TheAlgorithms/Python · error · IndexError

list index out of range

Error message

list index out of range

What it means

Raised by find_max_recursive() in maths/find_max.py when the left or right index argument falls outside the permitted range. Valid indices must satisfy -len(nums) <= idx < len(nums) (Python-style negative indexing allowed, but not >= len(nums)); the guard raises IndexError('list index out of range') — including the common mistake right = len(nums), since the recursion treats right as an inclusive element index, not an exclusive bound.

Source

Thrown at maths/find_max.py:69

    Traceback (most recent call last):
        ...
    IndexError: list index out of range
    >>> find_max_recursive(nums, -len(nums), -1) == max(nums)
    True
    >>> find_max_recursive(nums, -len(nums) - 1, -1) == max(nums)
    Traceback (most recent call last):
        ...
    IndexError: list index out of range
    """
    if len(nums) == 0:
        raise ValueError("find_max_recursive() arg is an empty sequence")
    if (
        left >= len(nums)
        or left < -len(nums)
        or right >= len(nums)
        or right < -len(nums)
    ):
        raise IndexError("list index out of range")
    if left == right:
        return nums[left]
    mid = (left + right) >> 1  # the middle
    left_max = find_max_recursive(nums, left, mid)  # find max in range[left, mid]
    right_max = find_max_recursive(
        nums, mid + 1, right
    )  # find max in range[mid + 1, right]

    return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
    import doctest

    doctest.testmod(verbose=True)

View on GitHub (pinned to f5988cc097)

Solutions

1. Use inclusive bounds: find_max_recursive(nums, 0, len(nums) - 1), or negative form (nums, -len(nums), -1).
2. Never pass len(nums) as right; subtract 1 first.
3. Wrap the helper in your own function that converts half-open [lo, hi) bounds to inclusive (lo, hi - 1) if your codebase uses slice semantics.

Example fix

# before
find_max_recursive(nums, 0, len(nums))    # IndexError: right == len(nums)

# after
find_max_recursive(nums, 0, len(nums) - 1)  # inclusive bounds

if not (-len(nums) <= left < len(nums) and -len(nums) <= right < len(nums) and left <= right):
    raise IndexError(f'bounds ({left}, {right}) invalid for length {len(nums)}')
m = find_max_recursive(nums, left, right)

When it happens

Trigger: Calling find_max_recursive(nums, 0, len(nums)) — right equals len(nums), which is out of range (doctest shows this exact failure). Also find_max_recursive(nums, -len(nums) - 1, -1), left >= len(nums), or right < -len(nums). Correct inclusive usage is (0, len(nums) - 1) or (-len(nums), -1).

Common situations: Passing slice-style exclusive bounds (0, len(nums)) to an API that expects inclusive bounds — the most frequent cause; porting code from binary-search helpers whose conventions differ; mixing negative and positive indices between calls.

Related errors

• list index out of range
• find_max_recursive() arg is an empty sequence
• Number should not be negative.
• find_max_iterative() arg is an empty sequence
• find_min_recursive() arg is an empty sequence

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/96925ea3c05ad61c. Report an issue: GitHub.