This calculator takes values that could be written in a browsers route path as a single string. It then returns the result as a number (or an error message).

Route paths use the '/' symbol so this can't be in our calculator. Instead we are using the '$' symbol as our divide operator.

You will be passed a string of any length containing numbers and operators:

* '+' = add        
* '-' = subtract  
* '*' = multiply 
* '$' = divide   

Your task is to break the string down and calculate the expression using this order of operations. (division => multiplication => subtraction => addition)

If you are given an invalid input (i.e. any character except `.0123456789+-*$`) you should return the error message:`'400: Bad request'`

### Remember:

1. Operations are infinite
2. Order of operations is imperitive
3. No `eval` or equivalent functions

**Examples:**
```python
calculate('1+1')     => '2'
calculate('10$2')    => '5'
calculate('1.5*3')   => '4.5'

calculate('5+5+5+5') => '20'

calculate('1000$2.5$5+5-5+6$6') =>'81'

calculate('10-9p')   =>  '400: Bad request'
```

### Further Notes - Parameters outside of this challenge:

- Brackets e.g. 10*(1+2)
- Square root, log, % or any other operators
- Unary minus (10*-1)
- Bad mathematical input (10**$10 or 5+5$)
- You may have to deal with floats

If enjoy this and want something harder please see http://www.codewars.com/kata/evaluate-mathematical-expression/ for making a much more complicated calculator. This is a good kata leading up to that.

Difficulty: MEDIUM

Starter code:
def calculate(expression):
	

Solutions:
import re
(ADDSUB, MULDIV) = ('+-', '*$')

def calculate(expression):
	return '400: Bad request' if re.search('[^+*$\\d.-]', expression) else parseAndEval(expression, ADDSUB)

def parseAndEval(expression, ops):
	v = 0
	for (op, part) in re.findall('([{0}])?([^{0}]+)'.format(ops), expression):
		if not op:
			v = float(part) if ops == MULDIV else parseAndEval(part, MULDIV)
		elif op == '*':
			v *= float(part)
		elif op == '$':
			v /= float(part)
		elif op == '+':
			v += parseAndEval(part, MULDIV)
		elif op == '-':
			v -= parseAndEval(part, MULDIV)
	return v


def tokenize(expression):
	result = []
	curr = ''
	for chr in expression:
		if chr.isdigit() or chr == '.':
			curr += chr
		elif chr in '$*-+':
			result.extend([float(curr), chr])
			curr = ''
		else:
			raise ValueError('invalid input')
	if curr:
		result.append(float(curr))
	return result

def calculate(expression):
	ops = {'+': lambda x, y: x + y, '-': lambda x, y: x - y, '*': lambda x, y: x * y, '$': lambda x, y: x / y}
	try:
		l = tokenize(expression)
	except ValueError:
		return '400: Bad request'
	for op in '$*-+':
		while op in l:
			i = l.index(op)
			l = l[:i - 1] + [ops[op](l[i - 1], l[i + 1])] + l[i + 2:]
	return l[0]


def calculate(s):
	if any((c not in '.0123456789+-*$' for c in s)):
		return '400: Bad request'
	tokens = [float(e) if e not in '$*-+' else e for e in s.replace('+', ' + ').replace('-', ' - ').replace('*', ' * ').replace('$', ' $ ').split()]
	for c in '$*-+':
		r = []
		for t in tokens:
			if r and r[-1] == c:
				r.pop()
				t = {'$': lambda a, b: a / b, '*': lambda a, b: a * b, '-': lambda a, b: a - b, '+': lambda a, b: a + b}[c](r.pop(), t)
			r.append(t)
		tokens = r
	return tokens.pop()


from operator import truediv, mul, sub, add
operators = {'/': truediv, '*': mul, '+': add, '-': sub}
order = [{'/', '*'}, {'-', '+'}]

