给定整数集的子集，其和为常数 N：Java

Question

Given a set of integers, how to find a subset that sums to a given value...the subset problem?

Example: S = {1,2,4,3,2,5} and n= 7 Finding the possible subsets whose sum is n. I tried to google out found many links,but were not clear. How can we solve this in java and what is the data structure to be used and its complexity?

Answer 1

In three steps:

1. Find the powerset of S (the set of all subsets of S)

2. Compute the sum of each subset

3. Filter out subsets that did not sum to 7.

Answer 2

I wont give you any code, but explain how it works.

1. Run a loop from 0 to (2^k-1)
2. For each value in 1, a 1 in its binary representation indicates that this value is chosen and 0 otherwise.
3. Test to see if the sum of chosen numbers is equal to n .

The above method will evaluate each possible subset of the given set.

If the upper limit of the values is small, then Dynamic Programming Approach could be used.