# Check whether binary tree is form of min heap

In this problem are determining whether a given binary tree is a valid representation of a min heap. A min heap is a binary tree data structure where each parent node has a value less than or equal to its child nodes. Your task is to check if a given binary tree follows the properties of a min heap.

## Problem Statement

Given a binary tree, you need to determine whether the tree represents a valid min heap or not.

## Example

Consider the given binary tree:

``````         1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11    ``````

In this case, the binary tree is a min heap because each parent node's value is less than or equal to its child nodes' values.

``````         1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2``````

Above tree is not min heap.

## Idea to Solve

To determine whether the given binary tree represents a min heap, you need to traverse the tree and check whether the min heap property is satisfied for each parent node and its children.

## Pseudocode

``````function insert(data):
create new_node
set new_node's data to data
set new_node's left and right pointers to NULL
return new_node

function is_min_heap(root):
if root is not NULL:
if (root has left child and root's left child value < root's value) or
(root has right child and root's right child value < root's value):
return false

if is_min_heap(root's left child) and is_min_heap(root's right child):
return true

return false

return true

function inorder(node):
if node is not NULL:
inorder(node's left child)
print node's data
inorder(node's right child)

main:
root = NULL
root = insert(1)
# Insert other nodes here

inorder(root)
if is_min_heap(root):
print "Min heap Binary Tree"
else:
print "Not a Min Heap Binary Tree"``````

## Algorithm Explanation

1. The `insert` function creates a new node for the binary tree with the given data value and initializes its left and right pointers.

2. The `is_min_heap` function checks whether the given node and its children satisfy the min heap property. If any violation is found, it returns false. It recursively checks the left and right subtrees as well.

3. The `inorder` function performs an inorder traversal of the binary tree and prints the node values.

## Code Solution

``````/*
C Program
Check whether binary tree is form of min heap
*/
#include <stdio.h>

#include <stdlib.h>
//structure of Binary Tree node
struct Node
{
int data;
struct Node*left,*right;
};

//Create a binary tree nodes and node fields (data,pointer)
//And returning the reference of newly nodes
struct Node* insert(int data)
{
//Create dynamic memory to new binary tree node
struct Node*new_node=(struct Node*)malloc(sizeof(struct Node));
if(new_node!=NULL){
//set data and pointer values
new_node->data=data;
new_node->left=NULL; //Initially node left-pointer is NULL
new_node->right=NULL;//Initially node right-pointer is NULL
}else
{
printf("Memory Overflow\n");
exit(0); //Terminate program execution
}
//return reference
return new_node;

}

//Check that given binary tree is form of min heap or not
int is_min_heap(struct Node*root)
{

if(root!=NULL)
{
if(root->left!=NULL && root->left->data < root->data ||
root->right!=NULL && root->right->data < root->data)

{
//When tree is not a min heap
return 0;
}

if(is_min_heap(root->left) && is_min_heap(root->right))
{
//When tree is min heap
return 1;
}

return 0;
}

return 1;

}
//Display tree element inorder form
void inorder(struct Node*node){

if(node){

inorder(node->left);
//Print node value
printf("  %d",node->data);
inorder(node->right);
}
}
int main(){

struct Node*root=NULL;

/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11

*/

//Insertion of binary tree nodes
root                    =insert(1);
root->left              =insert(5);
root->right             =insert(6);
root->right->right      =insert(10);
root->right->left       =insert(8);
root->left->left        =insert(9);
root->left->left->left  =insert(13);
root->left->right =insert(7);
root->left->right->right =insert(11);
root->left->right->left =insert(12);

inorder(root);
if(is_min_heap(root)==1)
{
printf("\n Min heap Binary Tree \n");
}
else
{
printf("\n Not a Min Heap Binary Tree \n");
}

/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2
*/
root->right->right->right = insert(2);
inorder(root);
if(is_min_heap(root)==1)
{
printf("\n Min heap Binary Tree \n");
}
else
{
printf("\n Not a Min Heap Binary Tree \n");
}
return 0;
}```
```

#### Output

