Clarification on subset sum

Question

This is programming project for a class of mine, I'm not looking for an answer but more of an explanation of the problem. I don't really understand what is being asked..

Here is another input/ output: input: 1 2 3 3 4 5 output: 1 2 3 3

I don't understand how we are getting this output, can someone explain it to me simpler? Thanks

Answer 1

If the input is 1 2 3 3 4 5, the subsequences are:

1
1 2
1 2 3
1 2 3 3
1 2 3 3 4
1 2 3 3 4 5
2
2 3
2 3 3
...

Over all the subsequences, 1 2 3 3 is such that |(1 + 2 + 3 + 3) - (4 + 5)| = 0 is minimal.

If we take the subsequence 2 3 3, we have |(2 + 3 + 3) - (1 + 4 + 5)| = |8 - 10| = 2 which is greater.

However, I'm also confused by the meaning of "subsequence". I thought that, the subsequences of 1 2 3 4 5 should be:

1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
2
2 3
2 3 4
2 3 4 5
3
3 4
3 4 5
4
4 5
5

But according to the subject, the optimal subsequence is 1 2 4 which is not in my list. It's in fact a subset of the set S. So be careful, there are many combinations.