np-complete


NP-complete or NP-hard?


Given a list of n positive integers (n even), divide the list into two sublists such that the difference between the sums of the integers in the two sublists is minimized. Would this be a NP-complete problem or a NP-hard problem?
TL;DR - it's np hard.
this is the optimization version of the partition problem.
the partition problem is deciding if a given list of positive integers can be divided into 2 subsets so that the sums of the subsets are equal.
the optimization version asks for the minimized difference (like you asked).
the partition problem is np-complete but the optimization is np hard.
you can read more on these problems in wiki:
https://en.wikipedia.org/wiki/Partition_problem

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