# Arrange first N natural numbers such that absolute difference between all adjacent elements > 1

Given an integer N. The task is to find the permutation of first N natural numbers such that the absolute difference between any two consecutive numbers > 1. If no such permutation is possible then print -1.

Examples:

Input: N = 5
Output: 5 3 1 4 2

Input: N = 3
Output: -1

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

Approach: There may be many such arrangements possible but one of the most common and greedy approach is to arrange all odd numbers in decreasing (or increasing) order and after that arrange all even numbers in decreasing (or increasing) order. Note that if N = 3 or N = 2 then there will be no such arrangement possible and if N = 1 then the sequence will consist of a single element i.e. 1.

Below is the implementation of the above approach:

## C++

 // C++ implementation of the approach #include using namespace std;    // Function to print the required permutation void arrange(int N) {        if (N == 1) {         cout << "1";         return;     }        // No permutation is possible     // satisfying the given condition     if (N == 2 || N == 3) {         cout << "-1";         return;     }        // Maximum even and odd elements < N     int even = -1, odd = -1;     if (N % 2 == 0) {         even = N;         odd = N - 1;     }     else {         odd = N;         even = N - 1;     }        // Print all odd elements in decreasing order     while (odd >= 1) {         cout << odd << " ";            // Next element must be odd         odd = odd - 2;     }        // Print all even elements in decreasing order     while (even >= 2) {         cout << even << " ";            // Next element must be even         even = even - 2;     } }    // Driver code int main() {     int N = 5;     arrange(N);        return 0; }

## Java

 // Java implementation of the approach class GFG  {     // Function to print the required  // permutation static void arrange(int N) {     if (N == 1)      {         System.out.println("1");         return;     }        // No permutation is possible     // satisfying the given condition     if (N == 2 || N == 3)      {         System.out.println("-1");         return;     }        // Maximum even and odd elements < N     int even = -1, odd = -1;     if (N % 2 == 0)      {         even = N;         odd = N - 1;     }     else     {         odd = N;         even = N - 1;     }        // Print all odd elements in     // decreasing order     while (odd >= 1)      {         System.out.print(odd);         System.out.print(" ");                // Next element must be odd         odd = odd - 2;     }        // Print all even elements in     // decreasing order     while (even >= 2)      {         System.out.print(even);         System.out.print(" ");            // Next element must be even         even = even - 2;     } }    // Driver code public static void main(String[] args)  {      int N = 5;     arrange(N); } }    // This code is contributed  // by Akanksha Rai

## Python 3

 # Python 3 implementation of the approach    # Function to print the required permutation def arrange(N):        if (N == 1) :         print("1")         return        # No permutation is possible     # satisfying the given condition     if (N == 2 or N == 3) :         print("-1")         return        # Maximum even and odd elements < N     even = -1     odd = -1     if (N % 2 == 0):         even = N         odd = N - 1     else :         odd = N         even = N - 1        # Print all odd elements in      # decreasing order     while (odd >= 1):         print(odd, end = " ")            # Next element must be odd         odd = odd - 2        # Print all even elements in      # decreasing order     while (even >= 2):         print(even, end = " ")            # Next element must be even         even = even - 2    # Driver code if __name__ == "__main__":        N = 5     arrange(N)    # This code is contributed by ita_c

## C#

 // C# implementation of the approach using System;     class GFG  {     // Function to print the required  // permutation static void arrange(int N) {     if (N == 1)      {         Console.WriteLine("1");         return;     }        // No permutation is possible     // satisfying the given condition     if (N == 2 || N == 3)      {         Console.WriteLine("-1");         return;     }        // Maximum even and odd elements < N     int even = -1, odd = -1;     if (N % 2 == 0)      {         even = N;         odd = N - 1;     }     else     {         odd = N;         even = N - 1;     }        // Print all odd elements in     // decreasing order     while (odd >= 1)      {         Console.Write(odd);         Console.Write(" ");                // Next element must be odd         odd = odd - 2;     }        // Print all even elements in     // decreasing order     while (even >= 2)      {         Console.Write(even);         Console.Write(" ");            // Next element must be even         even = even - 2;     } }    // Driver code public static void Main()  {      int N = 5;     arrange(N); } }    // This code is contributed  // by Shivi_Aggarwal

## PHP

 = 1)      {          echo \$odd, " ";             // Next element must be odd          \$odd = \$odd - 2;      }         // Print all even elements in      // decreasing order      while (\$even >= 2)      {          echo \$even, " ";             // Next element must be even          \$even = \$even - 2;      }  }     // Driver code  \$N = 5;  arrange(\$N);    // This code is contributed by Ryuga ?>

Output:

5 3 1 4 2

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