Check if a given array is form of max heap
The problem are determining whether a given array can be considered as a valid representation of a max heap. A max heap is a binary tree data structure where each parent node has a value greater than or equal to its child nodes. This ensures that the largest element is at the root of the heap. Your task is to check if a given array follows the properties of a max heap.
Problem Statement
Given an array of integers, you need to determine whether the array represents a valid max heap or not.
Example
Let's consider the given array: [15, 12, 10, 9, 2, 5, 7, 6, 3]
The array can be visualized as a binary tree:
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
In this case, the array represents a max heap because each parent node's value is greater than or equal to its child nodes' values.
Idea to Solve
To determine whether the given array represents a max heap, you need to traverse the array and check whether the max
heap property is satisfied for each parent node. For a parent node at index i, its left child will be
at index 2*i + 1 and its right child will be at index 2*i + 2.
Pseudocode
function heap(arr, size, root):
left = 2 * root + 1
right = 2 * root + 2
if left < size and (arr[left] > arr[root] or right < size and arr[right] > arr[root]):
return false
return true
function is_max_heap(arr, size):
status = true
for i from (size / 2) - 1 to 0:
status = heap(arr, size, i)
return status
main:
arr = [15, 12, 10, 9, 2, 5, 7, 6, 3]
size = length of arr
print arr
if is_max_heap(arr, size):
print "Yes"
else:
print "No"Algorithm Explanation
-
The
heapfunction takes an array, its size, and the index of the root node as arguments. It compares the values of the root node with its left and right children. If the max heap property is violated, it returns false. -
The
is_max_heapfunction iterates through the array, starting from the parent of the last leaf node up to the root. It calls theheapfunction for each parent node to check the max heap property. If any violation is found, it returns false. -
In the
mainfunction, the given array is printed, and theis_max_heapfunction is called to determine if the array represents a max heap or not.
Code Solution
//C Program
//Check whether array is form of max heap
#include <stdio.h>
int heap(int arr[],int size,int root)
{
//Get the location of left and right child
int left = 2*root+1;
int right = 2*root+2;
if(left < size && arr[left] > arr[root] ||
(right < size && arr[right] > arr[root]))
{
//Maximum heap properties are not satisfied
return 0;
}
return 1;
}
//Display array elements
void print_data(int arr[],int size)
{
for(int i = 0; i < size; i++)
{
printf("%3d",arr[i] );
}
printf("\n");
}
//Check if a given array is form of max heap or not
int is_max_heap(int arr[],int size)
{
int status = 1;
for (int i = (size/2)-1 ; i >= 0 && status==1; i--)
{
status = heap(arr,size,i);
}
return status;
}
int main()
{
//Define collection of array elements
int arr[] = {15, 12, 10, 9, 2, 5, 7, 6, 3};
//Get the size of array
int size = sizeof(arr)/sizeof(arr[0]);
//Display array elements
print_data(arr,size);
/*
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
*/
//Check max heap properties
if(is_max_heap(arr,size)==1)
{
printf(" Yes\n");
}
else
{
printf(" No\n");
}
return 0;
}
Output
15 12 10 9 2 5 7 6 3
Yes#include<iostream>
using namespace std;
/*
C++ Program
Check whether array is form of max heap
*/
class MyHeap {
public:
bool heap(int arr[], int size, int root) {
//Get the location of left and right child
int left = 2 *root + 1;
int right = 2 *root + 2;
if (left < size && arr[left] > arr[root] ||
(right < size && arr[right] > arr[root])) {
return
//Maximum heap properties are not satisfied
false;
}
return true;
}
//Display array elements
void print_data(int arr[], int size) {
for (int i = 0; i < size; i++) {
cout << " " << arr[i];
}
cout << "\n";
}
//Check if a given array is form of max heap or not
bool is_max_heap(int arr[], int size) {
bool status = true;
for (int i = (size / 2) - 1; i >= 0 && status == true; i--) {
status = this->heap(arr, size, i);
}
return status;
}
};
int main() {
MyHeap obj = MyHeap();
int arr[] = {
15,
12,
10,
9,
2,
5,
7,
6,
3
};
//Get the size of array
int size = sizeof(arr) / sizeof(arr[0]);
//Display array elements
obj.print_data(arr, size);
/*
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
*/
//Check max heap properties
if (obj.is_max_heap(arr, size) == true) {
cout << " Yes\n";
} else {
cout << " No\n";
}
return 0;
}
Output
15 12 10 9 2 5 7 6 3
Yes/*
Java Program
Check whether array is form of max heap
*/
public class MyHeap {
public boolean heap(int []arr,int size,int root)
{
//Get the location of left and right child
int left = 2*root+1;
int right = 2*root+2;
