children[dir2] =
DoubleRotate(g, last == 0 ? 1 : 0);
}
}
// Checking for correct
// position of node
if (q.data.Equals(data))
{
break;
}
last = dir;
// Finding the path to
// traverse [Either left
// or right ]
dir = q.data.CompareTo(data) < 0 ? 1 : 0;
if (g != null)
{
t = g;
}
// Rearranging pointers
g = p;
p = q;
q = q.children[dir];
}
tree.Root = temp.children[1];
}
// Assign black color
// to the root node
tree.Root.color = "B";
return tree.Root;
}
// Print nodes at each
// level in level order
// traversal
public void PrintLevel(TreeNode root, int i)
{
if (root == null)
{
return;
}
if (i == 1)
{
Console.Write("| " + root.data +
" | " + root.color + " |");
if (root.children[0] != null)
{
Console.Write(" " +
root.children[0].data + " |");
}
else
{
Console.Write(" " + "NULL" + " |");
}
if (root.children[1] != null)
{
Console.Write(" " +
root.children[1].data + " |");
}
else
{
Console.Write(" " + "NULL" + " |");
}
Console.Write(" ");
return;
}
PrintLevel(root.children[0], i - 1);
PrintLevel(root.children[1], i - 1);
}
// Utility Function to perform
// level order traversal
public void LevelOrder(TreeNode root)
{
int i;
for (i = 1; i < HeightT(root) + 1; i++)
{
PrintLevel(root, i);
Console.Write("\n\n");
}
}
}
// Class for representing
// a node of the tree
public class TreeNode
{
// Class variables
public String data, color;
public TreeNode []children;
public TreeNode(String data)
{
// Color R- Red
// and B - Black
this.data = data;
this.color = "R";
children = new TreeNode[2];
children[0] = null;
children[1] = null;
}
}
// Driver Code
public class Driver
{
public static void Main(String[] args)
{
// Tree Node Representation
// -------------------------------------------
// DATA | COLOR | LEFT CHILD | RIGHT CHILD |
// -------------------------------------------
RbTree Tree = new RbTree();
String Sentence, Word;
Sentence = "old is gold";
char[] spearator = { ' ', ' ' };
String []Word_Array = Sentence.Split(spearator,
StringSplitOptions.RemoveEmptyEntries);
for (int i = 0; i < Word_Array.Length; i++)
{
Tree.Root = Tree.Insert(Tree,
Word_Array[i]);
}
// Print Level Order Traversal
Console.WriteLine("The Level" +
"Order Traversal" +
"of the tree is:");
Tree.LevelOrder(Tree.Root);
Console.WriteLine("\nInserting a" +
" word in the tree:");
Word = "forever";
Tree.Root = Tree.Insert(Tree, Word);
Console.WriteLine("");
Tree.LevelOrder(Tree.Root);
}
}
// This code is contributed by Rajput-Ji
// Javascript implementation for Top-Down
// Red-Black Tree Insertion creating
// a red black tree and storing an
// English sentence into it using Top
// down insertion approach
// Class for performing
// RBTree operations
class RbTree {
constructor() {
this.Root = null;
}
// Function to calculate
// the height of the tree
HeightT(Root) {
let lefth = 0;
let righth = 0;
if (Root === null || (Root.children === null && Root.children[1] === null)) {
return 0;
}
lefth = this.HeightT(Root.children[0]);
righth = this.HeightT(Root.children[1]);
return (Math.max(lefth, righth) + 1);
}
// Function to check if
// dir is equal to 0
static check(dir) {
return (dir === 0) ? 1 : 0;
}
// Function to check if a
// node's color is red or not
static isRed(Node) {
return (Node !== null && Node.color === "R");
}
// Function to perform
// single rotation
SingleRotate(Node, dir) {
let temp = Node.children[this.constructor.check(dir)];
Node.children[this.constructor.check(dir)] = temp.children[dir];
temp.children[dir] = Node;
this.Root.color = "R";
temp.color = "B";
return temp;
}
// Function to perform double rotation
DoubleRotate(Node, dir) {
Node.children[this.constructor.check(dir)] = this.SingleRotate(Node.children[this.constructor.check(dir)], this.constructor.check(dir));
return this.SingleRotate(Node, dir);
}
// Function to insert a new
// node with given data
