```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) or not all(isinstance(weight, int) and weight >= 0 for weight in weights):
        raise ValueError("weights must be a non-empty list of non-negative integers")
    if sum(weights) == 0:
        raise ValueError("sum of weights must be greater than zero")
    if total_cents < 0:
        raise ValueError("total cents must be a non-negative integer")

    shares = [total_cents * weight // sum(weights) for weight in weights]
    remaining_cents = total_cents - sum(shares)

    for i, remainder in enumerate(sorted((weight % (sum(weights) // len(weights)), i) for i, weight in enumerate(weights))):
        if remaining_cents == 0:
            break
        shares[remainder[1]] += 1
        remaining_cents -= 1

    return shares
```