solution_27.py

from functools import reduce


def coding_problem_27(brace_yourself):
    """
    Given a string of round, curly, and square open and closing brackets, return whether the brackets are
    balanced (well-formed).
    Examples:

    >>> coding_problem_27('([])[]({})')
    True
    >>> coding_problem_27('([)]')
    False
    >>> coding_problem_27('((()')
    False

    Note: I get it. This wants me to keep track of all opening parenthesis in a stack, and remove the top after
    encountering a closing one, provided it's of the matching type. Such an algorithm requires bookkeeping and it's
    inherently sequential. My implementation below works instead in a number of passes that only depends on the nesting
    levels of the braces. Memory usage is O(n) for both solutions but since string operations are highly optimized,
    this alternate solution is much faster for any non-trivial example.
    """
    copy = None
    while brace_yourself and brace_yourself != copy:

        copy = brace_yourself
        brace_yourself = reduce(lambda s, p: s.replace(p, ''), ['()', '[]', '{}'], brace_yourself)

    return brace_yourself == ''


if __name__ == '__main__':

    import doctest
    doctest.testmod(verbose=True)