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.

**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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` |

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**Output:**

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

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

**Space Complexity:**O(1)## Recommended Posts:

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