Number of handshakes such that a person shakes hands only once (original) (raw)

Last Updated : 28 Dec, 2022

There is N number of people at a party. Find the total number of handshakes such that a person can handshake only once.

Examples:

Input : 5 Output : 10

Input : 9 Output : 36

We can see a recursive nature in the problem.

// n-th person has (n-1) choices and after // n-th person chooses a person, problem // recurs for n-1. handshake(n) = (n-1) + handshake(n-1)

// Base case handshake(0) = 0

Below is the implementation of the above recursive formula.

C++ `

// Recursive C++ program to count total number of handshakes // when a person can shake hand with only one. #include <bits/stdc++.h> using namespace std;

// Function to find all possible handshakes int handshake(int n) {

// When n becomes 0 that means all the persons have done
// handshake with other
if (n == 0)
    return 0;
else
    return (n - 1) + handshake(n - 1);

}

// Driver code int main() { int n = 9; cout << " " << handshake(n); return 0; }

// This code is contributed by Aditya Kumar (adityakumar129)

C

// Recursive C program to count total number of handshakes // when a person can shake hand with only one. #include <stdio.h>

// function to find all possible handshakes int handshake(int n) { // when n becomes 0 that means all the persons have done // handshake with other if (n == 0) return 0; else return (n - 1) + handshake(n - 1); }

int main() { int n = 9; printf("%d", handshake(n)); return 0; }

// This code is contributed by Aditya Kumar (adityakumar129)

Java

// Recursive Java program to count total number of // handshakes when a person can shake hand with only one. import java.io.*;

class GFG {

// function to find all possible handshakes
static int handshake(int n)
{
    // when n becomes 0 that means all the persons have
    // done handshake with other
    if (n == 0)
        return 0;
    else
        return (n - 1) + handshake(n - 1);
}

// Driver Code
public static void main(String[] args)
{
    int n = 9;
    System.out.print(handshake(n));
}

}

// This code is contributed by Aditya Kumar (adityakumar129)

Python3

Recursive Python program

to count total number of

handshakes when a person

can shake hand with only one.

function to find all

possible handshakes

def handshake(n):

# when n becomes 0 that means 
# all the persons have done
# handshake with other
if (n == 0):
    return 0
else:
    return (n - 1) + handshake(n - 1)

Driver Code

n = 9 print(handshake(n))

This code is contributed

by Shivi_Aggarwal

C#

// Recursive C# program to // count total number of // handshakes when a person // can shake hand with only one. using System;

class GFG {

// function to find all // possible handshakes static int handshake(int n) { // when n becomes 0 that // means all the persons // have done handshake // with other if (n == 0) return 0; else return (n - 1) + handshake(n - 1); }

// Driver Code public static void Main (String []args) { int n = 9; Console.WriteLine(handshake(n)); } }

// This code is contributed // by Arnab Kundu

PHP

JavaScript

Time Complexity: O(n)
Auxiliary Space: O(1), As the function is tail recursive the extra stack space will not be used.

We can come up with a direct formula by expanding the recursion.

handshake(n) = (n-1) + handshake(n-1) = (n-1) + (n-2) + handshake(n-2) = (n-1) + (n-2) + .... 1 + 0 = n * (n - 1)/2

C++ `

// Recursive CPP program to count total number of handshakes // when a person can shake hand with only one. #include <bits/stdc++.h> using namespace std;

// function to find all possible handshakes int handshake(int n) { return n * (n - 1) / 2; }

int main() { int n = 9; cout << handshake(n) << endl; return 0; }

// This code is contributed by Aditya Kumar (adityakumar129)

C

// Recursive CPP program to count total number of handshakes // when a person can shake hand with only one. #include <stdio.h>

// function to find all possible handshakes int handshake(int n) { return n * (n - 1) / 2; }

int main() { int n = 9; printf("%d", handshake(n)); return 0; }

// This code is contributed by Aditya Kumar (adityakumar129)

Java

// Recursive Java program to count total number of // handshakes when a person can shake hand with only one. class GFG {

// function to find all possible handshakes
static int handshake(int n) { return n * (n - 1) / 2; }

// Driver code
public static void main(String args[])
{
    int n = 9;
    System.out.println(handshake(n));
}

}

// This code is contributed by Aditya Kumar (adityakumar129)

Python3

Recursive Python program

to count total number of

handshakes when a person

can shake hand with only one.

function to find all

possible handshakes

def handshake(n):

return int(n * (n - 1) / 2)

Driver Code

n = 9 print(handshake(n))

This code is contributed

by Shivi_Aggarwal

C#

// Recursive C# program to // count total number of // handshakes when a person // can shake hand with only one. using System;

class GFG {

// function to find all // possible handshakes static int handshake(int n) { return n * (n - 1) / 2; }

// Driver code static public void Main () { int n = 9; Console.WriteLine(handshake(n)); } }

// This code is contributed by Sachin

PHP

n∗(n * (n∗(n - 1) / 2; } // Driver Code $n = 9; echo(handshake($n)); // This code is contributed // by Shivi_Aggarwal ?>

JavaScript

Time Complexity: O(1)
Auxiliary Space: O(1)