```python
"""Fixed-point money helpers: parse, format, and allocate integer cents."""

import re


def parse_amount(text: str) -> int:
    if not isinstance(text, str):
        raise ValueError("amount must be a string")
    match = re.fullmatch(r"(\d+)(?:\.(\d{2}))?", text)
    if match is None:
        raise ValueError(f"malformed amount: {text}")
    whole = int(match.group(1))
    cents = 0 if match.group(2) is None else int(match.group(2))
    return whole * 100 + cents


def format_amount(cents: int) -> str:
    if isinstance(cents, bool) or not isinstance(cents, int) or cents < 0:
        raise ValueError("cents must be a non-negative integer")
    return f"{cents // 100}.{cents % 100:02d}"


def allocate_cents(total_cents: int, weights: list) -> list:
    if not isinstance(weights, list):
        raise ValueError("weights must be a list of integers")
    for weight in weights:
        if not isinstance(weight, int) or weight < 0:
            raise ValueError(f"weight {weight} is not a non-negative integer")

    sum_w = sum(weights)
    if sum_w == 0:
        return [0] * len(weights)

    result = [total_cents * weight // sum_w for weight in weights]

    # Distribute any leftover cents
    leftover = total_cents - sum(result)
    i = 0
    while leftover > 0 and i < len(result):
        if result[i] % 1 != 0:
            result[i] += 1
            leftover -= 1
        i += 1

    return result
```