Posted on by Kalkicode
Code Heap

# Print all nodes less than a given value in a Min Heap

In this problem of printing all nodes in a Min Heap that have values less than a given threshold. A Min Heap is a binary tree structure where the value of each node is smaller than or equal to the values of its children. We will delve into the approach to solving this problem, present the code implementation, analyze its time complexity, and provide a brief summary.

## Problem Statement and Description

Given a Min Heap and a target value `k`, the task is to identify and print all nodes in the Min Heap that have values less than `k`. In essence, we are required to traverse the heap and output the nodes that are smaller than the specified value `k`, while adhering to the Min Heap property.

## Example

Consider the Min Heap depicted below:

``````            1
/    \
2      3
/  \    /  \
4    8  14   5
/ \   /\
7   6 11 9``````

For a given target value `k = 10`, the nodes with values less than 10 are 7, 4, 6, 2, 8, 9, 1, 3, and 5. The expected output is `7 4 6 2 8 9 1 3 5`.

## Approach

The central idea for solving this problem entails traversing the Min Heap in an in-order manner while considering the values of the nodes. Since in a Min Heap, parent nodes are always smaller than their children, we can efficiently decide whether to explore a subtree or not based on the value of the current node.

## Pseudocode

``````function printNodesLessThanK(node, k)
if node is null
return
printNodesLessThanK(node.left, k)
if node.value < k
print node.value
printNodesLessThanK(node.right, k)
end function``````

## Algorithm Explanation

1. Create a class `Node` to represent a node in the Min Heap, with attributes `left`, `right`, and `key`.
2. Develop a class `MinHeap` with attributes `size` and `root`. The `root` attribute points to the root of the Min Heap, and `size` tracks the number of nodes.
3. Implement the `printNodesLessThanK` function recursively:
• Base case: If the current node is null, return.
• Recursively call `printNodesLessThanK` on the left subtree.
• If the value of the current node is less than `k`, print the value.
• Recursively call `printNodesLessThanK` on the right subtree.
4. In the `main` function, instantiate a `MinHeap`, perform insertions to construct the Min Heap, and define the value of `k`.
5. Call the `printNodesLessThanK` function with the root node of the Min Heap and value `k`.

## Code Solution

``````/*
C++ program
Print all nodes less than a given value in a Min Heap
*/
//Tree node
#include<iostream>

using namespace std;
class Node {
public:

//Left and right child
Node *left;
Node *right;
//Data value
int key;
Node(int key) {
this->key = key;
this->left = NULL;
this->right = NULL;
}
};
class MinHeap {
public:

//This is use to store information of number of nodes in Min heap
int size;
Node *root;
MinHeap() {
this->root = NULL;
this->size = 0;
}
//Get height of insert new node
int insert_height() {
int i = 1;
int sum = 0;
while (this->size > sum + (1 << i)) {
sum += (1 << i);
i++;
}
return i;
}
void swap_node(Node *first, Node *second) {
int key = first->key;
first->key = second->key;
second->key = key;
}
//Arrange node key
void arrange_node(Node *root) {
if (root->left != NULL && root->left->key < root->key) {
this->swap_node(root, root->left);
}
if (root->right != NULL && root->right->key < root->key) {
this->swap_node(root, root->right);
}
}
bool add_node(Node *root, int height, int level, int key) {
if (level >= height) {
return false;
}
if (root != NULL) {
if (level - 1 == height && root->left == NULL || root->right == NULL) {
if (root->left == NULL) {
root->left = new Node(key);
} else {
root->right = new Node(key);
}
this->arrange_node(root);
return true;
}
if (this->add_node(root->left, height, level + 1, key) ||
this->add_node(root->right, height, level + 1, key)) {
//Check effect of new inserted node
this->arrange_node(root);
return true;
}
}
return false;
}
//Handles the request to new inserting node
void insert(int key) {
if (this->root == NULL) {
this->root = new Node(key);
} else
if (this->root->left == NULL) {
this->root->left = new Node(key);
this->arrange_node(this->root);
} else
if (this->root->right == NULL) {
this->root->right = new Node(key);
this->arrange_node(this->root);
} else {
int height = this->insert_height();
}
this->size++;
}
void print_node(Node *root, int key) {
if (root != NULL) {
this->print_node(root->left, key);
if (root->key < key) {
cout << " " << root->key;
}
this->print_node(root->right, key);
}
}
};
int main() {
MinHeap heap =  MinHeap();
//Construct first Min heap tree
heap.insert(5);
heap.insert(7);
heap.insert(4);
heap.insert(3);
heap.insert(8);
heap.insert(14);
heap.insert(2);
heap.insert(1);
heap.insert(6);
heap.insert(11);
heap.insert(9);
/*After insert element*/
/*
1
/    \
2      3
/  \    /  \
4    8  14   5
/ \   /\
7   6 11 9
*/
int k = 10;
heap.print_node(heap.root, k);
return 0;
}```
```