Insert(tree, data) {
if (tree.Root === null) {
tree.Root = new TreeNode(data);
if (tree.Root === null) {
return null;
}
} else {
// A temporary root
let temp = new TreeNode("");
// Garndparent and parent
let g = null;
let t = null;
let p = null;
let q = null;
let dir = 0;
let last = 0;
t = temp;
g = p = null;
t.children[1] = tree.Root;
q = t.children[1];
while (true) {
if (q === null) {
// Inserting root node
q = new TreeNode(data);
p.children[dir] = q;
}
// Sibling red
else if (this.constructor.isRed(q.children[0]) && this.constructor.isRed(q.children[1])) {
// recoloring if both
// both children are red
q.color = "R";
q.children[0].color = "B";
q.children[1].color = "B";
}
if (this.constructor.isRed(q) && this.constructor.isRed(p)) {
// Resolving red-red
// violation
let dir2 = 0;
if (t.children[1] === g) {
dir2 = 1;
} else {
dir2 = 0;
}
// If children and parent
// are left-left or
// right-right of grand-parent
if (q === p.children[last]) {
t.children[dir2] = this.SingleRotate(g, (last === 0) ? 1 : 0);
}
// If they are opposite
// childs i.e left-right
// or right-left
else {
t.children[dir2] = this.DoubleRotate(g, (last === 0) ? 1 : 0);
}
}
// Checking for correct
// position of node
if (q.data === data) {
break;
}
// Finding the path to
// traverse [Either left or right]
last = dir;
dir = (q.data < data) ? 1 : 0;
if (g !== null) {
t = g;
}
// Rearranging pointers
g = p;
p = q;
q = q.children[dir];
}
// Assign black color
// to the root node
tree.Root = temp.children[1];
}
tree.Root.color = "B";
return tree.Root;
}
// Print nodes at each
// level in level order
// traversal
PrintLevel(root, i) {
if (root == null) {
return;
}
if (i == 1) {
process.stdout.write(`| ${root.data} | ${root.color} |`);
if (root.children[0] != null) {
process.stdout.write(` ${root.children[0].data} |`);
} else {
process.stdout.write(` None |`);
}
if (root.children[1] != null) {
process.stdout.write(` ${root.children[1].data} |`);
} else {
process.stdout.write(` None |`);
}
return;
}
this.PrintLevel(root.children[0], i - 1);
this.PrintLevel(root.children[1], i - 1);
}
// Utility Function to perform
// level order traversal
LevelOrder(root) {
for (let i = 1; i <= this.HeightT(root) + 1; i++) {
this.PrintLevel(root, i);
console.log('\n');
}
}
}
// Class for representing
// a node of the tree
class TreeNode {
constructor(data) {
// Color R- Red
// and B - Black
this.data = data;
this.color = "R";
this.children = [null, null];
}
}
// Driver Code
// -------------------------------------------
// DATA | COLOR | LEFT CHILD | RIGHT CHILD |
// -------------------------------------------
let Tree = new RbTree();
let Sentence = "";
let Word = "";
Sentence = "old is gold";
let Word_Array = Sentence.split(" ");
for (let i = 0; i < Word_Array.length; i++) {
Tree.Root = Tree.Insert(Tree, Word_Array[i]);
}
// Print Level Order Traversal
console.log("The Level Order Traversal the tree is:\n\n");
Tree.LevelOrder(Tree.Root);
console.log("Inserting a word in the tree:\n\n");
Word = "forever";
Tree.Root = Tree.Insert(Tree, Word);
Tree.LevelOrder(Tree.Root);
// This code is contributed by codebraxnzt
# Python 3 implementation for Top-Down
# Red-Black Tree Insertion creating
# a red black tree and storing an
# English sentence into it using Top
# down insertion approach
# Class for performing
# RBTree operations
class RbTree:
Root = None
# Function to calculate
# the height of the tree
def HeightT(self,Root):
lefth, righth=0, 0
if (Root == None or (Root.children == None and Root.children[1] == None)):
return 0
lefth = self.HeightT(Root.children[0])
righth = self.HeightT(Root.children[1])
return (max(lefth, righth) + 1)
# Function to check if
# dir is equal to 0
@staticmethod
def check(dir):
return 1 if dir == 0 else 0
