to find a subset from a set whose sum equals to zero?

Question

I have a set of integers like this

{1,4,5,2,7,8,-3,-5,-6,9,3,-7,-1,5,6} 

the set can contain any number of items as input is taken from the

Answer 1

I came across this problem in my college days at Google interview and solved it in a very long way.

Think about it, for a set to be 0 there "has" to be negative number and there "has to be a set of positive number".

Steps:

1. Created a 2 arrays negativeNumArrays and POsitiveNumArrays
2. Create a new negative set(does not allows duplicate) which is possible sums of     negative arrays ex -
    [-1,-2,-3] = [-1,-2,-3, {-1-2=3},{-1,-3=-4},{-2,-3=-5},{-6}] = [-1,-2,-3,-4,-5,-6]
So the set looked like
Key:Value
"1" =-1
"2" = -2
...
"2:3"=-5 
"1:2:3"=-6

Here 
"N6" = -6

3. For this new set of negative array find combination in positive 
   array which matches any of the 6 negative arrays.

Same as above say positive numbers are 3 and 4
So the set would look like
"3"=3

"4"=4

"3:4"=7


Now simple compare the two sets and see which of these are equal
So for example Negative Set "1:3" = Positive Set "4"
and hence use Stringtokenizer to get the numbers from set key {-1,-3,4}