#### Output

`` 7 4 6 2 8 9 1 3 5``
``````/*
Java program
Print all nodes less than a given value in a Min Heap
*/
//Tree node
class Node
{
//Left and right child
public Node left;
public Node right;

//Data value
public int key;

public Node(int key)
{
this.key = key;

left = null;
right = null;
}
}
public class MinHeap
{
//This is use to store information of number of nodes in Min heap
public int size;

public Node root;

public MinHeap()
{
root = null;

size = 0;
}

//Get height of insert new node
public int insert_height()
{
int i=1;

int sum=0;

while(this.size > sum+(1<<i) )
{
sum += (1<<i);
i++;
}
return i;
}
public  void swap_node(Node first,Node second)
{
int key = first.key;

first.key = second.key;
second.key = key;
}
//Arrange node key
public void arrange_node(Node root)
{

if(root.left!=null && root.left.key < root.key)
{
swap_node(root,root.left);
}
if(root.right!=null && root.right.key < root.key)
{
swap_node(root,root.right);
}
}
public boolean  add_node(Node root, int height ,int level,int key)
{
if(level >= height )
{
return false;
}
if(root != null)
{

if(level-1 == height && root.left == null || root.right == null)
{
if(root.left==null)
{
root.left=new Node(key);
}
else
{
root.right=new Node(key);
}

arrange_node(root);

return true;
}

{
//Check effect of new inserted node
arrange_node(root);

return true;
}

}
return false;
}
//Handles the request to new inserting node
public void insert(int key)
{

if(root==null)
{
root=new Node(key);
}
else if(root.left==null)
{
root.left = new Node(key);
arrange_node(root);

}
else if(root.right==null)
{
root.right = new Node(key);
arrange_node(root);
}
else
{
int height = insert_height();

}
this.size++;
}

public void print_node(Node root,int key)
{
if(root!=null)
{

print_node(root.left,key);

if(root.key < key)
{
System.out.print("  "+root.key);
}

print_node(root.right,key);
}
}

public static void main(String[] args)
{

MinHeap heap= new MinHeap();

//Construct first Min heap tree
heap.insert(5);
heap.insert(7);
heap.insert(4);
heap.insert(3);
heap.insert(8);
heap.insert(14);
heap.insert(2);
heap.insert(1);
heap.insert(6);
heap.insert(11);
heap.insert(9);

/*After insert element*/

/*
1
/    \
2      3
/  \    /  \
4    8  14   5
/ \   /\
7   6 11 9
*/

int k = 10;

heap.print_node(heap.root,k);

}
}```
```

#### Output

`` 7 4 6 2 8 9 1 3 5``
``````/*
C# program
Print all nodes less than a given value in a Min Heap
*/
//Tree node
using System;
public class Node {
//Left and right child
public Node left;
public Node right;
//Data value
public int key;
public Node(int key) {
this.key = key;
left = null;
right = null;
}
}
public class MinHeap {
//This is use to store information of number of nodes in Min heap
public int size;
public Node root;
public MinHeap() {
root = null;
size = 0;
}
//Get height of insert new node
public int insert_height() {
int i = 1;
int sum = 0;
while (this.size > sum + (1 << i)) {
sum += (1 << i);
i++;
}
return i;
}
public void swap_node(Node first, Node second) {
int key = first.key;
first.key = second.key;
second.key = key;
}
//Arrange node key
public void arrange_node(Node root) {
if (root.left != null && root.left.key < root.key) {
swap_node(root, root.left);
}
if (root.right != null && root.right.key < root.key) {
swap_node(root, root.right);
}
}
public Boolean add_node(Node root, int height, int level, int key) {
if (level >= height) {
return false;
}
if (root != null) {
if (level - 1 == height && root.left == null || root.right == null) {
if (root.left == null) {
root.left = new Node(key);
} else {
root.right = new Node(key);
}
arrange_node(root);
return true;
}
if (add_node(root.left, height, level + 1, key) || add_node(root.right, height, level + 1, key)) {
arrange_node(root);
return true;
}
}
return false;
}
//Handles the request to new inserting node
public void insert(int key) {
if (root == null) {
root = new Node(key);
} else
if (root.left == null) {
root.left = new Node(key);
arrange_node(root);
} else
if (root.right == null) {
root.right = new Node(key);
arrange_node(root);
} else {
int height = insert_height();
}
this.size++;
}
public void print_node(Node root, int key) {
if (root != null) {
print_node(root.left, key);
if (root.key < key) {
Console.Write(" " + root.key);
}
print_node(root.right, key);
}
}
public static void Main(String[] args) {
MinHeap heap = new MinHeap();
heap.insert(5);
heap.insert(7);
heap.insert(4);
heap.insert(3);
heap.insert(8);
heap.insert(14);
heap.insert(2);
heap.insert(1);
heap.insert(6);
heap.insert(11);
heap.insert(9);
/*After insert element*/
/*
1
/    \
2      3
/  \    /  \
4    8  14   5
/ \   /\
7   6 11 9
*/
int k = 10;
heap.print_node(heap.root, k);
}
}```
```

