# Find the maximum number of handshakes

There are N persons in a room. Find the maximum number of Handshakes possible. Given the fact that any two persons shake hand exactly once.

Examples :

```Input : N = 2
Output : 1.
There are only 2 persons in the room. 1 handshake take place.

Input : N = 10
Output : 45.
```

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

To maximize the number of handshakes, each person should shake hand with every other person in the room. For the first person, there would be N-1 handshakes. For second person there would N-1 person available but he had already shaken hand with the first person. So there would be N-2 handshakes and so on.
So, Total number of handshake = N-1 + N-2 +….+ 1 + 0, which is equivalent to ((N-1)*N)/2
(using the formula of sum of first N natural number).

Below is the implementation of this problem.

## C++

 `// C++ program to find maximum number of ` `// handshakes. ` `#include ` `using` `namespace` `std; ` ` `  `// Calculating the maximum number of handshake ` `// using derived formula. ` `int` `maxHandshake(``int` `n) ` `{ ` `  ``return` `(n * (n - 1))/ 2; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `  ``int` `n = 10; ` `  ``cout << maxHandshake(n) <

## Java

 `// Java program to find maximum number of ` `// handshakes. ` ` `  `class` `GFG  ` `{ ` `    ``// Calculating the maximum number of  ` `    ``// handshake using derived formula. ` `    ``static` `int` `maxHandshake(``int` `n) ` `    ``{ ` `        ``return` `(n * (n - ``1``)) / ``2``; ` `    ``} ` `     `  `     `  `    ``// Driver code ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `n = ``10``; ` `        ``System.out.println( maxHandshake(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by Anant Agarwal. `

## Python3

 `# Python3 program to find maximum  ` `# number of handshakes. ` ` `  `# Calculating the maximum number  ` `# of handshake using derived formula. ` `def` `maxHandshake(n): ` ` `  `    ``return` `int``((n ``*` `(n ``-` `1``)) ``/` `2``) ` ` `  `# Driver Code ` `n ``=` `10` `print``(maxHandshake(n)) ` ` `  `# This code is contributed by Smitha Dinesh Semwal. `

## C#

 `// C# program to find maximum number of ` `// handshakes. ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `    ``// Calculating the maximum number of  ` `    ``// handshake using derived formula. ` `    ``static` `int` `maxHandshake(``int` `n) ` `    ``{ ` `        ``return` `(n * (n - 1)) / 2; ` `    ``} ` `     `  `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main () ` `    ``{ ` `        ``int` `n = 10; ` `        ``Console.Write( maxHandshake(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by nitin mittal. `

## PHP

 ` `

Output:

```45
```

Time Complexity : O(1)

This article is contributed by Anuj Chauhan(anuj0503). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

My Personal Notes arrow_drop_up

Improved By : nitin mittal, vt_m

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.