Question

If we have an array of integers, then is there any efficient way other than O(n^2) by which one can find the number of pairs of integers which differ by a given value?
E.g for the array 4,2,6,7 the number of pairs of integers differing by 2 is 2 {(2,4),(4,6)}.
Thanks.

Answer 1

Create a set from your list. Create another set which has all the elements incremented by the delta. Intersect the two sets. These are the upper values of your pairs.

In Python:

>>> s = [4,2,6,7]
>>> d = 2
>>> s0 = set(s)
>>> sd = set(x+d for x in s0)
>>> set((x-d, x) for x in (s0 & sd))
set([(2, 4), (4, 6)])

Creating the sets is O(n). Intersecting the sets is also O(n), so this is a linear-time algorithm.