Construct an Array of size N whose sum of cube of all elements is a perfect square

Last Updated : 20 Dec, 2022

Given an integer N, the tasks is to construct a sorted array arr[] of size N, such that the sum of cube of all elements is a perfect square, i.e. \sum_{}A_i^3=X^2 , where X is an integer.

Examples:

Input: N = 5
Output: 1 2 3 4 5
Explanation
Sum of cube of all elements = 1 + 8 + 27 + 64 + 125 = 225
which is a perfect square number.

Input: N = 1
Output: 1

Solution Approach:

The sum of cubes of first N natural number is given by:
(\frac{N \times(N+1)}{2})^2
So, the summation is itself, a perfect square of the integer X^2&=(\frac{N \times(N+1)}{2})^2
Therefore X&=(\frac{N \times(N+1)}{2}) , which is nothing but sum of N natural numbers.
So, just print the first N natural numbers to construct the array.

Below is the implementation of the above approach:

C++

// C++ implementation of the
// above approach

#include <bits/stdc++.h>
using namespace std;

// Function to construct an array
// of size N
void constructArray(int N)
{
    for (int i = 1; i <= N; i++) {

        // Prints the first N
        // natural numbers
        cout << i << " ";
    }
}

// Driver code
int main()
{
    int N = 5;
    constructArray(N);
    return 0;
}

Java

// Java implementation of the 
// above approach
import java.io.*;
public class GFG{
    
// Function to construct an array 
// of size N 
public static void constructArray(int N) 
{ 
    for(int i = 1; i <= N; i++)
    { 
       
       // Prints the first N 
       // natural numbers 
       System.out.print(i + " ");
    } 
} 

// Driver Code
public static void main(String[] args)
{
    int N = 5;
    constructArray(N); 
}
}

// This code is contributed by divyeshrabadiya07

Python3

# Python3 implementation of the 
# above approach 

# Function to construct an array 
# of size N 
def constructArray(N):
    
    for i in range(1, N + 1):
        
        # Prints the first N 
        # natural numbers 
        print(i, end = ' ')
        

# Driver code 
if __name__=='__main__':
    
    N = 5
    
    constructArray(N)

# This code is contributed by rutvik_56

// C# implementation of the 
// above approach 
using System;
class GFG{
    
// Function to construct an array 
// of size N 
public static void constructArray(int N) 
{ 
    for(int i = 1; i <= N; i++)
    { 
        
        // Prints the first N 
        // natural numbers 
        Console.Write(i + " ");
    } 
} 

// Driver Code
public static void Main(String[] args)
{
    int N = 5;
    constructArray(N); 
}
}

// This code is contributed by sapnasingh4991

JavaScript

<script>

// JavaScript implementation of the
// above approach

// Function to construct an array
// of size N
function constructArray(N)
{
    for(let i = 1; i <= N; i++)
    {
        
        // Prints the first N
        // natural numbers
        document.write(i + " ");
    }
}

// Driver code
let N = 5;

constructArray(N);

// This code is contributed by Surbhi Tyagi.

</script>