Question

Given an array, what is the most time- and space-efficient algorithm to find the sum of two elements farthest from zero in that array?

Edit
For example, [1, -1, 3, 6, -10] has the farthest sum equal to -11 which is equal to (-1)+(-10).

Answer 1

Using a tournament comparison method to find the largest and second largest elements uses the fewest comparisons, in total n+log(n)-2. Do this twice, once to find the largest and second largest elements, say Z and Y, and again to find the smallest and second smallest elements, say A and B. Then the answer is either Z+Y or -A-B, so one more comparison solves the problem. Overall, this takes 2n+2log(n)-3 comparisons. This is still O(n), but in practice is faster than scanning the entire list 4 times to find A,B,Y,Z (in total uses 4n-5 comparisons).

The tournament method is nicely explained with pictures and sample code in these two tutorials: one and two