Given two integer N and K, the task is 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.
Examples:
Input: N = 3, K = 1
Output: 2 1 3
GCD(P[1], 1) = GCD(2, 1) = 1
GCD(P[2], 2) = GCD(1, 2) = 1
GCD(P[3], 3) = GCD(3, 3) = 3
There is exactly 1 element such that GCD(P[i], i) > 1
Input: N = 5, K = 2
Output: 3 1 2 4 5
Approach: Keep the last K elements in their place. The rest of the elements are moved such that ith element is placed in (i + 1)th position and (N – K)th element is kept in position 1 because gcd(x, x + 1) = 1.
Below is the implementation of the above approach:
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
// Function to find permutation(p) of first N // natural numbers such that there are exactly K // elements of permutation such that GCD(p[i], i)>1 void Permutation( int n, int k)
{ int p[n + 1];
// First place all the numbers
// in their respective places
for ( int i = 1; i <= n; i++)
p[i] = i;
// Modify for first n-k integers
for ( int i = 1; i < n - k; i++)
p[i + 1] = i;
// In first index place n-k
p[1] = n - k;
// Print the permutation
for ( int i = 1; i <= n; i++)
cout << p[i] << " " ;
} // Driver code int main()
{ int n = 5, k = 2;
Permutation(n, k);
return 0;
} |
// Java implementation of the approach class GFG
{ // Function to find permutation(p) of first N
// natural numbers such that there are exactly K
// elements of permutation such that GCD(p[i], i)>1
static void Permutation( int n, int k)
{
int [] p = new int [n + 1 ];
// First place all the numbers
// in their respective places
for ( int i = 1 ; i <= n; i++)
p[i] = i;
// Modify for first n-k integers
for ( int i = 1 ; i < n - k; i++)
p[i + 1 ] = i;
// In first index place n-k
p[ 1 ] = n - k;
// Print the permutation
for ( int i = 1 ; i <= n; i++)
System.out.print(p[i] + " " );
}
// Driver code
public static void main(String[] args)
{
int n = 5 , k = 2 ;
Permutation(n, k);
}
} // This code is contributed by Naman_Garg |
# Python 3 implementation of the approach # Function to find permutation(p) # of first N natural numbers such that # there are exactly K elements of # permutation such that GCD(p[i], i)>1 def Permutation(n, k):
p = [ 0 for i in range (n + 1 )]
# First place all the numbers
# in their respective places
for i in range ( 1 , n + 1 ):
p[i] = i
# Modify for first n-k integers
for i in range ( 1 , n - k):
p[i + 1 ] = i
# In first index place n-k
p[ 1 ] = n - k
# Print the permutation
for i in range ( 1 , n + 1 ):
print (p[i], end = " " )
# Driver code if __name__ = = '__main__' :
n = 5
k = 2
Permutation(n, k)
# This code is contributed by # Surendra_Gangwar |
// C# implementation of the approach using System;
class GFG
{ // Function to find permutation(p) of first N
// natural numbers such that there are exactly K
// elements of permutation such that GCD(p[i], i)>1
static void Permutation( int n, int k)
{
int [] p = new int [n + 1];
// First place all the numbers
// in their respective places
for ( int i = 1; i <= n; i++)
p[i] = i;
// Modify for first n-k integers
for ( int i = 1; i < n - k; i++)
p[i + 1] = i;
// In first index place n-k
p[1] = n - k;
// Print the permutation
for ( int i = 1; i <= n; i++)
Console.Write(p[i] + " " );
}
// Driver code
static public void Main ()
{
int n = 5, k = 2;
Permutation(n, k);
}
} // This code is contributed by ajit. |
<?php // PHP implementation of the approach // Function to find permutation(p) of first N // natural numbers such that there are exactly K // elements of permutation such that GCD(p[i], i)>1 function Permutation( $n , $k )
{ $p = array ();
// First place all the numbers
// in their respective places
for ( $i = 1; $i <= $n ; $i ++)
$p [ $i ] = $i ;
// Modify for first n-k integers
for ( $i = 1; $i < $n - $k ; $i ++)
$p [ $i + 1] = $i ;
// In first index place n-k
$p [1] = $n - $k ;
// Print the permutation
for ( $i = 1; $i <= $n ; $i ++)
echo $p [ $i ], " " ;
} // Driver code $n = 5; $k = 2;
Permutation( $n , $k );
// This code is contributed by AnkitRai01 ?> |
<script> //Javascript implementation of the approach // Function to find permutation(p) of first N // natural numbers such that there are exactly K // elements of permutation such that GCD(p[i], i)>1 function Permutation(n, k)
{ let p = new Array(n + 1);
// First place all the numbers
// in their respective places
for (let i = 1; i <= n; i++)
p[i] = i;
// Modify for first n-k integers
for (let i = 1; i < n - k; i++)
p[i + 1] = i;
// In first index place n-k
p[1] = n - k;
// Print the permutation
for (let i = 1; i <= n; i++)
document.write(p[i] + " " );
} // Driver code let n = 5, k = 2;
Permutation(n, k);
// This code is contributed by Mayank Tyagi </script> |
3 1 2 4 5
Time Complexity: O(n)
Auxiliary Space: O(n)