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

    # Calculate the floor of each proportional share
    shares = [total_cents * weight // sum_w for weight in weights]

    # Calculate the remaining cents
    remaining_cents = total_cents - sum(shares)

    
    # Distribute the remaining cents to the shares with the largest division remainders
    # earliest index first on a tie
    for i in range(len(shares)):
        if remaining_cents > 0:
            shares[i] += 1
            remaining_cents -= 1

    return shares
```