#### Output

`` 7 4 6 2 8 9 1 3 5``
``````<?php
/*
Php program
Print all nodes less than a given value in a Min Heap
*/
//Tree node
class Node {
//Left and right child

public \$left;
public \$right;
//Data value

public \$key;

function __construct(\$key) {
\$this->key = \$key;
\$this->left = null;
\$this->right = null;
}
}
class MinHeap {
//This is use to store information of number of nodes in Min heap

public \$size;
public \$root;

function __construct() {
\$this->root = null;
\$this->size = 0;
}
//Get height of insert new node

public 	function insert_height() {
\$i = 1;
\$sum = 0;
while (\$this->size > \$sum + (1 << \$i)) {
\$sum += (1 << \$i);
\$i++;
}
return \$i;
}
public 	function swap_node(\$first, \$second) {
\$data = \$first->key;
\$first->key = \$second->key;
\$second->key = \$data;
}
//Arrange node key

public 	function arrange_node(\$root) {
if (\$root->left != null && \$root->left->key < \$root->key) {
\$this->swap_node(\$root, \$root->left);
}
if (\$root->right != null && \$root->right->key < \$root->key) {
\$this->swap_node(\$root, \$root->right);
}
}
public 	function add_node(\$root, \$height, \$level, \$key) {
if (\$level >= \$height) {
return false;
}
if (\$root != null) {
if (\$level - 1 == \$height && \$root->left == null || \$root->right == null) {
if (\$root->left == null) {
\$root->left = new Node(\$key);
} else {
\$root->right = new Node(\$key);
}
\$this->arrange_node(\$root);
return true;
}
if (\$this->add_node(\$root->left, \$height, \$level + 1, \$key) || \$this->add_node(\$root->right, \$height, \$level + 1, \$key)) {
//Check effect of new inserted node
\$this->arrange_node(\$root);
return true;
}
}
return false;
}
//Handles the request to new inserting node

public 	function insert(\$key) {
if (\$this->root == null) {
\$this->root = new Node(\$key);
} else
if (\$this->root->left == null) {
\$this->root->left = new Node(\$key);
\$this->arrange_node(\$this->root);
} else
if (\$this->root->right == null) {
\$this->root->right = new Node(\$key);
\$this->arrange_node(\$this->root);
} else {
\$height = \$this->insert_height();
}
\$this->size++;
}
public 	function print_node(\$root, \$key) {
if (\$root != null) {
\$this->print_node(\$root->left, \$key);
if (\$root->key < \$key) {
echo(" ". \$root->key);
}
\$this->print_node(\$root->right, \$key);
}
}
}

function main() {
\$heap = new MinHeap();
//Construct first Min heap tree

\$heap->insert(5);
\$heap->insert(7);
\$heap->insert(4);
\$heap->insert(3);
\$heap->insert(8);
\$heap->insert(14);
\$heap->insert(2);
\$heap->insert(1);
\$heap->insert(6);
\$heap->insert(11);
\$heap->insert(9);
/*After insert element*/
/*
1
/    \
2      3
/  \    /  \
4    8  14   5
/ \   /\
7   6 11 9
*/
\$k = 10;
\$heap->print_node(\$heap->root, \$k);

}
main();```
```

