Find a good permutation of the first N natural numbers C++

In this problem, we have an integer value N. Our task is to find a good permutation of the first N natural numbers.

Arrangement is the arrangement of all or part of a set of objects, taking into account the order of arrangement.

Good permutation is a permutation where $1\leqslant{i}\leqslant{N}$ satisfies the following conditions:

$P_{pi}\:= \:i$

$P_{p!}\:=\:i$

Let us give an example to understand this problem,

Input : N = 1
Output : -1

Solution Approach

A simple solution to the problem is by finding permutations p such that p_i = i.

Then we will reconsider the equation to satisfy p_i != i. So, for a value x such that $2x \leqslant x$, we have p^{2x - 1} and p^2k. Now, we have an equation that satisfies the permutation equation for n. Here, the solution for the equation.

Example

Program to illustrate the working of our solution

#include <iostream>
using namespace std;
void printGoodPermutation(int n) {
   if (n % 2 != 0)
      cout<<-1;
   else
      for (int i = 1; i <= n / 2; i++)
         cout<<(2*i)<<"\t"<<((2*i) - 1)<<"\t";
}
int main() {
   int n = 4;
   cout<<"Good Permutation of first N natural Numbers : \n"; printGoodPermutation(n);
   return 0;
}

Output

Good Permutation of first N natural Numbers :
2 1 4 3

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