if(left < size && arr[left] > arr[root] ||
(right < size && arr[right] > arr[root]))
{
//Maximum heap properties are not satisfied
return false;
}
return true;
}
//Display array elements
public void print_data(int []arr,int size)
{
for(int i = 0; i < size; i++)
{
System.out.print(" "+arr[i] );
}
System.out.print("\n");
}
//Check if a given array is form of max heap or not
public boolean is_max_heap(int []arr,int size)
{
boolean status = true;
for (int i = (size/2)-1 ; i >= 0 && status==true; i--)
{
status = heap(arr,size,i);
}
return status;
}
public static void main(String[] args) {
MyHeap obj = new MyHeap();
//Define Collection of array elements
int []arr = {15, 12, 10, 9, 2, 5, 7, 6, 3};
//Get the size of array
int size = arr.length;
//Display array elements
obj.print_data(arr,size);
/*
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
*/
//Check max heap properties
if(obj.is_max_heap(arr,size)==true)
{
System.out.print(" Yes\n");
}
else
{
System.out.print(" No\n");
}
}
}
Output
15 12 10 9 2 5 7 6 3
Yes/*
C# Program
Check whether array is form of max heap
*/
using System;
public class MyHeap {
public Boolean heap(int[] arr, int size, int root) {
//Get the location of left and right child
int left = 2 * root + 1;
int right = 2 * root + 2;
if (left < size && arr[left] > arr[root] ||
(right < size && arr[right] > arr[root])) {
return false;
}
return true;
}
//Display array elements
public void print_data(int[] arr, int size) {
for (int i = 0; i < size; i++) {
Console.Write(" " + arr[i]);
}
Console.Write("\n");
}
//Check if a given array is form of max heap or not
public Boolean is_max_heap(int[] arr, int size) {
Boolean status = true;
for (int i = (size / 2) - 1; i >= 0 && status == true; i--) {
status = heap(arr, size, i);
}
return status;
}
public static void Main(String[] args) {
MyHeap obj = new MyHeap();
int[]
//Define Collection of array elements
arr = {
15,
12,
10,
9,
2,
5,
7,
6,
3
};
//Get the size of array
int size = arr.Length;
obj.print_data(arr, size);
/*
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
*/
//Check max heap properties
if (obj.is_max_heap(arr, size) == true) {
Console.Write(" Yes\n");
} else {
Console.Write(" No\n");
}
}
}
Output
15 12 10 9 2 5 7 6 3
Yes<?php
/*
Php Program
Check whether array is form of max heap
*/
class MyHeap {
public function heap($arr, $size, $root) {
//Get the location of left and right child
$left = 2 *$root + 1;
$right = 2 *$root + 2;
if ($left < $size && $arr[$left] > $arr[$root] ||
($right < $size && $arr[$right] > $arr[$root])) {
return false;
}
return true;
}
//Display array elements
public function print_data($arr, $size) {
for ($i = 0; $i < $size; $i++) {
echo(" ". $arr[$i]);
}
echo("\n");
}
//Check if a given array is form of max heap or not
public function is_max_heap($arr, $size) {
$status = true;
for ($i = (intval($size / 2)) - 1; $i >= 0 && $status == true; $i--) {
$status = $this->heap($arr, $size, $i);
}
return $status;
}
}
function main() {
$obj = new MyHeap();
//Define Collection of array elements
$arr = array(15, 12, 10, 9, 2, 5, 7, 6, 3);
//Get the size of array
$size = count($arr);
//Display array elements
$obj->print_data($arr, $size);
/*
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
*/
//Check max heap properties
if (
$obj->is_max_heap($arr, $size) == true) {
echo(" Yes\n");
} else {
echo(" No\n");
}
}
main();
Output
15 12 10 9 2 5 7 6 3
Yes/*
Node Js Program
Check whether array is form of max heap
*/
class MyHeap {
heap(arr, size, root) {
//Get the location of left and right child
var left = 2 *root + 1;
var right = 2 *root + 2;
if (left < size && arr[left] > arr[root] ||
(right < size && arr[right] > arr[root])) {
return false;
}
return true;
}
//Display array elements
print_data(arr, size) {
for (var i = 0; i < size; i++) {
process.stdout.write(" " + arr[i]);
}
process.stdout.write("\n");
}
//Check if a given array is form of max heap or not
is_max_heap(arr, size) {
var status = true;
for (var i = (parseInt(size / 2)) - 1; i >= 0 && status == true; i--) {
status = this.heap(arr, size, i);
}
return status;
}
}
function main(args) {
var obj = new MyHeap();
//Define Collection of array elements
var arr = [15, 12, 10, 9, 2, 5, 7, 6, 3];
//Get the size of array
var size = arr.length;
//Display array elements
obj.print_data(arr, size);
/*
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
*/
//Check max heap properties
if (obj.is_max_heap(arr, size) == true) {
process.stdout.write(" Yes\n");
} else {
process.stdout.write(" No\n");
}
}
main();
Output
15 12 10 9 2 5 7 6 3
Yes# Python 3 Program
# Check whether array is form of max heap
class MyHeap :
def heap(self, arr, size, root) :
# Get the location of left and right child
left = 2 * root + 1
right = 2 * root + 2
