Hints and ideas needed?

In case you don't just want to look up how other people solved it (which is a great approach!):
 The problem is labeled "easy", so it's not necessary to use more advanced approaches like dynamic programming. That implies there's a simple  usually O(n)  algorithm to solve the problem.
 Try a naive approach to the problem: maybe you could keep track of each running total? This is rarely the right answer, since the amount of space you'll use with larger arrays is too large  but it might give you ideas on how else to solve the problem.
 Try an incremental logic approach (math/logic reasoning): Suppose you have an array that is its own largest subset already. Now pretend this is just the final answer that's embedded in a larger array  so to get backward to the original array, you need to append some numbers to the answer subset  but they have to be the kind that would make the nowlonger subset no larger than you already have. For example, suppose the answer subset is
[4,1,2,1]
. Let's append some numbers: you can't add anything 1 or larger  otherwise the answer would be larger than 6, so... [you can probably figure this out!]  Also try to add some extreme numbers in a sample array: if it's
[...,2,3,1000000,4,5,...]
 are there any cases when you can include the 1000000 in the answer subset?  Do you think there's a way to use running sums to use these new facts? When you have N of those, you don't really use any math logic, so maybe you can use only a few running sums, instead?
HTH