Question

I have few arrays of integers. Elements in each array are ordered. Arrays does not have duplicates.

I need to join all arrays into one so the resulting array contains only elements which exist in every array.

For example, I have arrays

(1,2,3,4,5)
(2,3,5)
(1,2,4,5)

The result has to be (2,5)

What is the best way to do it to achieve best performance?

Answer 1

If the arrays are expected to contain many different numbers and only few present in all of them,

• pick the two smallest arrays, compute their intersection by stepping through them sequentially (like for a mergesort), O(len1 + len2)
• while not all arrays have been scanned, pick the next smallest array, and compute its intersection with the intersection of the previously handled arrays, using a sequential scan if length(intersection)*log(length(array)) >= length(array), and looking up the elements of the intersection in array otherwise.

Worst case complexity is O(sum(lengths)), if you’re lucky, you get around k * sum(log(length)), where k is the number of elements in the intersection.