# Find permutation of first N natural numbers that satisfies the given condition in C++

C++Server Side ProgrammingProgramming

Suppose we have two integers N and K, and we have to find the permutation P of first N natural numbers such that there are exactly K elements which satisfies the condition GCD(P[i], i) > 1 for all 1 <= i <= N. So when N = 3 and K = 1, then output will be 2, 1, 3. And gcd(2, 1) = 1, gcd(1, 2) = 1, gcd(3, 3) = 3

The approach is simple, we will keep the last k elements in their place, the rest of the elements are moved, such that ith element will be placed in (i + 1)th position and (N - K)th element is kept in position 1, because gcd(x, x+1) = 1.

## Example

Live Demo

#include<iostream>
using namespace std;
void findPermutation(int n, int k) {
int permutation[n + 1];
for (int i = 1; i <= n; i++)
permutation[i] = i;
for (int i = 1; i < n - k; i++)
permutation[i + 1] = i;
permutation[1] = n - k;
for (int i = 1; i <= n; i++)
cout << permutation[i] << " ";
}
int main() {
int n = 5, k = 2;
cout << "The permutation is: ";
findPermutation(n, k);
}

## Output

The permutation is: 3 1 2 4 5
Updated on 18-Dec-2019 12:52:46