Permutations to arrange N persons around a circular table

Given N, the number of persons. The task is to arrange N person around a circular table.

Examples:

Input: N = 4
Output: 6

Input: N = 5
Output: 24


Approach: It is the concept of Circular permutation i.e. there is no specific starting point in the arrangement, any element can be considered as the start of the arrangement.

For N = 4, Arrangements will be:

Below is the formula to find Circular permutations:

Circular Permutations = (N - 1)!

Below is the impplementation of above idea:

C++

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// C++ code to demonstrate Circular Permutation
#include <bits/stdc++.h>
using namespace std;
  
// Function to find no. of permutations
int Circular(int n)
{
  
    int Result = 1;
  
    while (n > 0) {
        Result = Result * n;
        n--;
    }
  
    return Result;
}
  
// Driver Code
int main()
{
    int n = 4;
  
    cout << Circular(n - 1);
}

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Java

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// Java code to demonstrate 
// Circular Permutation 
import java.io.*;
  
class GFG
{
// Function to find no. 
// of permutations 
static int Circular(int n) 
  
    int Result = 1
  
    while (n > 0
    
        Result = Result * n; 
        n--; 
    
  
    return Result; 
  
// Driver Code
public static void main(String[] args)
{
    int n = 4;
      
    System.out.println(Circular(n - 1));
}
}
  
// This code is contributed 
// by Naman_Garg

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Python 3

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# Python 3 Program to demonstrate Circular Permutation  
  
# Function to find no. of permutations
def Circular(n) :
    Result = 1
  
    while n > 0 :
        Result = Result * n
        n -= 1
  
    return Result
      
# Driver Code
if __name__ == "__main__" :
    n = 4
  
    # function calling
    print(Circular(n-1))
  
# This code is contributed by ANKITRAI1

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C#

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// C# code to demonstrate 
// Circular Permutation 
using System;
                      
  
public class GFG {
  
// Function to find no. 
// of permutations 
static int Circular(int n) 
   
    int Result = 1; 
   
    while (n > 0) 
    
        Result = Result * n; 
        n--; 
    
   
    return Result; 
   
// Driver Code
public static void Main()
{
    int n = 4;
       
    Console.Write(Circular(n - 1));
}
}
   
/* This Java code is contributed by 29AjayKumar*/

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PHP

0)
{
$Result = $Result * $n;
$n–;
}

return $Result;
}

// Driver Code
$n = 4;

echo Circular($n – 1);

// This code is contributed by mits
?>

Output:

6


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