```python
def parse_amount(text: str) -> int:
    """Convert a decimal amount string to 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; too many dots.")
    
    integer_part = parts[0].strip()
    fraction_part = parts[1] if len(parts) == 2 else '00'
    
    if not integer_part.isdigit() or not fraction_part.isdigit():
        raise ValueError("Invalid characters in amount string.")
    
    if len(fraction_part) != 2:
        raise ValueError("Fractional part must be exactly two digits.")
    
    return int(integer_part + fraction_part)


def format_amount(cents: int) -> str:
    """Convert non-negative integer cents to a dotted decimal string."""
    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:
    """Split total_cents across weights proportionally."""
    if not isinstance(weights, list) or len(weights) == 0:
        raise ValueError("Weights must be a non-empty list.")
    
    for weight in weights:
        if not isinstance(weight, int) or weight < 0:
            raise ValueError("All weights must be 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.")
    
    shares = [total_cents * weight // sum(weights) for weight in weights]
    remainder = total_cents - sum(shares)
    
    for i in range(remainder):
        shares[i] += 1
    
    return shares
```