test.rb

def main str
  nums = str.scan(/\d+/)
  marks = str.scan(/[+,\-,*,\/]/)
  analyze nums, marks
end

def find_match_index arr, regx
  arr.each_with_index do |e, index|
    return index if e.match(regx)
  end
  return nil
end

def cal num1, num2, mark
  case mark
  when '+'
    num1 + num2
  when '-'
    num1 - num2
  when '*'
    num1 * num2
  when '/'
    num1 / num2
  end
end

def analyze nums, marks
  index = find_match_index(marks, /[*, \/]/)
  index = find_match_index(marks, /[+, \-]/) unless index
  mark = marks.delete_at index
  num1 = nums.delete_at index
  num2 = nums.delete_at index
  result = cal num1.to_i, num2.to_i, mark
  return result if marks == []
  nums.insert(index, result)
  analyze nums, marks
end

def split_str str
  return (main str) unless str.index('(')
  index_l = str.rindex('(')
  str1 = str[index_l, str.length]
  index_r = str1.index(')')
  formula = str[index_l, index_r]
  result = main formula
  str.gsub! formula, result.to_s
  split_str str
end

p split_str "3*(12+1)"
p split_str "2*(1+1)*(199+1)"