Question

For my algorithm design class homework came this brain teaser:

Given a list of N distinct positive integers, partition the list into two 
sublists of n/2 size such that the difference between sums of the sublists 
is maximized.
Assume that n is even and determine the time complexity.

At first glance, the solution seems to be

1. sort the list via mergesort
2. select the n/2 location
3. for all elements greater than, add to high array
4. for all elements lower than, add to low array

This would have a time complexity of O((n log n)+ n)

Are there any better algorithm choices for this problem?

Answer 1

Since you can calculate median in O(n) time you can also solve this problem in O(n) time. Calculate median, and using it as threshold, create high array and low array.

See http://en.wikipedia.org/wiki/Median_search on calculating median in O(n) time.