# 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 = 1Output:4Explanation:Cube of 4 is 64, and 64 is perfect square.Input:N = 6Output:5 10 5 10 5 5Explanation: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

Nnatural 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 <bits/stdc++.h>` `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

`<script>` `// JavaScript program to construct an array` `// that cube sum of all element` `// is a perfect square` `// Function to create` `// and print the array` `function` `constructArray(N)` `{` ` ` `let arr = ` `new` `Array(N);` ` ` `// initialise the array of size N` ` ` `for` `(let i = 1; i <= N; i++)` ` ` `{` ` ` `arr[i - 1] = i;` ` ` `}` ` ` `// Print the array` ` ` `for` `(let i = 0; i < N; i++)` ` ` `{` ` ` `document.write(arr[i] + ` `", "` `);` ` ` `}` `}` `// Driver code` `let N = 6;` `constructArray(N);` `// This code is contributed by Manoj.` `</script>` |

**Output:**

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

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

**Space Complexity:**O(1)