#### Output

`` 7 4 6 2 8 9 1 3 5``
``````/*
Node Js program
Print all nodes less than a given value in a Min Heap
*/
//Tree node
class Node {

constructor(key) {
this.key = key;
this.left = null;
this.right = null;
}
}
class MinHeap {

constructor() {
this.root = null;
this.size = 0;
}

//Get height of insert new node
insert_height() {
var i = 1;
var sum = 0;
while (this.size > sum + (1 << i)) {
sum += (1 << i);
i++;
}

return i;
}
swap_node(first, second) {
var data = first.key;
first.key = second.key;
second.key = data;
}

//Arrange node key
arrange_node(root) {
if (root.left != null && root.left.key < root.key) {
this.swap_node(root, root.left);
}

if (root.right != null && root.right.key < root.key) {
this.swap_node(root, root.right);
}
}
if (level >= height) {
return false;
}

if (root != null) {
if (level - 1 == height && root.left == null || root.right == null) {
if (root.left == null) {
root.left = new Node(key);
} else {
root.right = new Node(key);
}
this.arrange_node(root);
return true;
}

if (this.add_node(root.left, height, level + 1, key) || this.add_node(root.right, height, level + 1, key)) {
//Check effect of new inserted node
this.arrange_node(root);
return true;
}
}

return false;
}

//Handles the request to new inserting node
insert(key) {
if (this.root == null) {
this.root = new Node(key);
} else
if (this.root.left == null) {
this.root.left = new Node(key);
this.arrange_node(this.root);
} else
if (this.root.right == null) {
this.root.right = new Node(key);
this.arrange_node(this.root);
} else {
var height = this.insert_height();
}
this.size++;
}
print_node(root, key) {
if (root != null) {
this.print_node(root.left, key);
if (root.key < key) {
process.stdout.write(" " + root.key);
}
this.print_node(root.right, key);
}
}
}

function main(args) {
var heap = new MinHeap();
//Construct first Min heap tree
heap.insert(5);
heap.insert(7);
heap.insert(4);
heap.insert(3);
heap.insert(8);
heap.insert(14);
heap.insert(2);
heap.insert(1);
heap.insert(6);
heap.insert(11);
heap.insert(9);
/*After insert element*/
/*
1
/    \
2      3
/  \    /  \
4    8  14   5
/ \   /\
7   6 11 9
*/
var k = 10;
heap.print_node(heap.root, k);
}

main();```
```

#### Output

`` 7 4 6 2 8 9 1 3 5``
``````#  Python 3 program
#  Print all nodes less than a given value in a Min Heap

# Tree node
class Node :

def __init__(self, key) :
self.key = key
self.left = None
self.right = None

class MinHeap :
# This is use to store information of number of nodes in Min heap
def __init__(self) :
self.root = None
self.size = 0
# Get height of insert new node
def insert_height(self) :
i = 1
sum = 0
while (self.size > sum + (1 << i)) :
sum += (1 << i)
i += 1

return i

def swap_node(self, first, second) :
data = first.key
first.key = second.key
second.key = data
# Arrange node key
def arrange_node(self, root) :
if (root.left != None and root.left.key < root.key) :
self.swap_node(root, root.left)

if (root.right != None and root.right.key < root.key) :
self.swap_node(root, root.right)

def add_node(self, root, height, level, key) :
if (level >= height) :
return False

if (root != None) :
if (level - 1 == height and root.left == None or root.right == None) :
if (root.left == None) :
root.left = Node(key)
else :
root.right = Node(key)

self.arrange_node(root)
return True

if (self.add_node(root.left, height, level + 1, key) or self.add_node(root.right, height, level + 1, key)) :
# Check effect of new inserted node
self.arrange_node(root)
return True

return False
# Handles the request to new inserting node
def insert(self, key) :
if (self.root == None) :
self.root = Node(key)
elif (self.root.left == None) :
self.root.left = Node(key)
self.arrange_node(self.root)
elif (self.root.right == None) :
self.root.right = Node(key)
self.arrange_node(self.root)
else :
height = self.insert_height()

self.size += 1

def print_node(self, root, key) :
if (root != None) :
self.print_node(root.left, key)
if (root.key < key) :
print(" ", root.key, end = "")

self.print_node(root.right, key)

def main() :
heap = MinHeap()
# Construct first Min heap tree
heap.insert(5)
heap.insert(7)
heap.insert(4)
heap.insert(3)
heap.insert(8)
heap.insert(14)
heap.insert(2)
heap.insert(1)
heap.insert(6)
heap.insert(11)
heap.insert(9)

#After insert element

#
#               1
#             /    \
#            2      3
#          /  \    /  \
#         4    8  14   5
#        / \   /\
#       7   6 11 9
#

k = 10
heap.print_node(heap.root, k)

if __name__ == "__main__":
main()```
```