``````  13  9  5  12  7  11  1  8  6  10
Min heap Binary Tree
13  9  5  12  7  11  1  8  6  10  2
Not a Min Heap Binary Tree``````
``````/*
C++ Program
Check whether binary tree is form of min heap
*/
#include<iostream>

using namespace std;

//Structure of Binary Tree node
class Node {
public:
int data;
Node *left;
Node *right;
//make a tree node

Node(int data) {
//assign field values
this->data = data;
this->left = NULL;
this->right = NULL;
}
};
class MyHeap {
public:
Node *root;
MyHeap() {
this->root = NULL;
}
//Check that given binary tree is form of min heap or not
bool is_min_heap(Node *root) {
if (root != NULL) {
if (root->left != NULL && root->left->data < root->data || root->right != NULL && root->right->data < root->data) {
return
//When tree is not a min heap
false;
}
if (this->is_min_heap(root->left) == true && this->is_min_heap(root->right) == true) {
return
//When the tree is in the form of a min heap
true;
}
return false;
}
return true;
}
//Display tree elements in order form
void inorder(Node *node) {
if (node != NULL) {
this->inorder(node->left);
//Print node value

cout << " " << node->data;
this->inorder(node->right);
}
}
};
int main() {
MyHeap obj = MyHeap();
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11

*/
//Insertion of binary tree nodes
obj.root = new Node(1);
obj.root->left = new Node(5);
obj.root->right = new Node(6);
obj.root->right->right = new Node(10);
obj.root->right->left = new Node(8);
obj.root->left->left = new Node(9);
obj.root->left->left->left = new Node(13);
obj.root->left->right = new Node(7);
obj.root->left->right->right = new Node(11);
obj.root->left->right->left = new Node(12);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
cout << "\n Min heap Binary Tree \n";
} else {
cout << "\n Not a Min Heap Binary Tree \n";
}
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2
*/
obj.root->right->right->right = new Node(2);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
cout << "\n Min heap Binary Tree \n";
} else {
cout << "\n Not a Min Heap Binary Tree \n";
}
return 0;
}```
```

#### Output

`````` 13 9 5 12 7 11 1 8 6 10
Min heap Binary Tree
13 9 5 12 7 11 1 8 6 10 2
Not a Min Heap Binary Tree``````
``````/*
Java Program
Check whether binary tree is form of min heap
*/
//Structure of Binary Tree node
class Node {

public int data;
public Node left;
public Node right;
//make a tree node
public Node(int data) {
//assign field values
this.data = data;
left = null;
right = null;
}
}
public class MyHeap {

public Node root;
public MyHeap() {
root = null;
}
//Check that given binary tree is form of min heap or not
public boolean is_min_heap(Node root) {

if (root != null) {
if (root.left != null && root.left.data < root.data ||
root.right != null && root.right.data < root.data) {
//When tree is not a min heap
return false;
}

if (is_min_heap(root.left) == true && is_min_heap(root.right) == true) {
//When the tree is in the form of a min heap
return true;
}

return false;
}

return true;

}
//Display tree elements in order form
public void inorder(Node node) {

if (node != null) {
inorder(node.left);
//Print node value
System.out.print("  "+ node.data);
inorder(node.right);
}

}
public static void main(String[] args) {
MyHeap obj = new MyHeap();
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11

*/

//Insertion of binary tree nodes
obj.root = new Node(1);
obj.root.left = new Node(5);
obj.root.right = new Node(6);
obj.root.right.right = new Node(10);
obj.root.right.left = new Node(8);
obj.root.left.left = new Node(9);
obj.root.left.left.left = new Node(13);
obj.root.left.right = new Node(7);
obj.root.left.right.right = new Node(11);
obj.root.left.right.left = new Node(12);

obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
System.out.print("\n Min heap Binary Tree \n");
} else {
System.out.print("\n Not a Min Heap Binary Tree \n");
}