def calculate(expression):
	expression = expression.replace('$', '/')
	for i in '+*/-':
		expression = expression.replace(i, ' ' + i + ' ')
	l = expression.split()
	try:
		for i in range(2):
			n = 0
			while n < len(l):
				if l[n] in order[i]:
					l[n - 1] = operators[l[n]](float(l.pop(n - 1)), float(l.pop(n)))
				else:
					n += 1
		return float(l[0])
	except:
		return '400: Bad request'


import re

def calculate(expression):
	if re.search('[^\\.0123456789+\\-*$]', expression):
		return '400: Bad request'
	if re.match('^(?:\\d+\\.)?\\d+$', expression):
		return float(expression)
	return (lambda m: (lambda x, o, y: {'+': x + y, '-': x - y, '*': x * y, '$': x / y}[o])(calculate(m.group(1)), m.group(2), calculate(m.group(3))) if m else 0)(re.search('(.+)([+-])(.+)', expression) or re.search('(.+)([*$])(.+)', expression))


def calculate(s):
	try:
		s = re.sub('([+*\\-$])', ' \\1 ', s).split()

		def doall(s_):
			while s_ in s:
				find = s.index(s_)
				(t, t1) = (float(s[find - 1]), float(s.pop(find + 1)))
				s[find - 1] = t / t1 if s_ == '$' else t * t1 if s_ == '*' else t - t1 if s_ == '-' else t + t1
				s.pop(find)
		doall('$')
		doall('*')
		doall('-')
		doall('+')
		return float(s[0])
	except:
		return '400: Bad request'


def operation(op1, op2, op):
	if op == '*':
		return op1 * op2
	elif op == '+':
		return op1 + op2
	elif op == '-':
		return op1 - op2
	else:
		return op1 / op2

def calculate(expression):
	(i, lst, num) = (0, [], '')
	if '.' in expression:
		if expression.replace('.', '').isdigit():
			return float(expression)
	while i < len(expression):
		if not expression[i].isdigit():
			if expression[i] in '+-*$':
				lst.append(int(num))
				lst.append(expression[i])
				num = ''
			else:
				return '400: Bad request'
		else:
			num += expression[i]
		i += 1
	if expression[i - 1].isdigit():
		lst.append(int(num))
	length = len(lst)
	while True:
		if '*' in lst and '$' in lst:
			(index1, index2) = (lst.index('*'), lst.index('$'))
			if index1 < index2 and index1 - 1 > -1 and (index1 + 1 < length) and (type(lst[index1 - 1]) == int or type(lst[index1 - 1]) == float) and (type(lst[index1 + 1]) == int or type(lst[index1 + 1]) == float):
				lst[index1 - 1] = operation(lst.pop(index1 - 1), lst.pop(index1), lst[index1 - 1])
			elif index2 - 1 > -1 and index2 + 1 < length and (type(lst[index2 - 1]) == int or type(lst[index2 - 1]) == float) and (type(lst[index2 + 1]) == int or type(lst[index2 + 1]) == float):
				lst[index2 - 1] = operation(lst.pop(index2 - 1), lst.pop(index2), lst[index2 - 1])
			else:
				return '400: Bad request'
		elif '*' in lst:
			index = lst.index('*')
			if index - 1 > -1 and index + 1 < length and (type(lst[index - 1]) == int or type(lst[index - 1]) == float) and (type(lst[index + 1]) == int or type(lst[index + 1]) == float):
				lst[index - 1] = operation(lst.pop(index - 1), lst.pop(index), lst[index - 1])
			else:
				return '400: Bad request'
		elif '$' in lst:
			index = lst.index('$')
			if index - 1 > -1 and index + 1 < length and (type(lst[index - 1]) == int or type(lst[index - 1]) == float) and (type(lst[index + 1]) == int or type(lst[index + 1]) == float):
				lst[index - 1] = operation(lst.pop(index - 1), lst.pop(index), lst[index - 1])
			else:
				return '400: Bad request'
		elif '+' in lst and '-' in lst:
			(index1, index2) = (lst.index('+'), lst.index('-'))
			if index1 < index2 and index1 - 1 > -1 and (index1 + 1 < length) and (type(lst[index1 - 1]) == int or type(lst[index1 - 1]) == float) and (type(lst[index1 + 1]) == int or type(lst[index1 + 1]) == float):
				lst[index1 - 1] = operation(lst.pop(index1 - 1), lst.pop(index1), lst[index1 - 1])
			elif index2 - 1 > -1 and index2 + 1 < length and (type(lst[index2 - 1]) == int or type(lst[index2 - 1]) == float) and (type(lst[index2 + 1]) == int or type(lst[index2 + 1]) == float):
				lst[index2 - 1] = operation(lst.pop(index2 - 1), lst.pop(index2), lst[index2 - 1])
			else:
				return '400: Bad request'
		elif '+' in lst:
			index = lst.index('+')
			if index - 1 > -1 and index + 1 < length and (type(lst[index - 1]) == int or type(lst[index - 1]) == float) and (type(lst[index + 1]) == int or type(lst[index + 1]) == float):
				lst[index - 1] = operation(lst.pop(index - 1), lst.pop(index), lst[index - 1])
			else:
				return '400: Bad request'
		elif '-' in lst:
			index = lst.index('-')
			if index - 1 > -1 and index + 1 < length and (type(lst[index - 1]) == int or type(lst[index - 1]) == float) and (type(lst[index + 1]) == int or type(lst[index + 1]) == float):
				lst[index - 1] = operation(lst.pop(index - 1), lst.pop(index), lst[index - 1])
			else:
				return '400: Bad request'
		else:
			break
	return lst.pop()


