beads.java

import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Set;


public class Beads {
	public static int rotated_index(int position, int length) {
		return position % length;
	}
	
	
	public static void main(String[] args) {
		ArrayList<Integer> nums = new ArrayList<Integer>();
		
		for (String num : args) {
			nums.add(Integer.parseInt(num));
		}
		
		System.out.println(
			findMax(allSums(nums))
		);
	}
	
	
	public static Set<Integer> sums(ArrayList<Integer> beads, int n) {
		Set<Integer> solutions = new HashSet<Integer>();
		
		if (n < 1 || beads.size() == 0) {
			return solutions;
		}
		
		for (int i = 0; i < beads.size(); i++) {
			ArrayList<Integer> single_solution = new ArrayList<Integer>();		

			for (int j = 0; j < n; j++) {
				single_solution.add(
					beads.get(rotated_index(i + j , beads.size()))
				);
			}
			
			Integer sum = 0;
			for (Integer integer : single_solution) {
				sum += integer;
			}
			
			solutions.add(sum);
		}
		return solutions;
	}
	
	
	public static Set<Integer> allSums (ArrayList<Integer> beads) {
		Set<Integer> solutions = new HashSet<Integer>();
		if (beads.size() == 0) {
			return solutions;
		}
		
		for (int n = 0; n < beads.size() + 1; n++) {
			for (Integer solution : sums(beads, n)) {
				solutions.add(solution);
			}
		}
		
		return solutions;
	}
	
	public static int findMax (Set<Integer> nums) {
		
		Integer max = 0;
		for (Integer n: nums) {
			if (n > max) {
				max = n;
			}
		}
		
		if (nums.size()==0) {
			return 0;
		}
		
		
		for (int i = 1; i <= max; i++) {
			if (!nums.contains(i)) {
				return i-1;
			}
		}
		return 0;
		
	}
}