Positive Negative Sign

Solution

The problem statement has confirmed that n = 2*m. Which means that the series is always possible to be split up in pairs. Let's observe the series for example of n = 12 and m = 3 :

Series  = - 1 - 2 - 3 + 4 + 5 + 6 - 7 - 8 - 9 + 10 + 11 + 12
        = (4-1) + (5-2) + (6-3) + (10-7) + (11-8) + (12-9)
        = 3 + 3 + 3 + 3 + 3 + 3
        = 3 * 6
        = 18

In the above observation, we can see that each pair produced 3 and here 3 = m. More clearly, i-th positive number + i-th negative number = m. Examples: 1st positive number is 4 and 1st negative number is -1 and 4 + (-1) = 3. And since the problem has stated that n = 2*m, we are sure to find a i-th postive number for a corresponding i-th negative number. Also, 3 has occured 6 times where, 6 = 12/2 = n/2. So, the sum = 18 = 6*3 = (n/2)*m.

Caution : Remember, we need long or similar data type that can hold integer values more than 10⁹ because even if n and m alone does not need any data type more than 10⁹, but n*m does!

The above implementation is accepted.

Solution in C

#include <stdio.h>
int main()
{
    int t;
    long n, m, sum;
    scanf("%d", &t);
    for (int i = 1; i <= t; i++)
    {
        scanf("%ld %ld", &n, &m);
        sum = (n / 2) * m;
        printf("Case %d: %ld\n", i, sum);
    }
    return 0;
}

Tutorial source