Minimum Number of Mails Required to Distribute Questions Using C++

Problem statement

Given N questions in a test and K students in the class. Out of the batch of K students, N students memorized exactly one question each. A mail can contain about a maximum of X questions.

Find the minimum number of mails required so that the entire class gets to know about all the questions

If N = 3, K = 3, X = 1 then one has to send 6 mails −

• Student 1 sends his question to student 2 and student 3 (2 mails),
• So does student 2 and student 3 so total mails = 2 * 3 = 6

Algorithm

The final answer can be calculated using the below formula −

ceil(N/X) * (K-N) + (( ceil((N-1)/X)) * (N-1)) + (N-1)

Example

#include <iostream>
#include <cmath>
using namespace std;
int minMailsToBeSent(int n, int k, int x){
   int m = (n - 1) + ceil((n - 1) * 1.0 / x) * (n - 1) + ceil(n * 1.0 / x) * (k- n);
   return m;
}
int main(){
   int questions = 3;
   int students = 3;
   int X = 1;
   cout << "No of mails to be sent: " << minMailsToBeSent(questions, students, X) << endl;
   return 0;
}

Output

When you compile and execute the above program. It generates the following output −

No of mails to be sent: 6