Tree.java

import java.util.Stack;
import java.util.Queue;
import java.util.ArrayList;
import java.util.List;
import java.util.ArrayDeque;
import java.util.LinkedList;

public class Tree {
    private Node root = null;

    public class Node {
        public List<Node> childList;
        public List<Integer> numberList;

        public Node() {
            this.childList = new ArrayList<Node>();
            this.numberList = new ArrayList<Integer>();
        }
    }

    public class ExpressionException extends Exception  {
        public ExpressionException(String message) {
            super(message);
        }
    }

    public Tree(String[] treeStr) throws Tree.ExpressionException {
        root = buildTree(treeStr);
    }

    public void printSums() {
        Queue<Node> queue = new LinkedList<Node>();
        queue.add(root);

        while (!queue.isEmpty()) {
            Node node = queue.remove();

            int sum = 0;

            for(Integer i : node.numberList)
                sum += i;

            System.out.println(sum);

            for (Node subNode : node.childList)
                queue.add(subNode);
        }
    }

    private Node buildTree(String[] treeStr) throws Tree.ExpressionException {
        Stack<Node> stack = new Stack<Node>();
        Node root = null;

        for (int i = 0; i < treeStr.length; i++) {
            if (treeStr[i].equals("[")) {
                Node node = new Node();

                if (!stack.isEmpty()) {
                    Node parent = stack.peek();
                    parent.childList.add(node);
                }

                stack.push(node);

            } else if (treeStr[i].equals("]")) {
                if (stack.isEmpty())
                    throw new Tree.ExpressionException("wrong parentheses");

                root = stack.pop();
            } else if (Character.isDigit(treeStr[i].charAt(0))) {
                Node node = stack.peek();
                node.numberList.add(Integer.parseInt(treeStr[i]));
            }
        }

        if (!stack.isEmpty())
            throw new Tree.ExpressionException("wrong parentheses");

        return root;
    }

    public static void main(String[] args) throws Tree.ExpressionException {
        String[] treeStr = { "[","1","[","2","3","]","4","[","5","[","6","7","]","]","[","8","]","]" };

        Tree tree = new Tree(treeStr);
        tree.printSums();
    }
}