ADD = '+'
SUB = '-'
MUL = '*'
DIV = '$'
OPS = {ADD: lambda x, y: x + y, SUB: lambda x, y: x - y, MUL: lambda x, y: x * y, DIV: lambda x, y: x / y}
DIGITS = '0123456789'
DECIMAL = '.'
eMsg = '400: Bad request'

class RouteError(ValueError):
	pass

class Scaner:

	def init(self, expression):
		self.exp = expression
		self.pos = 0
		self.len = len(expression)

	def get_digits(self):
		res = ''
		while self.pos < self.len:
			chr = self.exp[self.pos]
			if chr not in DIGITS:
				break
			res += chr
			self.pos += 1
		return res

	def get_number(self):
		num = self.get_digits()
		if self.pos >= self.len:
			return num
		if self.exp[self.pos] == DECIMAL:
			self.pos += 1
			num += DECIMAL + self.get_digits()
		if num == DECIMAL:
			raise RouteError('No digits in number.')
		return num

	def token(self):
		if self.pos >= self.len:
			return None
		chr = self.exp[self.pos]
		if chr in OPS:
			self.pos += 1
			return chr
		if chr in DIGITS or chr == DECIMAL:
			return self.get_number()
		self.pos += 1
		raise RouteError('Illegal character in expression.')

class Parser:

	def init(self):
		self.stk = []
		self.rpn = []

	def pop(self):
		return self.stk.pop(0) if self.stk else None

	def token(self):
		return self.stk[0] if self.stk else None

	def generate_rpn(self):
		self.generate_subtraction()
		while self.token() == ADD:
			self.pop()
			self.generate_subtraction()
			self.generate_op(ADD)
		if self.stk:
			raise RouteError('Unexpected token ' + self.token() + '.')

	def generate_subtraction(self):
		self.generate_multiplication()
		while self.token() == SUB:
			self.pop()
			self.generate_multiplication()
			self.generate_op(SUB)

	def generate_multiplication(self):
		self.generate_division()
		while self.token() == MUL:
			self.pop()
			self.generate_division()
			self.generate_op(MUL)

	def generate_division(self):
		if self.token() == None:
			raise RouteError('Missing operand 1.')
		self.generate_operand()
		while self.token() == DIV:
			self.pop()
			self.generate_operand()
			self.generate_op(DIV)

	def generate_operand(self):
		if not self.stk:
			raise RouteError('Missing operand 2.')
		if self.token() in OPS:
			raise RouteError('Unexpected operator ' + self.token() + '.')
		tok = self.pop()
		self.rpn.append(float(tok) if DECIMAL in tok else int(tok))

