shunting_yard.py

import re

PRECEDENCES = {'+': 2, '-': 2, '*': 3, '/': 3, '^': 4}


def has_greater_precedence(operator, comparison):
    return PRECEDENCES[operator] > PRECEDENCES[comparison]


def peek(stack):
    return stack[-1] if len(stack) > 0 else None


def parse_expr(expr):
    tokens = re.findall("[\^+/*()-]|\d+", expr)
    operators = []
    output = []
    for token in tokens:
        if token.isnumeric():
            output.append(int(token))
        elif token == '(':
            operators.append(token)
        elif token == ')':
            top = peek(operators)
            while top is not None and top != '(':
                output.append(operators.pop())
                top = peek(operators)
            operators.pop()
        else:
            top = peek(operators)
            while top is not None and top not in ['(', ')'] and has_greater_precedence(top, token):
                output.append(operators.pop())
                top = peek(operators)
            operators.append(token)

    while peek(operators) is not None:
        output.append(operators.pop())

    return output