TheAlgorithms/Python · error · ValueError

All numbers must be positive

Error message

All numbers must be positive

What it means

Raised by msd_radix_sort in sorts/msd_radix_sort.py when the input list contains a negative number. The MSD radix sort recursively partitions numbers by individual bits using bin(x)[2:], which has no sign bit representation for negatives, so the function guards with min(list_of_ints) < 0 and rejects the whole list with ValueError. An empty list returns [] before the check, and 0 is fine.

Source

Thrown at sorts/msd_radix_sort.py:34

    :return: Returns the sorted list
    >>> msd_radix_sort([40, 12, 1, 100, 4])
    [1, 4, 12, 40, 100]
    >>> msd_radix_sort([])
    []
    >>> msd_radix_sort([123, 345, 123, 80])
    [80, 123, 123, 345]
    >>> msd_radix_sort([1209, 834598, 1, 540402, 45])
    [1, 45, 1209, 540402, 834598]
    >>> msd_radix_sort([-1, 34, 45])
    Traceback (most recent call last):
        ...
    ValueError: All numbers must be positive
    """
    if not list_of_ints:
        return []

    if min(list_of_ints) < 0:
        raise ValueError("All numbers must be positive")

    most_bits = max(len(bin(x)[2:]) for x in list_of_ints)
    return _msd_radix_sort(list_of_ints, most_bits)


def _msd_radix_sort(list_of_ints: list[int], bit_position: int) -> list[int]:
    """
    Sort the given list based on the bit at bit_position. Numbers with a
    0 at that position will be at the start of the list, numbers with a
    1 at the end.
    :param list_of_ints: A list of integers
    :param bit_position: the position of the bit that gets compared
    :return: Returns a partially sorted list
    >>> _msd_radix_sort([45, 2, 32], 1)
    [2, 32, 45]
    >>> _msd_radix_sort([10, 4, 12], 2)
    [4, 12, 10]
    """

View on GitHub (pinned to f5988cc097)

Solutions

1. Use a sort that supports negatives (sorted(), radix sort with sign handling) if negatives are legitimate data.
2. Offset-encode: shift all values by -min(list) so they become non-negative, sort, then shift back.
3. Filter or reject negatives before calling: if min(data) < 0: raise ValueError(...).

Example fix

# before
msd_radix_sort([-1, 34, 23, 4, -42])  # ValueError

# after
offset = min(data)
shifted = msd_radix_sort([x - offset for x in data])
sorted_data = [x + offset for x in shifted]

if any(x < 0 for x in data):
    offset = min(data)
    data = [x - offset for x in data]
result = msd_radix_sort(data)
# then add offset back to result if original values are needed

def is_non_negative_ints(lst) -> bool:
    return all(isinstance(x, int) and x >= 0 for x in lst)

try:
    out = msd_radix_sort(data)
except ValueError:
    m = min(data)
    out = [x + m for x in msd_radix_sort([x - m for x in data])]

When it happens

Trigger: msd_radix_sort([-1, 34, 45]); msd_radix_sort([0, -42, 7]); any single negative value anywhere in the list, even if the rest are valid.

Common situations: Feeding sensor/financial data with negatives; reusing the function on user input that allows minus signs; assuming radix sort handles all ints like Python's sorted() does.

Related errors

• number of qubits too large to simulate(>10).
• k integer must be greater or equal to zero.
• Sequence must be list of non-negative integers
• The elements inside the sequence must contains only {colors}
• Expected a_coeffs to have {self.order + 1} elements for {sel

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/85af74ece54cac19. Report an issue: GitHub.