# usage
c = Calculator()
print('result: {:f}'.formart(c.get_result('1.11+2.22-3.33*4.44/5.55')))
# output:
result: 0.666000

Test No.1: (1.11) = 1.110000
Test No.2: 1.11+2.22-3.33*4.44/5.55 = 0.666000
Test No.3: 1.11+(2.22-3.33)*4.44/5.55 = 0.222000
Test No.4: 1.11+(2.22-3.33)*(4.44+5.55)/6.66 = -0.555000
Test No.5: 1.11*((2.22-3.33)*(4.44+5.55))/(6.66+7.77) = -0.852992
Test No.6: (1.11+2.22)*(3.33+4.44)/5.55*6.66 = 31.048920
Test No.7: (1.11-2.22)/(3.33+4.44)/5.55*(6.66+7.77)/(8.88) = -0.041828
Test No.8: Error: (1.11+2.22)*(3.33+4.44: missing ")", please check your expression
Test No.9: Error: (1.11+2.22)*3.33/0+(34-45): divisor cannot be zero
Test No.10: Error: 12+89^7: invalid character: ^

class Stack(object):
  """
  The structure of a Stack.
  The user don't have to know the definition.
  """
  def __init__(self):
    self.__container = list()
  def __is_empty(self):
    """
    Test if the stack is empty or not
    :return: True or False
    """
    return len(self.__container) == 0
  def push(self, element):
    """
    Add a new element to the stack
    :param element: the element you want to add
    :return: None
    """
    self.__container.append(element)
  def top(self):
    """
    Get the top element of the stack
    :return: top element
    """
    if self.__is_empty():
      return None
    return self.__container[-1]
  def pop(self):
    """
    Remove the top element of the stack
    :return: None or the top element of the stack
    """
    return None if self.__is_empty() else self.__container.pop()
  def clear(self):
    """
    We'll make an empty stack
    :return: self
    """
    self.__container.clear()
    return self

class Calculator(object):
  """
  A simple calculator, just for fun
  """
  def __init__(self):
    self.__exp = ''
  def __validate(self):
    """
    We have to make sure the expression is legal.
    1. We only accept the `()` to specify the priority of a sub-expression. Notes: `[ {` and `] }` will be
    replaced by `(` and `)` respectively.
    2. Valid characters should be `+`, `-`, `*`, `/`, `(`, `)` and numbers(int, float)
    - Invalid expression examples, but we can only handle the 4th case. The implementation will
    be much more sophisticated if we want to handle all the possible cases.:
      1. `a+b-+c`
      2. `a+b+-`
      3. `a+(b+c`
      4. `a+(+b-)`
      5. etc
    :return: True or False
    """
    if not isinstance(self.__exp, str):
      print('Error: {}: expression should be a string'.format(self.__exp))
      return False
    # Save the non-space expression
    val_exp = ''
    s = Stack()
    for x in self.__exp:
      # We should ignore the space characters
      if x == ' ':
        continue
      if self.__is_bracket(x) or self.__is_digit(x) or self.__is_operators(x)           or x == '.':
        if x == '(':
          s.push(x)
        elif x == ')':
          s.pop()
        val_exp += x
      else:
        print('Error: {}: invalid character: {}'.format(self.__exp, x))
        return False
    if s.top():
      print('Error: {}: missing ")", please check your expression'.format(self.__exp))
      return False
    self.__exp = val_exp
    return True
  def __convert2postfix_exp(self):
    """
    Convert the infix expression to a postfix expression
    :return: the converted expression
    """
    # highest priority: ()
    # middle: * /
    # lowest: + -
    converted_exp = ''
    stk = Stack()
    for x in self.__exp:
      if self.__is_digit(x) or x == '.':
        converted_exp += x
      elif self.__is_operators(x):
        converted_exp += ' '
        tp = stk.top()
        if tp:
          if tp == '(':
            stk.push(x)
            continue
          x_pri = self.__get_priority(x)
          tp_pri = self.__get_priority(tp)
          if x_pri > tp_pri:
            stk.push(x)
          elif x_pri == tp_pri:
            converted_exp += stk.pop() + ' '
            stk.push(x)
          else:
            while stk.top():
              if self.__get_priority(stk.top()) != x_pri:
                converted_exp += stk.pop() + ' '
              else:
                break
            stk.push(x)
        else:
          stk.push(x)
      elif self.__is_bracket(x):
        converted_exp += ' '
        if x == '(':
          stk.push(x)
        else:
          while stk.top() and stk.top() != '(':
            converted_exp += stk.pop() + ' '
          stk.pop()
    # pop all the operators
    while stk.top():
      converted_exp += ' ' + stk.pop() + ' '
    return converted_exp
  def __get_result(self, operand_2, operand_1, operator):
    if operator == '+':
      return operand_1 + operand_2
    elif operator == '-':
      return operand_1 - operand_2
    elif operator == '*':
      return operand_1 * operand_2
    elif operator == '/':
      if operand_2 != 0:
        return operand_1 / operand_2
      else:
        print('Error: {}: divisor cannot be zero'.format(self.__exp))
        return None
  def __calc_postfix_exp(self, exp):
    """
    Get the result from a converted postfix expression
    e.g. 6 5 2 3 + 8 * + 3 + *
    :return: result
    """
    assert isinstance(exp, str)
    stk = Stack()
    exp_split = exp.strip().split()
    for x in exp_split:
      if self.__is_operators(x):
        # pop two top numbers in the stack
        r = self.__get_result(stk.pop(), stk.pop(), x)
        if r is None:
          return None
        else:
          stk.push(r)
      else:
        # push the converted number to the stack
        stk.push(float(x))
    return stk.pop()
  def __calc(self):
    """
    Try to get the result of the expression
    :return: None or result
    """
    # Validate
    if self.__validate():
      # Convert, then run the algorithm to get the result
      return self.__calc_postfix_exp(self.__convert2postfix_exp())
    else:
      return None
  def get_result(self, expression):
    """
    Get the result of an expression
    Suppose we have got a valid expression
    :return: None or result
    """
    self.__exp = expression.strip()
    return self.__calc()
  """
  Utilities
  """
  @staticmethod
  def __is_operators(x):
    return x in ['+', '-', '*', '/']
  @staticmethod
  def __is_bracket(x):
    return x in ['(', ')']
  @staticmethod
  def __is_digit(x):
    return x.isdigit()
  @staticmethod
  def __get_priority(op):
    if op in ['+', '-']:
      return 0
    elif op in ['*', '/']:
      return 1