Patched code sample

def fixed_emphasis_parser(text: str):
    """
    This function demonstrates the principle of the linear-time fix for the
    vulnerability.

    The vulnerable method would re-scan the string forward from each potential
    opening marker ('**'), leading to quadratic (O(n^2)) behavior. This fixed
    approach scans the string only once, using a stack to track opening markers
    and pairing them with closers. This results in linear (O(n)) time complexity,
    preventing a denial of service.
    """
    # A stack to hold the indices of opening '**' markers.
    opener_stack = []
    i = 0

    # A single pass over the string to find and pair markers.
    while i < len(text):
        if text.startswith('**', i):
            # Simplified logic: a real parser validates markers based on
            # surrounding whitespace.

            # If the stack has an unmatched opener, this is a closer.
            if opener_stack:
                # Pair found. Pop the last opener from the stack.
                opener_stack.pop()
            # Otherwise, this is a new opener.
            else:
                opener_stack.append(i)

            # Advance index past the '**' marker.
            i += 2
        else:
            # Advance index by one character.
            i += 1
    # After the single pass, any remaining items in opener_stack represent
    # unclosed tags. This efficient algorithm avoids the costly re-scans
    # of the vulnerable version.