import java.util.Set;
import java.util.TreeSet;
import java.util.List;
import java.util.ArrayList;

/**
 * A class to demonstrate backtracking to solve subset sum
 *
 * by Scot Drysdale for CS 10
 */
 
public class SubsetSum {

	/**
	 * Finds all subsets of the numbers in List that add up to target.
	 * 
	 * @param numbers  The list of positive integers (cannot have duplicates!)
	 * @param pos      The current position in numbers to be considered
	 * @param subset   The current subset
	 * @param sum      The sum of the integers in subset
	 * @param target   The goal number that the sum should equal
	 */
	public static void findSubsets(List<Integer> numbers, int pos, 
			Set<Integer> subset, int sum, int target) {
		if(sum == target)
			System.out.println("Subset: " + subset);
		else if(sum < target && pos < numbers.size()) {  // Do nothing if sum already too large
			Integer m = numbers.get(pos);
			subset.add(m);
			findSubsets(numbers, pos+1, subset, sum+m, target); // Include pos
			subset.remove(m);
			
			findSubsets(numbers, pos+1, subset, sum, target);  // Don't include pos
		}
	}
	
	public static void main(String [] args) {
		List<Integer> numbers = new ArrayList<Integer>();
		Set<Integer> subset = new TreeSet<Integer>();
		
		numbers.add(2);
		numbers.add(15);
		numbers.add(3);
		numbers.add(5);
		numbers.add(10);
		
		findSubsets(numbers, 0, subset, 0, 20);
	}
}