# Print N distinct numbers following the given operations

Given an integer N which is always an even number, our task is to print N distinct numbers following the given conditions:

• The first half numbers are even whereas the other half numbers are odd
• Sum of the elements of first half numbers and sum of elements of second half numbers should be equal

Print the array if the above conditions satisfy otherwise output “-1”.

Examples:

Input: N = 4
Output: 2 4 1 5
Explanation:
Given number 4 we are required to print 4 numbers. First Half = 2, 4 and their sum is 6, other half = 1, 5 and their sum is also 6.

Input: N = 22
Output: -1
Explanation:
It is not possible to print the required array.

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

Approach:

To solve the problem mentioned above we have to observe that the integer N has to be a multiple of 4.

• We know that the sum of the first N/2 even numbers will be even, so if the sum of the other N/2 integers is also even then N/2 must be even, because the sum of an odd number of odd integers is always odd.
• If N/2 is even then N is a multiple of 4, so if n is not divisible by 4 then the answer is “-1”, otherwise, there will be a possible array.
• For printing the array we will consider two parts such that the first half that is N/2 elements will be simply multiples of 2 and the other half will be multiple of 2 – 1. For the last element in the array, we will calculate the integer by applying the direct formula N + N / 2 – 1 because we are supposed to make the sum for two halves equal.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to Print N distinct numbers ` `#include ` `using` `namespace` `std; ` ` `  `// Function to print the required array ` `bool` `printArr(``int` `n) ` `{ ` ` `  `    ``// Check if number is a multiple of 4 ` `    ``if` `(n % 4 == 0) { ` `        ``// Printing Left Half of the array ` `        ``for` `(``int` `i = 1; i <= n / 2; i++) ` `            ``cout << i * 2 << ``' '``; ` ` `  `        ``// Printing Right Half of the array ` `        ``for` `(``int` `i = 1; i < n / 2; i++) ` `            ``cout << i * 2 - 1 << ``' '``; ` `        ``cout << n + n / 2 - 1 << ``'\n'``; ` `    ``} ` ` `  `    ``else` `        ``cout << ``"-1"``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 22; ` ` `  `    ``printArr(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation to print N distinct numbers ` `import` `java.util.*; ` ` `  `class` `GFG{ ` ` `  `// Function to print the required array ` `static` `void` `printArr(``int` `n) ` `{ ` ` `  `    ``// Check if number is a multiple of 4 ` `    ``if``(n % ``4` `== ``0``) ` `    ``{ ` `       ``// Printing left half of the array ` `       ``for``(``int` `i = ``1``; i <= n / ``2``; i++) ` `           ``System.out.print(i * ``2` `+ ``" "``); ` ` `  `       ``// Printing Right Half of the array ` `       ``for``(``int` `i = ``1``; i < n / ``2``; i++) ` `           ``System.out.print(i * ``2` `- ``1` `+ ``" "``); ` ` `  `       ``System.out.println(n + n / ``2` `- ``1``); ` `    ``} ` `    ``else` `        ``System.out.print(``"-1"``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``22``; ` `    ``printArr(n); ` `} ` `} ` ` `  `// This code is contributed by amal kumar choubey `

## Python3

 `# Python3 implementation to print  ` `# N distinct numbers  ` ` `  `# Function to print the required array  ` `def` `printArr(n):  ` ` `  `    ``# Check if number is a multiple of 4  ` `    ``if` `(n ``%` `4` `=``=` `0``): ` `         `  `        ``# Printing Left Half of the array  ` `        ``for` `i ``in` `range``(``1``, (n ``/` `2``) ``+` `1``): ` `            ``print` `(i ``*` `2``, end ``=` `" "``)  ` ` `  `        ``# Printing Right Half of the array  ` `        ``for` `i ``in` `range``(``1``, n ``/` `2``): ` `            ``print` `(i ``*` `2` `-` `1``, end ``=` `" "``)  ` `             `  `        ``print` `(n ``+` `n ``/` `2` `-` `1``, end ``=` `"\n"``)  ` ` `  `    ``else``: ` `        ``print` `(``"-1"``)  ` ` `  `# Driver code ` `n ``=` `22` `printArr(n) ` ` `  `# This code is contributed by PratikBasu `

## C#

 `// C# implementation to print N distinct numbers ` `using` `System; ` ` `  `public` `class` `GFG{ ` ` `  `// Function to print the required array ` `static` `void` `printArr(``int` `n) ` `{ ` ` `  `    ``// Check if number is a multiple of 4 ` `    ``if``(n % 4 == 0) ` `    ``{ ` `         `  `    ``// Printing left half of the array ` `    ``for``(``int` `i = 1; i <= n / 2; i++) ` `        ``Console.Write(i * 2 + ``" "``); ` ` `  `    ``// Printing Right Half of the array ` `    ``for``(``int` `i = 1; i < n / 2; i++) ` `        ``Console.Write(i * 2 - 1 + ``" "``); ` ` `  `    ``Console.WriteLine(n + n / 2 - 1); ` `    ``} ` `     `  `    ``else` `        ``Console.Write(``"-1"``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `n = 22; ` `    ``printArr(n); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```-1
```

Time Complexity: O(N)

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