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Permutations to arrange N persons around a circular table

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  • Difficulty Level : Medium
  • Last Updated : 08 Jun, 2022

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 implementation of above idea: 
 

C++




// 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);
}


Java




// 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


Python 3




# 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


C#




// 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*/


PHP




<?php
// PHP code to demonstrate Circular Permutation
 
// Function to find no. of permutations
function Circular($n)
{
    $Result = 1;
 
    while ($n > 0)
    {
        $Result = $Result * $n;
        $n--;
    }
 
    return $Result;
}
 
// Driver Code
$n = 4;
 
echo Circular($n - 1);
 
// This code is contributed by mits
?>


Javascript




<script>
// javascript code to demonstrate
// Circular Permutation
 
    // Function to find no.
    // of permutations
    function Circular(n)
    {
        var Result = 1;
        while (n > 0)
        {
            Result = Result * n;
            n--;
        }
 
        return Result;
    }
 
    // Driver Code
    var n = 4;
    document.write(Circular(n - 1));
 
// This code is contributed by Rajput-Ji
</script>


Output: 

6

 

Time Complexity: O(N) where N is the number of persons.
Auxiliary Space: O(1)


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