Is there a polynomial time algorithm to know whether a set of integers can be partitioned into two of equal sum?

Question

If there are, it would be my great pleasure if anyone can direct me to any. Preferable with a computer program that works for that purpose.

I'm actually referring to a polynomial time algorithm that will only test (without the actual partitioning) if a set of integers can be partitioned into two of equal sum. Like if yes, program return true and if no return false.

Says it's NP complete here: https://en.wikipedia.org/wiki/Partition_problem — Baldrick, Jun 10 '16 at 08:41
However, there are pseudo-polynomial methods listed in the above article. — Baldrick, Jun 10 '16 at 08:42

score 1 · Answer 1 · answered Jun 10 '16 at 09:12

It is NP-Hard( NP-Complete also ).

What I mean is that we have not been able to find a polynomial time algorithm, and we have not proved that one doesn't exist. It is believed by everyone that no polynomial time algorithm exists since we have tried a lot over years. There are many such NP-Complete problems for which we have neither proved the existence of polynomial time algorithm nor disproved the existence of one.

But it turns out that if you prove or disprove the existence of polynomial time algorithm for one such problem, the same applies to all the elements of the NP-Complete class.

Is there a polynomial time algorithm to know whether a set of integers can be partitioned into two of equal sum?

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