Find all triplets in array with sum less than or equal to given sum

Question

This was recently asked to a friend in an interview and we do not know of any solution other than the simple O(n³) one.

Is there some better algorithm?

Answer 1

From a worst-case asymptotic perspective, there is no better algorithm since the size of the output is potentially O(n³).

e.g. Let the array be the numbers 1 through n. Let S = 3n. Clearly, any subset of three array elements will be less than S and there are (n choose 3) = O(n³) subsets.

There are a few ways you can speed up non-worst cases though. For example, try sorting the array first. That should give you some hints.