C++ Program to find the maximum number of handshakes

September 30, 2022

Maximum Number of Handshakes in C++

Here we will discuss how to find the maximum number of handshakes which can happen between N number of people given the fact that any two people shake hands exactly once using C++ programming language.

Maximum number of handshakes

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
Maximum number of handshakes in C++
While loop in C
 
 

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C++ Code

Run 
// C++ program to find the maximum number of handshakesM
#include<iostream>
using namespace std; 

int main()
{

    //fill the code
    int num = 9;

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

    cout<<"For "<<num<<" people there will "<<total<<" handshakes";

    return 0;

}

Output

For 8 people there will be 28 handshakes
While loop in C

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While loop in C

One comment on “C++ Program to find the maximum number of handshakes”


  • aditya pratap

    #include
    #include
    using namespace std;
    int main(){
    int n=9,no_of_handshake=0;
    for(int i=1;i<n;i++){
    no_of_handshake+=n-i;
    }
    cout<<no_of_handshake;
    return 0;
    }

    0