if (left < size and arr[left] > arr[root] or(right < size and arr[right] > arr[root])) :
return False
return True
# Display array elements
def print_data(self, arr, size) :
i = 0
while (i < size) :
print(" ", arr[i], end = "")
i += 1
print("\n", end = "")
# Check if a given array is form of max heap or not
def is_max_heap(self, arr, size) :
status = True
i = (int(size / 2)) - 1
while (i >= 0 and status == True) :
status = self.heap(arr, size, i)
i -= 1
return status
def main() :
obj = MyHeap()
# Define Collection of array elements
arr = [15, 12, 10, 9, 2, 5, 7, 6, 3]
# Get the size of array
size = len(arr)
# Display array elements
obj.print_data(arr, size)
# 15
# / \
# 12 10
# / \ / \
# 9 2 5 7
# / \
# 6 3
#
# Check max heap properties
if (obj.is_max_heap(arr, size) == True) :
print(" Yes\n", end = "")
else :
print(" No\n", end = "")
if __name__ == "__main__":
main()
Output
15 12 10 9 2 5 7 6 3
Yes# Ruby Program
# Check whether array is form of max heap
class MyHeap
def heap(arr, size, root)
# Get the location of left and right child
left = 2 * root + 1
right = 2 * root + 2
if (left < size && arr[left] > arr[root] ||
(right < size && arr[right] > arr[root]))
return false
end
return true
end
# Display array elements
def print_data(arr, size)
i = 0
while (i < size)
print(" ", arr[i])
i += 1
end
print("\n")
end
# Check if a given array is form of max heap or not
def is_max_heap(arr, size)
status = true
i = (size / 2) - 1
while (i >= 0 && status == true)
status = self.heap(arr, size, i)
i -= 1
end
return status
end
end
def main()
obj = MyHeap.new()
# Define Collection of array elements
arr = [15, 12, 10, 9, 2, 5, 7, 6, 3]
# Get the size of array
size = arr.length
# Display array elements
obj.print_data(arr, size)
# 15
# / \
# 12 10
# / \ / \
# 9 2 5 7
# / \
# 6 3
#
# Check max heap properties
if (obj.is_max_heap(arr, size) == true)
print(" Yes\n")
else
print(" No\n")
end
end
main()
Output
15 12 10 9 2 5 7 6 3
Yes
/*
Scala Program
Check whether array is form of max heap
*/
class MyHeap {
def heap(arr: Array[Int], size: Int, root: Int): Boolean = {
//Get the location of left and right child
val left: Int = 2 * root + 1;
val right: Int = 2 * root + 2;
if (left < size && arr(left) > arr(root) ||
(right < size && arr(right) > arr(root))) {
return false;
}
return true;
}
//Display array elements
def print_data(arr: Array[Int], size: Int): Unit = {
var i: Int = 0;
while (i < size) {
print(" " + arr(i));
i += 1;
}
print("\n");
}
//Check if a given array is form of max heap or not
def is_max_heap(arr: Array[Int], size: Int): Boolean = {
var status: Boolean = true;
var i: Int = ((size / 2).toInt) - 1;
while (i >= 0 && status == true) {
status = this.heap(arr, size, i);
i -= 1;
}
return status;
}
}
object Main {
def main(args: Array[String]): Unit = {
val obj: MyHeap = new MyHeap();
//Define Collection of array elements
val arr: Array[Int] = Array(15, 12, 10, 9, 2, 5, 7, 6, 3);
//Get the size of array
val size: Int = arr.length;
//Display array elements
obj.print_data(arr, size);
/*
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
*/
//Check max heap properties
if (obj.is_max_heap(arr, size) == true) {
print(" Yes\n");
} else {
print(" No\n");
}
}
}
Output
15 12 10 9 2 5 7 6 3
Yes/*
Swift Program
Check whether array is form of max heap
*/
class MyHeap {
func heap(_ arr: [Int], _ size: Int, _ root: Int) -> Bool {
//Get the location of left and right child
let left: Int = 2 * root + 1;
let right: Int = 2 * root + 2;
if (left < size && arr[left] > arr[root] ||
(right < size && arr[right] > arr[root])) {
return false;
}
return true;
}
//Display array elements
func print_data(_ arr: [Int], _ size: Int) {
var i: Int = 0;
while (i < size) {
print(" ", arr[i], terminator: "");
i += 1;
}
print("\n", terminator: "");
}
//Check if a given array is form of max heap or not
func is_max_heap(_ arr: [Int], _ size: Int) -> Bool {
var status: Bool = true;
var i: Int = (size / 2) - 1;
while (i >= 0 && status == true) {
status = self.heap(arr, size, i);
i -= 1;
}
return status;
}
}
func main() {
let obj: MyHeap = MyHeap();
//Define Collection of array elements
let arr: [Int] = [15, 12, 10, 9, 2, 5, 7, 6, 3];
//Get the size of array
let size: Int = arr.count;
//Display array elements
obj.print_data(arr, size);
/*
15
/ \
12 10
/ \ / \
9 2 5 7
/ \
6 3
*/
//Check max heap properties
if (obj.is_max_heap(arr, size) == true) {
print(" Yes");
} else {
print(" No");
}
}
main();
Output
15 12 10 9 2 5 7 6 3
YesTime Complexity
The time complexity of this algorithm depends on the size of the array, n. The is_max_heap
function iterates through at most n/2 parent nodes, and for each parent node, the heap
function performs constant-time operations. Hence, the overall time complexity is O(n).
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