# Program to find the maximum number of handshakes | The Handshakes Problem

Program to find the maximum number of handshakes is discussed here. Given a positive integer n, find out the total number of handshakes possible.

DESCRIPTION

It was Raj’s first day at school. His teacher Anu asked the students to meet every other student in the class and to introduce about themselves. The teacher asked them to do handshakes when they meet each other.
If there are n number of students in the class then find the total number of handshakes made by the students.

Input format and output format:

• Input consists of 1 integer.
• First input corresponds to the total number of students.
• Output consists of 1 integer.

Sample Input:
15

Sample output:
105

## Algorithm to find the maximum number of handshakes

• Input the number of people (n).
• Find nC2, calculated as n * (n-1) / 2.
• Print the calculated result.

Program to find the maximum number of handshakes is given below

// C program to find the maximum number of handshakes

#include
int main()
{
//fill the code
int num;
scanf(“%d”,&num);
int total = num * (num-1) / 2; // Combination nC2
printf(“%d”,total);
return 0;
}

// C++ program to find the maximum number of handshakes

#include
using namespace std;

int main()
{
//fill the code
int num;
cin >> num;
int total = num * (num-1) / 2; // Combination nC2
cout << total;
return 0;
}

// Java program to find the maximum number of handshakes

import java.util.*;
public class Main
{
public static void main(String[] args)
{
int num;
Scanner sc = new Scanner(System.in);
num = sc.nextInt();
int total = num * (num-1) / 2; // Combination nC2
System.out.print(total);
}
}

# Python program to find the maximum number of handshakes

num = int(input())
total = 0
total = num * (num – 1) / 2 // Combination nC2
print(int(total))

Output: 