/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2
*/
obj.root.right.right.right = new Node(2);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
System.out.print("\n Min heap Binary Tree \n");
} else {
System.out.print("\n Not a Min Heap Binary Tree \n");
}
}
}```
```

#### Output

`````` 13 9 5 12 7 11 1 8 6 10
Min heap Binary Tree
13 9 5 12 7 11 1 8 6 10 2
Not a Min Heap Binary Tree``````
``````/*
C# Program
Check whether binary tree is form of min heap
*/
using System;

//Structure of Binary Tree node
public class Node {
public int data;
public Node left;
public Node right;
//make a tree node
public Node(int data) {
//assign field values
this.data = data;
left = null;
right = null;
}
}
public class MyHeap {
public Node root;
public MyHeap() {
root = null;
}
//Check that given binary tree is form of min heap or not
public Boolean is_min_heap(Node root) {
if (root != null) {
if (root.left != null && root.left.data < root.data || root.right != null && root.right.data < root.data) {
return false;
}
if (is_min_heap(root.left) == true && is_min_heap(root.right) == true) {
return true;
}
return false;
}
return true;
}
//Display tree elements in order form
public void inorder(Node node) {
if (node != null) {
inorder(node.left);
Console.Write(" " + node.data);
inorder(node.right);
}
}
public static void Main(String[] args) {
MyHeap obj = new MyHeap();
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11

*/
//Insertion of binary tree nodes
obj.root = new Node(1);
obj.root.left = new Node(5);
obj.root.right = new Node(6);
obj.root.right.right = new Node(10);
obj.root.right.left = new Node(8);
obj.root.left.left = new Node(9);
obj.root.left.left.left = new Node(13);
obj.root.left.right = new Node(7);
obj.root.left.right.right = new Node(11);
obj.root.left.right.left = new Node(12);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
Console.Write("\n Min heap Binary Tree \n");
} else {
Console.Write("\n Not a Min Heap Binary Tree \n");
}
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2
*/
obj.root.right.right.right = new Node(2);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
Console.Write("\n Min heap Binary Tree \n");
} else {
Console.Write("\n Not a Min Heap Binary Tree \n");
}
}
}```
```

#### Output

`````` 13 9 5 12 7 11 1 8 6 10
Min heap Binary Tree
13 9 5 12 7 11 1 8 6 10 2
Not a Min Heap Binary Tree``````
``````<?php
/*
Php Program
Check whether binary tree is form of min heap
*/
//Structure of Binary Tree node
class Node {
public \$data;
public \$left;
public \$right;
//make a tree node

function __construct(\$data) {
//assign field values
\$this->data = \$data;
\$this->left = null;
\$this->right = null;
}
}
class MyHeap {
public \$root;

function __construct() {
\$this->root = null;
}
//Check that given binary tree is form of min heap or not

public 	function is_min_heap(\$root) {
if (\$root != null) {
if (\$root->left != null && \$root->left->data < \$root->data || \$root->right != null && \$root->right->data < \$root->data) {
return false;
}
if (\$this->is_min_heap(\$root->left) == true && \$this->is_min_heap(\$root->right) == true) {
return true;
}
return false;
}
return true;
}
//Display tree elements in order form

public 	function inorder(\$node) {
if (\$node != null) {
\$this->inorder(\$node->left);
//Print node value

echo(" ". \$node->data);
\$this->inorder(\$node->right);
}
}
}

function main() {
\$obj = new MyHeap();
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11

*/
//Insertion of binary tree nodes
\$obj->root = new Node(1);
\$obj->root->left = new Node(5);
\$obj->root->right = new Node(6);
\$obj->root->right->right = new Node(10);
\$obj->root->right->left = new Node(8);
\$obj->root->left->left = new Node(9);
\$obj->root->left->left->left = new Node(13);
\$obj->root->left->right = new Node(7);
\$obj->root->left->right->right = new Node(11);
\$obj->root->left->right->left = new Node(12);
\$obj->inorder(\$obj->root);
if (
\$obj->is_min_heap(\$obj->root) == true) {
echo("\n Min heap Binary Tree \n");
} else {
echo("\n Not a Min Heap Binary Tree \n");
}
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2
*/
\$obj->root->right->right->right = new Node(2);
\$obj->inorder(\$obj->root);
if (
\$obj->is_min_heap(\$obj->root) == true) {
echo("\n Min heap Binary Tree \n");
} else {
echo("\n Not a Min Heap Binary Tree \n");
}

