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# Construct an Array such that cube sum of all element is a perfect square

Given the size of array N, the task is to construct an array of size N with positive integer elements such that the cube sum of all elements of this array is a perfect square.
Note: Repetitions of integers are allowed.
Example:

Input: N = 1
Output:
Explanation: Cube of 4 is 64, and 64 is perfect square.
Input: N = 6
Output: 5 10 5 10 5 5
Explanation: Cubic sum of array element is (5)3 + (10)3 + (5)3 + (10)3 + (5)3 + (5)3 = 2500, and 2500 is perfect square.

Approach: The idea is to construct array of size, N which contain first N natural number. If closely observed,

cubic sum of first N natural number: (1)3 + (2)3 + (3)3 + (4)3 + …….(N)3 is always perfect square.
as

Below is the implementation of the above approach.

## C++

 // C++ program to construct an array // that cube sum of all element // is a perfect square   #include  using namespace std;   // Function to create // and print the array void constructArray(int N) {     int arr[N];       // initialise the array of size N     for (int i = 1; i <= N; i++) {         arr[i - 1] = i;     }       // Print the array     for (int i = 0; i < N; i++) {         cout << arr[i] << ", ";     } }   // Driver code int main() {     int N = 6;       constructArray(N);       return 0; }

## Java

 // Java program to construct array // that cube sum of all element // is a perfect square import java.util.*;   class GFG{   // Function to create // and print the array static void constructArray(int N) {     int arr[] = new int[N];       // Initialise the array of size N     for(int i = 1; i <= N; i++)     {        arr[i - 1] = i;     }       // Print the array     for(int i = 0; i < N; i++)      {         System.out.print(arr[i] + ", ");     } }   // Driver code public static void main(String[] args) {     int N = 6;       constructArray(N); } }   // This code is contributed by AbhiThakur

## Python3

 # Python3 program to construct  # array that cube sum of all   # element is a perfect square    # Function to create  # and print the array  def constructArray(N):       arr = [0] * N       # Initialise the array of size N      for i in range(1, N + 1):         arr[i - 1] = i;            # Print the array      for i in range(N):          print(arr[i], end = ", ")    # Driver code  N = 6;  constructArray(N);    # This code is contributed by grand_master

## C#

 // C# program to construct array // that cube sum of all element // is a perfect square using System;   class GFG{   // Function to create // and print the array static void constructArray(int N) {     int []arr = new int[N];       // Initialise the array of size N     for(int i = 1; i <= N; i++)     {        arr[i - 1] = i;     }       // Print the array     for(int i = 0; i < N; i++)      {        Console.Write(arr[i] + ", ");     } }   // Driver code public static void Main() {     int N = 6;       constructArray(N); } }   // This code is contributed by Code_Mech

## Javascript

 

Output:

1, 2, 3, 4, 5, 6,

Time Complexity: O(N) where N is the size of the Array.
Space Complexity: O(N), for creating an array to store the answer.

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