# Function to check if a
# node's color is red or not
@staticmethod
def isRed(Node):
return Node != None and Node.color=="R"
# Function to perform
# single rotation
def SingleRotate(self, Node, dir):
temp = Node.children[self.check(dir)]
Node.children[self.check(dir)] = temp.children[dir]
temp.children[dir] = Node
self.Root.color = "R"
temp.color = "B"
return temp
# Function to perform double rotation
def DoubleRotate(self, Node, dir):
Node.children[self.check(dir)] = self.SingleRotate(Node.children[self.check(dir)], self.check(dir))
return self.SingleRotate(Node, dir)
# Function to insert a new
# node with given data
def Insert(self, tree, data):
if (tree.Root == None):
tree.Root = TreeNode(data)
if (tree.Root == None):
return None
else:
# A temporary root
temp = TreeNode("")
# Grandparent and Parent
g, t=None,None
p, q=None,None
dir = 0; last = 0
t = temp
g = p = None
t.children[1] = tree.Root
q = t.children[1]
while (True):
if (q == None):
# Inserting root node
q = TreeNode(data)
p.children[dir] = q
# Sibling is red
elif (self.isRed(q.children[0]) and self.isRed(q.children[1])):
# Recoloring if both
# children are red
q.color = "R"
q.children[0].color = "B"
q.children[1].color = "B"
if (self.isRed(q) and self.isRed(p)):
# Resolving red-red
# violation
dir2=0
if (t.children[1] == g):
dir2 = 1
else:
dir2 = 0
# If children and parent
# are left-left or
# right-right of grand-parent
if (q == p.children[last]):
t.children[dir2] = self.SingleRotate(g, 1 if last == 0 else 0)
# If they are opposite
# childs i.e left-right
# or right-left
else:
t.children[dir2] = self.DoubleRotate(g,1 if last == 0 else 0)
# Checking for correct
# position of node
if (q.data==data):
break
last = dir
# Finding the path to
# traverse [Either left
# or right ]
dir = 1 if q.data<data else 0
if (g != None):
t = g
# Rearranging pointers
g = p
p = q
q = q.children[dir]
tree.Root = temp.children[1]
# Assign black color
# to the root node
tree.Root.color = "B"
return tree.Root
# Print nodes at each
# level in level order
# traversal
def PrintLevel(self, root, i):
if (root == None):
return
if (i == 1):
print("| {} | {} |".format(root.data,root.color),end='')
if (root.children[0] != None):
print(" {} |".format(root.children[0].data),end='')
else:
print(" None |",end='')
if (root.children[1] != None):
print(" {} |".format(root.children[1].data),end='')
else:
print(" None |",end='')
return
self.PrintLevel(root.children[0], i - 1)
self.PrintLevel(root.children[1], i - 1)
# Utility Function to perform
# level order traversal
def LevelOrder(self, root):
for i in range(self.HeightT(root) + 1):
self.PrintLevel(root, i)
print('\n')
# Class for representing
# a node of the tree
class TreeNode:
def __init__(self, data):
# Color R- Red
# and B - Black
self.data = data
self.color = "R"
self.children = [None,None]
# Driver Code
if __name__=='__main__':
# Tree Node Representation
# -------------------------------------------
# DATA | COLOR | LEFT CHILD | RIGHT CHILD |
# -------------------------------------------
Tree = RbTree()
Sentence, Word='',''
Sentence = "old is gold"
Word_Array = Sentence.split()
for i in range(len(Word_Array)):
Tree.Root = Tree.Insert(Tree, Word_Array[i])
# Print Level Order Traversal
print("The Level Order Traversal the tree is:")
Tree.LevelOrder(Tree.Root)
print("\nInserting a word in the tree:")
Word = "forever"
Tree.Root = Tree.Insert(Tree, Word)
Tree.LevelOrder(Tree.Root)
# This code is contributed by Amartya Ghosh
OutputThe LevelOrder Traversalof the tree is:
| is | B | gold | old |
| gold | R | NULL | NULL | | old | R | NULL | NULL |
Inserting a word in the tree:
| is | B | gold | old |
| gold | B | forever | NULL | | old | B | NULL | NULL |
| forever | R | NULL | NULL |
References:
Red Black Trees – UMBC CSEE
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