}
main();```
```

#### Output

`````` 13 9 5 12 7 11 1 8 6 10
Min heap Binary Tree
13 9 5 12 7 11 1 8 6 10 2
Not a Min Heap Binary Tree``````
``````/*
Node Js Program
Check whether binary tree is form of min heap
*/
//Structure of Binary Tree node
class Node {
//make a tree node

constructor(data) {
//assign field values
this.data = data;
this.left = null;
this.right = null;
}
}
class MyHeap {
constructor() {
this.root = null;
}

//Check that given binary tree is form of min heap or not
is_min_heap(root) {
if (root != null) {
if (root.left != null && root.left.data < root.data || root.right != null && root.right.data < root.data) {
return false;
}

if (this.is_min_heap(root.left) == true && this.is_min_heap(root.right) == true) {
return true;
}

return false;
}

return true;
}

//Display tree elements in order form
inorder(node) {
if (node != null) {
this.inorder(node.left);
//Print node value

process.stdout.write(" " + node.data);
this.inorder(node.right);
}
}
}

function main(args) {
var obj = new MyHeap();
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11

*/
//Insertion of binary tree nodes
obj.root = new Node(1);
obj.root.left = new Node(5);
obj.root.right = new Node(6);
obj.root.right.right = new Node(10);
obj.root.right.left = new Node(8);
obj.root.left.left = new Node(9);
obj.root.left.left.left = new Node(13);
obj.root.left.right = new Node(7);
obj.root.left.right.right = new Node(11);
obj.root.left.right.left = new Node(12);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
process.stdout.write("\n Min heap Binary Tree \n");
} else {
process.stdout.write("\n Not a Min Heap Binary Tree \n");
}

/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2
*/
obj.root.right.right.right = new Node(2);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
process.stdout.write("\n Min heap Binary Tree \n");
} else {
process.stdout.write("\n Not a Min Heap Binary Tree \n");
}
}

main();```
```

#### Output

`````` 13 9 5 12 7 11 1 8 6 10
Min heap Binary Tree
13 9 5 12 7 11 1 8 6 10 2
Not a Min Heap Binary Tree``````
``````# Python 3 Program
# Check whether binary tree is form of min heap

# Structure of Binary Tree node
class Node :

# make a tree node
def __init__(self, data) :
# assign field values
self.data = data
self.left = None
self.right = None

class MyHeap :

def __init__(self) :
self.root = None

# Check that given binary tree is form of min heap or not
def is_min_heap(self, root) :
if (root != None) :
if (root.left != None and root.left.data < root.data or
root.right != None and root.right.data < root.data) :
return False

if (self.is_min_heap(root.left) == True and
self.is_min_heap(root.right) == True) :
return True

return False

return True

# Display tree elements in order form
def inorder(self, node) :
if (node != None) :
self.inorder(node.left)
print(" ", node.data, end = "")
self.inorder(node.right)

def main() :
obj = MyHeap()

#     Make A Binary Tree
#     -----------------------
#                1
#              /   \
#             5     6
#            / \    / \
#           9   7  8   10
#          /   /  \
#         13  12   11
#
#
#
# Insertion of binary tree nodes
obj.root = Node(1)
obj.root.left = Node(5)
obj.root.right = Node(6)
obj.root.right.right = Node(10)
obj.root.right.left = Node(8)
obj.root.left.left = Node(9)
obj.root.left.left.left = Node(13)
obj.root.left.right = Node(7)
obj.root.left.right.right = Node(11)
obj.root.left.right.left = Node(12)
obj.inorder(obj.root)
if (obj.is_min_heap(obj.root) == True) :
print("\n Min heap Binary Tree \n", end = "")
else :
print("\n Not a Min Heap Binary Tree \n", end = "")

