Adding Up in a Loop

Loops can do more than print. Very often, they add up many values. According to a famous story, the young Carl Friedrich Gauss, later a great mathematician, had to add up all the numbers from 1 to 100 at school. A loop does it in a moment:

int total = 0;
for (int i = 1; i <= 100; i++) {
    total += i;
}
printf("Total: %d\n", total);

Total: 5050

The variable total collects the sum. It starts at 0, because before you add anything, the sum is zero. In each iteration, total += i adds one number: after the first iteration, total is 1, then 3 (1 + 2), 6 (1 + 2 + 3), 10, and at the end 5050.

Where each line goes matters:

• int total = 0; goes before the loop, so that it runs only once. Inside the loop's block, it would create a new total with the value 0 in every iteration. And after the loop, total wouldn't exist at all: a variable created in a block exists only in that block, just like the i of a for loop. The compiler would report error: use of undeclared identifier 'total'.
• printf goes after the loop, when the sum is complete. Inside the loop, it would print every partial sum: 1, 3, 6, 10 and so on, a hundred lines.

The average is the sum divided by the number of values. Watch out for integer division. Here is the average of the numbers from 1 to 10:

int total = 0;
for (int i = 1; i <= 10; i++) {
    total += i;
}
double average = total / 10;
printf("Average: %.1f\n", average);

Average: 5.0

The sum is 55, so the real average is 5.5. But both total and 10 are whole numbers, so / divides them as whole numbers and drops the .5, just like 7 / 2 gives 3. Storing the result in a double doesn't help, because by then the division is already done. Convert the sum to a double before dividing:

int total = 0;
for (int i = 1; i <= 10; i++) {
    total += i;
}
double average = (double)total / 10;
printf("Average: %.1f\n", average);

Average: 5.5

(double)total turns the sum into a decimal number, and a decimal number divided by a whole number gives a decimal number. Put (double) right before total. (double)(total / 10) would only convert the result of the integer division, and you would get 5.0 again.