Maximum number of handshakes in java

May 28, 2022

Maximum number of handshakes in Java

Here, we will discuss the maximum number of handshakes in java. The given program will find the maximum number of handshakes in a room. Suppose there are N persons in a room. We have to find the maximum number of Handshakes possible. Given the fact that any two persons shake hand only once.

Approach :

For the number of handshakes to be maximum, every person should hand-shake with every other person in the room

i.e. all persons present should shake hands.

For the first person, there will be N-1 people to shake hands with
For second person, there will be N -1 people available but as he has already shaken hands with the first person, there will be N-1-1 = N-2 shake-hands
For third person, there will be N-1-1-1 = N-3, and So On…

Therefore the total number of handshake = ( N – 1 + N – 2 +….+ 1 + 0 ) = ( (N-1) * N ) / 2.

Algorithm

For N = 8
handshakes = ( (N-1) * N ) / 2 = ( 8 x 7 )/2 = 28
Print Result

Java Code

Run

public class Main
{
	public static void main(String[] args) {
	     //fill the code
    int num = 10;

    int total = num * (num-1) / 2; // Combination nC2

		System.out.println("For "+ num +" people there will be " +total+" handshakes");
	}
}

Output

Maximum number of handshakes for 30 people are 435