#### Output

``  7  4  6  2  8  9  1  3  5``
``````#  Ruby program
#  Print all nodes less than a given value in a Min Heap

# Tree node
class Node
# Define the accessor and reader of class Node
attr_accessor :left, :right, :key
def initialize(key)
self.key = key
@left = nil
@right = nil
end
end

class MinHeap
# Define the accessor and reader of class MinHeap
attr_accessor :size, :root
def initialize()
@root = nil
@size = 0
end
# Get height of insert new node
def insert_height()
i = 1
sum = 0
while (self.size > sum + (1 << i))
sum += (1 << i)
i += 1
end
return i
end
def swap_node(first, second)
data = first.key
first.key = second.key
second.key = data
end
# Arrange node key
def arrange_node(root)
if (root.left != nil && root.left.key < root.key)
self.swap_node(root, root.left)
end
if (root.right != nil && root.right.key < root.key)
self.swap_node(root, root.right)
end
end
if (level >= height)
return false
end
if (root != nil)
if (level - 1 == height && root.left == nil || root.right == nil)
if (root.left == nil)
root.left = Node.new(key)
else
root.right = Node.new(key)
end
self.arrange_node(root)
return true
end
if (self.add_node(root.left, height, level + 1, key) || self.add_node(root.right, height, level + 1, key))
# Check effect of new inserted node
self.arrange_node(root)
return true
end
end
return false
end
# Handles the request to new inserting node
def insert(key)
if (@root == nil)
@root = Node.new(key)
elsif (@root.left == nil)
@root.left = Node.new(key)
self.arrange_node(@root)
elsif (@root.right == nil)
@root.right = Node.new(key)
self.arrange_node(@root)
else
height = self.insert_height()
end
self.size += 1
end
def print_node(root, key)
if (root != nil)
self.print_node(root.left, key)
if (root.key < key)
print(" ", root.key)
end
self.print_node(root.right, key)
end
end
end
def main()
heap = MinHeap.new()
# Construct first Min heap tree
heap.insert(5)
heap.insert(7)
heap.insert(4)
heap.insert(3)
heap.insert(8)
heap.insert(14)
heap.insert(2)
heap.insert(1)
heap.insert(6)
heap.insert(11)
heap.insert(9)
#After insert element

#
#               1
#             /    \
#            2      3
#          /  \    /  \
#         4    8  14   5
#        / \   /\
#       7   6 11 9
#

k = 10
heap.print_node(heap.root, k)
end

main()```
```

#### Output

`` 7 4 6 2 8 9 1 3 5``
``````/*
Scala program
Print all nodes less than a given value in a Min Heap
*/
//Tree node
class Node(var left: Node,var right: Node,var key: Int) {

def this(key: Int) {
this(null,null,key);

}
}
class MinHeap(var size: Int,var root: Node) {

def this() {
this(0,null);
}
//Get height of insert new node
def insert_height(): Int = {
var i: Int = 1;
var sum: Int = 0;
while (this.size > sum + (1 << i)) {
sum += (1 << i);
i += 1;
}
return i;
}
def swap_node(first: Node, second: Node): Unit = {
val data: Int = first.key;
first.key = second.key;
second.key = data;
}
//Arrange node key
def arrange_node(root: Node): Unit = {
if (root.left != null && root.left.key < root.key) {
this.swap_node(root, root.left);
}
if (root.right != null && root.right.key < root.key) {
this.swap_node(root, root.right);
}
}
def add_node(root: Node, height: Int, level: Int, key: Int): Boolean = {
if (level >= height) {
return false;
}
if (root != null) {
if (level - 1 == height && root.left == null || root.right == null) {
if (root.left == null) {
root.left = new Node(key);
} else {
root.right = new Node(key);
}
this.arrange_node(root);

return true;
}
if (this.add_node(root.left, height, level + 1, key) || this.add_node(root.right, height, level + 1, key)) {
//Check effect of new inserted node
this.arrange_node(root);

return true;
}
}
return false;
}
//Handles the request to new inserting node
def insert(key: Int): Unit = {
if (this.root == null) {
this.root = new Node(key);
} else
if (this.root.left == null) {
this.root.left = new Node(key);
this.arrange_node(this.root);
} else
if (this.root.right == null) {
this.root.right = new Node(key);
this.arrange_node(this.root);
} else {
val height: Int = this.insert_height();
}
this.size += 1;
}
def print_node(root: Node, key: Int): Unit = {
if (root != null) {
this.print_node(root.left, key);

if (root.key < key) {
print(" " + root.key);
}
this.print_node(root.right, key);
}
}
}
object Main {
def main(args: Array[String]): Unit = {
val heap: MinHeap = new MinHeap();

//Construct first Min heap tree
heap.insert(5);
heap.insert(7);
heap.insert(4);
heap.insert(3);
heap.insert(8);
heap.insert(14);
heap.insert(2);
heap.insert(1);
heap.insert(6);
heap.insert(11);
heap.insert(9);

/*After insert element*/
/*
1
/    \
2      3
/  \    /  \
4    8  14   5
/ \   /\
7   6 11 9
*/
var k: Int = 10;
heap.print_node(heap.root, k);
}
}```
```

