TheAlgorithms/Python · error · ValueError

max_set_length must be non-negative

Error message

max_set_length must be non-negative

What it means

Raised by bell_numbers() in maths/special_numbers/bell_numbers.py when max_set_length is negative. The function pre-allocates bell = [0] * (max_set_length + 1) and builds the Bell triangle recurrence; a negative length would break indexing and is meaningless (bell_numbers(0) legitimately returns [1]). Only negativity is checked — non-int types are not validated here and may fail separately.

Source

Thrown at maths/special_numbers/bell_numbers.py:36

        Bell numbers are calculated.

    Returns:
        list: A list of Bell numbers for sets of lengths from 0 to max_set_length.

    Examples:
    >>> bell_numbers(-2)
    Traceback (most recent call last):
        ...
    ValueError: max_set_length must be non-negative
    >>> bell_numbers(0)
    [1]
    >>> bell_numbers(1)
    [1, 1]
    >>> bell_numbers(5)
    [1, 1, 2, 5, 15, 52]
    """
    if max_set_length < 0:
        raise ValueError("max_set_length must be non-negative")

    bell = [0] * (max_set_length + 1)
    bell[0] = 1

    for i in range(1, max_set_length + 1):
        for j in range(i):
            bell[i] += _binomial_coefficient(i - 1, j) * bell[j]

    return bell


def _binomial_coefficient(total_elements: int, elements_to_choose: int) -> int:
    """
    Calculate the binomial coefficient C(total_elements, elements_to_choose)

    Args:
        total_elements (int): The total number of elements.
        elements_to_choose (int): The number of elements to choose.

View on GitHub (pinned to f5988cc097)

Solutions

1. Clamp: bell_numbers(max(0, max_set_length))
2. Validate the computation that produces the length: assert k <= n before subtracting
3. Return an empty/short list yourself for negative requests instead of calling the function

Example fix

# before
bells = bell_numbers(n - k)  # negative when k > n

# after
bells = bell_numbers(n - k) if n >= k else []

bells = bell_numbers(max_set_length) if max_set_length >= 0 else []

def is_non_negative_int(value: object) -> bool:
    return isinstance(value, int) and not isinstance(value, bool) and value >= 0

When it happens

Trigger: Calling bell_numbers(-2) or bell_numbers(-1). A computed max_set_length from subtraction (e.g. n - k) that goes negative is the usual source. bell_numbers(0) and bell_numbers(1) are valid and return [1] and [1, 1].

Common situations: Combinatorics helper code where the requested set size exceeds available elements (k > n making n - k negative); CLI args with bad defaults; loop bounds off by one.

Related errors

• Input list must be a non empty list
• Input list must be a non empty list
• Length must be a positive integer.
• {num}: Invalid input, please enter a positive integer.
• Number {n} must instead be a positive integer

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/4b1a86f6fa32a7e0. Report an issue: GitHub.