shunting_yard

import re


def precedence(operator):
    if operator == '+':
        return 2
    elif operator == '-':
        return 2
    elif operator == '*':
        return 3
    elif operator == '/':
        return 3


def associativity(operator):
    if operator in ['*', '/', '+', '-']:
        return "left"
    elif operator in ['^']:
        return "right"


def reverse_polish(formula):
    tokens = formula.split(" ")
    operators = []  # The operator stack
    output = []

    for i in range(len(tokens)):
        # If the token is a number
        if re.match("[0-9]", tokens[i]):
            output += tokens[i]
                while re.match("[-+*/]", operators[-1]) and (precedence(operators[0]) > precedence(tokens[i])) or ((precedence(operators[0]) == precedence(tokens[i])) and associativity(tokens[0]) == "left") and (tokens[0] != '('):
                        print(operators)
                        # pop the operator off of the operator stack and onto the output queue
                        output += operators.pop()
                # push it onto the operator stack
                operators += tokens[i]
            # If the current token is a left parenthesis, push it onto the operator stack
            elif tokens[i] == '(':
                operators += tokens[i]
            # If the current token is a right parenthesis, then keep popping operators off the operator stack until you
            # find the corresponding left parenthesis
            elif tokens[i] == ')':
                while operators[0] != '(':
                    output += operators.pop()
                if operators[0] == '(':
                    operators.pop()
    # There are still operators on the operator stack at this point
    while operators:
        output += operators.pop()
    print("".join(output))
    print(operators)


def main():
    reverse_polish("3 + 4 * 2")


if __name__ == "__main__":
    main()