将组分为两半的方式，以使两个元素位于不同的组中

给定2n个女孩，并随机分为两个子组，每个子组包含n个女孩。任务是计算形成小组的方式的数量，以使两个漂亮的女孩成为不同的小组。
例子：

Input: 4 
Output: 4 
Let group be r1, r2, b1, b2 where b1 and b2 are beautiful girls 
Groups are: ((r1, b1) (r2, b2)), ((r1, b2) (r2, b1)), ((r2, b2) (r1, b1)), ((r2, b1) (r1, b2))
Input: 8 
Output: 40 

方法：有两个方法可以将两个漂亮的女孩分在不同的组中，并分别将剩余的(2n – 2)个女孩分为两个组： ${2n-2}_C_{n-1}$
因此，总数为2 * ${2n-2}_C_{n-1}$
实施代码：

C++

// CPP Program to count
// Number of ways in which two
// Beautiful girls are in different group
#include 
using namespace std;
 
// This function will
// return the factorial of a given number
int factorial(int n)
{
    int result = 1;
    for (int i = 1; i <= n; i++)
        result = result * i;
    return result;
}
 
// This function will calculate nCr of given
// n and r
int nCr(int n, int r)
{
    return factorial(n) / (factorial(r) * factorial(n - r));
}
 
// This function will
// Calculate number of ways
int calculate_result(int n)
{
    int result = 2 * nCr((n - 2), (n / 2 - 1));
    return result;
}
 
// Driver Code
int main(void)
{
    int a = 2, b = 4;
    cout << calculate_result(2 * a) << endl;
    cout << calculate_result(2 * b) << endl;
 
    return 0;
}

Java

//Java Program to count
// Number of ways in which two
// Beautiful girls are in different group
 
import java.io.*;
 
class GFG {
 
// This function will
// return the factorial of a given number
static int factorial(int n)
{
    int result = 1;
    for (int i = 1; i <= n; i++)
        result = result * i;
    return result;
}
 
// This function will calculate nCr of given
// n and r
static int nCr(int n, int r)
{
    return factorial(n) / (factorial(r) * factorial(n - r));
}
 
// This function will
// Calculate number of ways
static int calculate_result(int n)
{
    int result = 2 * nCr((n - 2), (n / 2 - 1));
    return result;
}
 
// Driver Code
 
    public static void main (String[] args) {
        int a = 2, b = 4;
    System.out.println( calculate_result(2 * a));
    System.out.print(calculate_result(2 * b));
 
    }
}
 
// This code is contributed by inder_verma..

Python3

# Python3 Program to count
# Number of ways in which two
# Beautiful girls are in different group
 
# This function will
# return the factorial of a
# given number
def factorial(n) :
 
    result = 1
    for i in range(1, n + 1) :
        result *= i
         
    return result
 
# This function will calculate nCr of given
# n and r
def nCr(n, r) :
 
    return (factorial(n) // (factorial(r)
            * factorial(n - r)))
 
 
# This function will
# Calculate number of ways
def calculate_result(n) :
 
    result = 2 * nCr((n -2), (n // 2 - 1))
 
    return result
 
 
# Driver code
if __name__ == "__main__" :
 
    a, b = 2, 4
    print(calculate_result(2 * a))
    print(calculate_result(2 * b))
 
# This code is contributed by
# ANKITRAI1

C#

//C# Program to count
// Number of ways in which two
// Beautiful girls are in different groupusing System;
 
using System;
 
public class GFG {
  
// This function will
// return the factorial of a given number
static int factorial(int n)
{
    int result = 1;
    for (int i = 1; i <= n; i++)
        result = result * i;
    return result;
}
  
// This function will calculate nCr of given
// n and r
static int nCr(int n, int r)
{
    return factorial(n) / (factorial(r) * factorial(n - r));
}
  
// This function will
// Calculate number of ways
static int calculate_result(int n)
{
    int result = 2 * nCr((n - 2), (n / 2 - 1));
    return result;
}
  
// Driver Code
  
    public static void Main () {
        int a = 2, b = 4;
    Console.WriteLine( calculate_result(2 * a));
    Console.Write(calculate_result(2 * b));
  
    }
}
  
// This code is contributed by Subhadeep

输出：

4
40

时间复杂度： O(N)

辅助空间： O(1)