	def generate_op(self, op):
		self.rpn.append(op)

def tryint(num):
	inum = int(num)
	return inum if num == inum else num

def Evaluate(rpn):
	stk = []
	for t in rpn:
		if t in OPS:
			op0 = stk.pop()
			stk[-1] = OPS[t](stk[-1], op0)
		else:
			stk.append(t)
	return tryint(stk[0])

def calculate(expression):
	s = Scaner()
	s.init(expression)
	p = Parser()
	p.init()
	try:
		while True:
			t = s.token()
			if t:
				p.stk.append(t)
			else:
				p.generate_rpn()
				break
		res = Evaluate(p.rpn)
	except RouteError:
		res = eMsg
	except ZeroDivisionError:
		res = eMsg
	return res


def calculate(exp):
	import re
	s = [float(i) for i in re.findall('[.\\d]+', exp)]
	ops = exp
	for i in range(10):
		ops = ops.replace(str(i), '')
	ops = ops.replace('.', '')
	p = list(ops)
	for i in ['+', '-', '*', '$']:
		ops = ops.replace(i, '')
	if ops != '' or len(p) >= len(s):
		return '400: Bad request'
	for i in range(len(p)):
		if p[i] == '$':
			o = i
			j = i + 1
			while True:
				if s[j] == 'o':
					j = j + 1
				else:
					break
			while True:
				if s[o] == 'o':
					o = o - 1
				else:
					break
			s[o] = s[o] / s[j]
			s[j] = 'o'
	for i in range(len(p)):
		if p[i] == '*':
			o = i
			j = i + 1
			while True:
				if s[j] == 'o':
					j = j + 1
				else:
					break
			while True:
				if s[o] == 'o':
					o = o - 1
				else:
					break
			s[o] = s[o] * s[j]
			s[j] = 'o'
	for i in range(len(p)):
		if p[i] == '-':
			o = i
			j = i + 1
			while True:
				if s[j] == 'o':
					j = j + 1
				else:
					break
			while True:
				if s[o] == 'o':
					o = o - 1
				else:
					break
			s[o] = s[o] - s[j]
			s[j] = 'o'
	for i in range(len(p)):
		if p[i] == '+':
			o = i
			j = i + 1
			while True:
				if s[j] == 'o':
					j = j + 1
				else:
					break
			while True:
				if s[o] == 'o':
					o = o - 1
				else:
					break
			s[o] = s[o] + s[j]
			s[j] = 'o'
	for i in s:
		if i != 'o':
			return i


def calculate(expression):
	print(expression)
	expression = ''.join([' {} '.format(num) if num in '+-*$' else num for num in expression]).split()
	while '$' in expression:
		try:
			for num in expression:
				if num == '$':
					first = expression.pop(expression.index(num) - 1)
					second = expression.pop(expression.index(num) + 1)
					ans = str(float(float(first) / float(second)))
					expression[expression.index(num)] = ans
		except ValueError:
			return '400: Bad request'
	while '*' in expression:
		try:
			for num in expression:
				if num == '*':
					first = expression.pop(expression.index(num) - 1)
					second = expression.pop(expression.index(num) + 1)
					ans = str(float(float(first) * float(second)))
					expression[expression.index(num)] = ans
		except ValueError:
			return '400: Bad request'
	while '-' in expression:
		try:
			for num in expression:
				if num == '-':
					first = expression.pop(expression.index(num) - 1)
					second = expression.pop(expression.index(num) + 1)
					ans = str(float(float(first) - float(second)))
					expression[expression.index(num)] = ans
		except ValueError:
			return '400: Bad request'
	while '+' in expression:
		try:
			for num in expression:
				if num == '+':
					first = expression.pop(expression.index(num) - 1)
					second = expression.pop(expression.index(num) + 1)
					ans = str(float(float(first) + float(second)))
					expression[expression.index(num)] = ans
		except ValueError:
			return '400: Bad request'
	try:
		return float(expression[0])
	except ValueError:
		return '400: Bad request'