Question

Given an array, find the sum of the absolute difference of every pair of integers.

For example: Given a[]= {2,3, 5, 7 };

output would be (3-2) + (5-2) + (7-2) + (5-3) + (7-3) + (7-5) = 17.

It must be done better than O(n^2).

The original array isn’t necessarily sorted.

Answer 1

note you add each number exactly k times (where k is its place if you sort the list)

also, you subtract each number exactly n-1-k times

you can sort the list (O(nlogn)) and then iterate over the sorted array, multiplying each element as mentioned above.