C++ Program to find the maximum number of handshakes
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.
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
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
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#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;
}