Find Good Permutation of First N Natural Numbers in C++

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

permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

Good Permutation is a permutation in which $1\leqslant{i}\leqslant{N}$ and follows,

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

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

Let's take an example to understand the 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