#     Make A Binary Tree
#     -----------------------
#                1
#              /   \
#             5     6
#            / \    / \
#           9   7  8   10
#          /   /  \     \
#         13  12   11    2
#
obj.root.right.right.right = Node(2)
obj.inorder(obj.root)
if (obj.is_min_heap(obj.root) == True) :
print("\n Min heap Binary Tree \n", end = "")
else :
print("\n Not a Min Heap Binary Tree \n", end = "")

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

#### Output

``````  13  9  5  12  7  11  1  8  6  10
Min heap Binary Tree
13  9  5  12  7  11  1  8  6  10  2
Not a Min Heap Binary Tree``````
``````#   Ruby Program
#   Check whether binary tree is form of min heap
# Structure of Binary Tree node
class Node
# Define the accessor and reader of class Node
attr_accessor :data, :left, :right
# make a tree node
def initialize(data)
# assign field values
self.data = data
@left = nil
@right = nil
end
end

class MyHeap
# Define the accessor and reader of class MyHeap
attr_accessor :root
def initialize()
@root = nil
end
# Check that given binary tree is form of min heap or not
def is_min_heap(root)
if (root != nil)
if (root.left != nil && root.left.data < root.data || root.right != nil && root.right.data < root.data)
return false
end
if (self.is_min_heap(root.left) == true && self.is_min_heap(root.right) == true)
return true
end
return false
end
return true
end
# Display tree elements in order form
def inorder(node)
if (node != nil)
self.inorder(node.left)
# Print node value

print(" ", node.data)
self.inorder(node.right)
end
end
end
def main()
obj = MyHeap.new()

#     Make A Binary Tree
#     -----------------------
#                1
#              /   \
#             5     6
#            / \    / \
#           9   7  8   10
#          /   /  \
#         13  12   11
#
#
#
# Insertion of binary tree nodes
obj.root = Node.new(1)
obj.root.left = Node.new(5)
obj.root.right = Node.new(6)
obj.root.right.right = Node.new(10)
obj.root.right.left = Node.new(8)
obj.root.left.left = Node.new(9)
obj.root.left.left.left = Node.new(13)
obj.root.left.right = Node.new(7)
obj.root.left.right.right = Node.new(11)
obj.root.left.right.left = Node.new(12)
obj.inorder(obj.root)
if (obj.is_min_heap(obj.root) == true)
print("\n Min heap Binary Tree \n")
else
print("\n Not a Min Heap Binary Tree \n")
end

#     Make A Binary Tree
#     -----------------------
#                1
#              /   \
#             5     6
#            / \    / \
#           9   7  8   10
#          /   /  \     \
#         13  12   11    2
#
obj.root.right.right.right = Node.new(2)
obj.inorder(obj.root)
if (obj.is_min_heap(obj.root) == true)
print("\n Min heap Binary Tree \n")
else
print("\n Not a Min Heap Binary Tree \n")
end
end

main()```
```

#### Output

`````` 13 9 5 12 7 11 1 8 6 10
Min heap Binary Tree
13 9 5 12 7 11 1 8 6 10 2
Not a Min Heap Binary Tree
``````
``````/*
Scala Program
Check whether binary tree is form of min heap
*/
//Structure of Binary Tree node
//Structure of Binary Tree node
class Node(var data: Int,var left: Node,var right: Node) {
//make a tree node
def this(data: Int) {
//assign field values
this(data, null,null);
}
}
class MyHeap(var root: Node) {

def this() {
this(null);
}
//Check that given binary tree is form of min heap or not
def is_min_heap(root: Node): Boolean = {
if (root != null) {
if (root.left != null && root.left.data < root.data || root.right != null && root.right.data < root.data) {
return false;
}
if (this.is_min_heap(root.left) == true && this.is_min_heap(root.right) == true) {
return true;
}
return false;
}
return true;
}
//Display tree elements in order form
def inorder(node: Node): Unit = {
if (node != null) {
this.inorder(node.left);

