Permutations to arrange N persons around a circular table

Last Updated : 31 Aug, 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# 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:

Time Complexity: O(N) where N is the number of persons.
Auxiliary Space: O(1), since no extra space has been taken.

Count the number of ways to give ranks for N students such that same ranks are possible

Naman_Garg

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Permutations to arrange N persons around a circular table

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