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

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:



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

Below is the implementation of the above approach:

C++

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// 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;
}

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Java

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// Java implementation of the 
// above approach 
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    

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Python3

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# 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    

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C#

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// 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

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Output:

1 2 3 4 5

Time Complexity: O(N)
Auxiliary Space: O(1)

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