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# Find the good permutation of first N natural numbers 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

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