binary_expression_parsing.py

def is_number(character):
	return character.isdigit()

def is_operator(character):
	return character == '+' or character == '*'

def handle_operation(operand_one, operator, operand_two):
	if operator == '+':
		return operand_one + operand_two
	elif operator == '*':
		return operand_one * operand_two
	raise ValueError('Invalid operator: {}'.format(operator))

def handle_number(stack, number):
	if len(stack) == 0:
		stack.append(number)
		return

	if stack[-1] == '(':
		# Remove opening parenthesis
		stack.pop()
		stack.append(number)
		return

	# Top of stack is an operator
	operator = stack[-1]
	operand = stack[-2]
	result = handle_operation(operand, operator, number)

	# Pop first two elements and push result into stack
	stack.pop()
	stack.pop()
	stack.append(result)

def handle_closing_paren(stack):
	operand = stack.pop()

	# Pop first two elements off stack
	handle_number(stack, operand)

def parse_expression(expr):
	stack = []
	for i in range(len(expr)):
		character = expr[i]
		if character == '(':
			stack.append(character)
		elif character == ')':
			handle_closing_paren(stack)
		elif is_number(character):
			handle_number(stack, int(character))
		elif is_operator(character):
			stack.append(character)

	return stack[0]


if __name__ == '__main__':
	print(parse_expression('((1+2)*3)'))
	print(parse_expression('(1+(2*3))'))
	print(parse_expression('(2+3)'))
	print(parse_expression('((1+((2+3)*4))+5)'))