//Print node value
print(" " + node.data);
this.inorder(node.right);
}
}
}
object Main {
def main(args: Array[String]): Unit = {
val obj: MyHeap = new MyHeap();

/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11

*/
//Insertion of binary tree nodes
obj.root = new Node(1);
obj.root.left = new Node(5);
obj.root.right = new Node(6);
obj.root.right.right = new Node(10);
obj.root.right.left = new Node(8);
obj.root.left.left = new Node(9);
obj.root.left.left.left = new Node(13);
obj.root.left.right = new Node(7);
obj.root.left.right.right = new Node(11);
obj.root.left.right.left = new Node(12);
obj.inorder(obj.root);

if (obj.is_min_heap(obj.root) == true) {
print("\n Min heap Binary Tree \n");
} else {
print("\n Not a Min Heap Binary Tree \n");
}
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2
*/
obj.root.right.right.right = new Node(2);
obj.inorder(obj.root);

if (obj.is_min_heap(obj.root) == true) {
print("\n Min heap Binary Tree \n");
} else {
print("\n Not a Min Heap Binary Tree \n");
}
}
}```
```

#### Output

`````` 13 9 5 12 7 11 1 8 6 10
Min heap Binary Tree
13 9 5 12 7 11 1 8 6 10 2
Not a Min Heap Binary Tree``````
``````/*
Swift Program
Check whether binary tree is form of min heap
*/
//Structure of Binary Tree node
class Node {
var data: Int;
var left: Node?;
var right: Node?;
//make a tree node

init(_ data: Int) {
//assign field values
self.data = data;
self.left = nil;
self.right = nil;
}
}
class MyHeap {
var root: Node?;
init() {
self.root = nil;
}
//Check that given binary tree is form of min heap or not
func is_min_heap(_ root: Node?) -> Bool {
if (root != nil) {
if (root!.left != nil && root!.left!.data < root!.data || root!.right != nil && root!.right!.data < root!.data) {
return false;
}
if (self.is_min_heap(root!.left) == true && self.is_min_heap(root!.right) == true) {
return true;
}
return false;
}
return true;
}
//Display tree elements in order form
func inorder(_ node: Node?) {
if (node != nil) {
self.inorder(node!.left);
print(" ", node!.data, terminator: "");
self.inorder(node!.right);
}
}
}
func main() {
let obj: MyHeap = MyHeap();
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \
13  12   11

*/
//Insertion of binary tree nodes
obj.root = Node(1);
obj.root!.left = Node(5);
obj.root!.right = Node(6);
obj.root!.right!.right = Node(10);
obj.root!.right!.left = Node(8);
obj.root!.left!.left = Node(9);
obj.root!.left!.left!.left = Node(13);
obj.root!.left!.right = Node(7);
obj.root!.left!.right!.right = Node(11);
obj.root!.left!.right!.left = Node(12);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
print("\n Min heap Binary Tree \n", terminator: "");
} else {
print("\n Not a Min Heap Binary Tree \n", terminator: "");
}
/*
Make A Binary Tree
-----------------------
1
/   \
5     6
/ \    / \
9   7  8   10
/   /  \     \
13  12   11    2
*/
obj.root!.right!.right!.right = Node(2);
obj.inorder(obj.root);
if (obj.is_min_heap(obj.root) == true) {
print("\n Min heap Binary Tree \n", terminator: "");
} else {
print("\n Not a Min Heap Binary Tree \n", terminator: "");
}
}
main();```
```

#### Output

``````  13  9  5  12  7  11  1  8  6  10
Min heap Binary Tree
13  9  5  12  7  11  1  8  6  10  2
Not a Min Heap Binary Tree``````

## Time Complexity

The time complexity of the `is_min_heap` function is O(n), where n is the number of nodes in the binary tree. This is because each node is visited exactly once during the traversal.

## Comment

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