Question

I know that this must be quite a basic use case, but I don’t know what keywords to search for.

Given a nested for loop like this:

for (i = 0; i < size; i++) {
  for (j = i+1; j < size; j++) {
    doComparision(i, j);
  }
}

I know that I can calculate the total number of comparisons with n = size * (size-1) / 2.

The problem is that I want to parallelize this loop. Each thread should do only a certain range of the outer for-loop:

for (i = beginOffset; i <= endOffset; i++) {
  for (j = i+1; j < size; j++) {
    doComparision(i, j);
  }
}

How can I calculate the number of comparisons in such loops?

In the end I want to make sure that each thread has roughly the same amount of work.

Answer 1

It may be possible to simplify this, but here is an equation that should work:

n = (end-begin+1)*(size-begin-1) - (end-begin+1)*(end-begin)/2

Here is a description of each term which may help in understanding why this works:

• (end-begin+1) : Outer loop iterations
• (size-begin-1) : Maximum number of inner loop iterations
• (end-begin+1)*(end-begin)/2 : 1 + 2 + … + (end – begin)