TheAlgorithms/Python · error · ValueError

Invalid input: num must be >= 0 and sides must be >= 3.

Error message

Invalid input: num must be >= 0 and sides must be >= 3.

What it means

Raised by polygonal_num(sides, num) in maths/special_numbers/polygonal_numbers.py when num < 0 or sides < 3. The closed-form formula ((sides-2)*num^2 - (sides-4)*num) // 2 needs a non-negative index and at least 3 sides (a polygon cannot have fewer), hence the combined guard with a single message.

Source

Thrown at maths/special_numbers/polygonal_numbers.py:24

    >>> polygonal_num(0, 3)
    0
    >>> polygonal_num(3, 3)
    6
    >>> polygonal_num(5, 4)
    25
    >>> polygonal_num(2, 5)
    5
    >>> polygonal_num(-1, 0)
    Traceback (most recent call last):
        ...
    ValueError: Invalid input: num must be >= 0 and sides must be >= 3.
    >>> polygonal_num(0, 2)
    Traceback (most recent call last):
        ...
    ValueError: Invalid input: num must be >= 0 and sides must be >= 3.
    """
    if num < 0 or sides < 3:
        raise ValueError("Invalid input: num must be >= 0 and sides must be >= 3.")

    return ((sides - 2) * num**2 - (sides - 4) * num) // 2


if __name__ == "__main__":
    import doctest

    doctest.testmod()

View on GitHub (pinned to f5988cc097)

Solutions

1. Double-check argument order: index first, sides second
2. Ensure sides >= 3 (triangles are the minimum) and num >= 0 in your loops and inputs
3. Use keyword arguments if unsure: polygonal_num(num=2, sides=5)

Example fix

// before
val = polygonal_num(0, 2)  # ValueError: sides < 3

// after
val = polygonal_num(0, 3)  # first triangular number

def safe_polygonal(num: int, sides: int) -> int:
    if num < 0:
        raise ValueError('num (index) must be >= 0')
    if sides < 3:
        raise ValueError('sides must be >= 3 (triangle is the minimum)')
    return polygonal_num(num, sides)

When it happens

Trigger: Calling polygonal_num(-1, 0) (negative num) or polygonal_num(0, 2) (sides < 3). Note the parameter order in the doctests: the first argument is the index (num), the second is sides — polygonal_num(2, 5) returns the 2nd pentagonal number, 5.

Common situations: Swapping the two positional arguments so a valid sides value lands in num's slot; looping sides from 2 (forgetting that digons are excluded); passing a negative index for 'previous element' semantics this API does not have.

Related errors

• surface_area_cube() only accepts non-negative values
• surface_area_cuboid() only accepts non-negative values
• surface_area_sphere() only accepts non-negative values
• surface_area_hemisphere() only accepts non-negative values
• surface_area_cone() only accepts non-negative values

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/f3af4716706687a3. Report an issue: GitHub.