tree.rb

class Node
  attr_accessor :numbers
  attr_accessor :children

  def initialize
    @numbers = []
    @children = []
  end
end

class Tree
  include Enumerable

  def initialize(str)
    @root = build(str)
  end

  def each
    queue = Array(@root)

    while !queue.empty?
      node, *queue = queue

      yield node.numbers

      node.children.each do |sub|
        queue.push sub
      end
    end
  end

  private

  def build(str)
    root = nil
    stack = []
    str.each do |token|
      if token == '['
        node = Node.new
        parent = stack.last
        parent.children << node unless parent.nil?
        stack.push node
      elsif integer?(token)
        node = stack.last
        node.numbers << token.to_i
      else
        root = stack.pop
      end
    end
    root
  end

  def integer?(str)
    /\A[+-]?\d+\z/ === str
  end
end

tree_str = ['[','1','[','2','3',']','4','[','5','[','6','7',']',']','[','8',']',']']

tree = Tree.new(tree_str)
tree.each { |numbers| puts numbers.reduce(&:+) }