# 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: Repititions of integers are allowed.

Example:

Input: N = 1
Output: 4
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.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++ 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 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 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 =  * 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# 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

Output:
1, 2, 3, 4, 5, 6,


Time Complexity: O(N) where N is the size of the Array.
Space Complexity: O(1)