Question

Can anyone show me how to create a mathematical expression for the number of time the statement total++; will run in the following code?

I understand that the ‘i loop’ will iterate n/P times and I know that total++; will run a total of ‘i loop iterations’ * ‘j loop iterations’. But I don’t know how to get a mathematical expression from this that is in terms of n and P.

#include <iostream>

using namespace std;

int total = 0;
int n = 20;
int P = 2;
int id = 1;
int test = 0;

int main()
{

    for (int i = id*n/P; i < ((1+id)*n/P); i++)
    {
        cout << i << endl;
        test++;
        for (int j = 1; j <= i-1; j++) {
            total++;
        }
    }

    cout << test << endl;
    cout << total;
    return 0;
}

Answer 1

Look at the sum of the integers.

The inner loop runs i times, for each of a series of integer values of i, starting at one value and running to the other. If you have the sum of the integers from 1 to the first value, and the sum of the integers from 1 to the other, the difference is your answer.

The sum of the integers from 1 to n is a formula worth learning.