# 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.

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<bits/stdc++.h>` `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) <<endl;` ` ` `return` `0;` `}` |

## 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

`<?php` `// PHP program to` `// find maximum number` `// of handshakes.` `// Calculating the maximum` `// number of handshake` `// using derived formula.` `function` `maxHandshake(` `$n` `)` `{` ` ` `return` `(` `$n` `* (` `$n` `- 1))/ 2;` `}` `// Driver Code` `$n` `= 10;` `echo` `maxHandshake(` `$n` `);` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// JavaScript program to find maximum` `// number of handshakes.` `// Calculating the maximum number of` `// handshake using derived formula.` `function` `maxHandshake(n)` `{` ` ` `return` `(n * (n - 1)) / 2;` `}` ` ` `// Driver Code` `let n = 10;` `document.write( maxHandshake(n));` `// This code is contributed by souravghosh0416 ` `</script>` |

**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.

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