mathparser.py

from __future__ import print_function
from collections import deque

OPEN_BRACES = set('([{')
CLOSE_BRACES = set(')]}')
OPERATORS = set('+-*/')

class Stack:
    def __init__(self, items):
        self.items = iter(items)
        self.buffer = deque()

    def __iter__(self):
        return self

    def __next__(self):
        if self.buffer:
            return self.buffer.popleft()
        return next(self.items)

    next = __next__

    def push_back(self, item):
        self.buffer.appendleft(item)


def tokenize(term):
    tokens = []
    chars = Stack(term)
    for char in chars:
        if char in OPEN_BRACES:
            tokens.append(tokenize(chars))
        elif char in CLOSE_BRACES:
            return tokens
        elif char in OPERATORS:
            tokens.append(char)
        elif char.isdigit():
            digits = [char]
            for char in chars:
                if not char.isdigit():
                    chars.push_back(char)
                    break
                digits.append(char)
            integer = int(''.join(digits))
            tokens.append(integer)
        else:
            if not char.isspace():
                msg = 'unknown character: {!r}'
                raise ValueError(msg.format(char))
    return tokens

def main():
    term = '42  +   23  -  [1 * (3  +   243) - 5]/ 234'
    print('tokenize({!r})'.format(term))
    print('->', tokenize(term))

if __name__ == '__main__':
    main()