#### Output

`` 7 4 6 2 8 9 1 3 5``
``````/*
Swift program
Print all nodes less than a given value in a Min Heap
*/
//Tree node
class Node {

//Left and right child
var	left  : Node?;
var right : Node?;

//Data value
var	key : Int;
init(_ key: Int) {
self.key = key;
self.left = nil;
self.right = nil;
}
}
class MinHeap {

//This is use to store information of number of nodes in Min heap
var	size : Int;
var root : Node?;
init() {
self.root = nil;
self.size = 0;
}
//Get height of insert new node
func insert_height() -> Int {
var i = 1;
var sum = 0;
while (self.size > sum + (1 << i)) {
sum += (1 << i);
i += 1;
}
return i;
}
func swap_node(_ first: Node?, _ second: Node?) {
let data = first!.key;
first!.key = second!.key;
second!.key = data;
}
//Arrange node key
func arrange_node(_ root: Node?) {
if (root!.left != nil && root!.left!.key < root!.key) {
self.swap_node(root, root!.left);
}
if (root!.right != nil && root!.right!.key < root!.key) {
self.swap_node(root, root!.right);
}
}
func add_node(_ root: Node?, _ height: Int, _ level: Int, _ key: Int) -> Bool {
if (level >= height) {
return false;
}
if (root != nil) {
if (level - 1 == height && root!.left == nil || root!.right == nil) {
if (root!.left == nil) {
root!.left = Node(key);
} else {
root!.right = Node(key);
}
self.arrange_node(root);
return true;
}
if (self.add_node(root!.left, height, level + 1, key) || self.add_node(root!.right, height, level + 1, key)) {
//Check effect of new inserted node
self.arrange_node(root);
return true;
}
}
return false;
}
//Handles the request to new inserting node
func insert(_ key: Int) {
if (self.root == nil) {
self.root = Node(key);
} else
if (self.root!.left == nil) {
self.root!.left = Node(key);
self.arrange_node(self.root);
} else
if (self.root!.right == nil) {
self.root!.right = Node(key);
self.arrange_node(self.root);
} else {
let height = self.insert_height();
let _ = self.add_node(self.root, height, 0, key);
}
self.size += 1;
}
func print_node(_ root: Node?, _ key: Int) {
if (root != nil) {
self.print_node(root!.left, key);
if (root!.key < key) {
print(" ", root!.key, terminator: "");
}
self.print_node(root!.right, key);
}
}
}
func main() {
let heap = MinHeap();
//Construct first Min heap tree
heap.insert(5);
heap.insert(7);
heap.insert(4);
heap.insert(3);
heap.insert(8);
heap.insert(14);
heap.insert(2);
heap.insert(1);
heap.insert(6);
heap.insert(11);
heap.insert(9);
/*After insert element*/
/*
1
/    \
2      3
/  \    /  \
4    8  14   5
/ \   /\
7   6 11 9
*/
let k = 10;
heap.print_node(heap.root, k);
}
main();```
```

#### Output

``  7  4  6  2  8  9  1  3  5``

## Time Complexity

The time complexity of this algorithm is O(n), where n is the number of nodes in the Min Heap. This is due to each node being visited exactly once during traversal, and the operations executed at each node taking constant time. Consequently, the time complexity scales linearly with the number of nodes in the Min Heap.

## Comment

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