```python
def parse_amount(text: str) -> int:
    """Turns a decimal amount string into integer cents."""
    if not isinstance(text, str):
        raise ValueError("Input must be a string")
    parts = text.split('.')
    if len(parts) > 2:
        raise ValueError("Invalid format")
    integer_part = parts[0].lstrip('0') or '0'
    fraction_part = parts[1] if len(parts) == 2 else '00'
    if not integer_part.isdigit() or not fraction_part.isdigit():
        raise ValueError("Invalid format")
    return int(integer_part) * 100 + int(fraction_part)

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

def allocate_cents(total_cents: int, weights: list) -> list:
    """Splits total_cents across a list of integer weights proportionally."""
    if not isinstance(weights, list) or not all(isinstance(w, int) and w >= 0 for w 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 not isinstance(total_cents, int) or total_cents < 0:
        raise ValueError("Total cents must be a non-negative integer")

    total_weight = sum(weights)
    base_share = [total_cents * w // total_weight for w in weights]
    remainder = total_cents - sum(base_share)

    for i in range(remainder):
        max_remainder_index = max(range(len(weights)), key=lambda j: (weights[j] * base_share[j] % weights[j], -j))
        base_share[max_remainder_index] += 1

    return base_share
```