"""

Number of Digits

Count the number of digits in an integer using logarithmic computation

for O(1) time complexity.

Reference: https://en.wikipedia.org/wiki/Logarithm

Complexity:

Time: O(1)

Space: O(1)

"""

from __future__ import annotations

import math

def num_digits(n: int) -> int:

"""Count the number of digits in an integer.

Args:

n: An integer (negative values use their absolute value).

Returns:

The number of digits in n.

Examples:

>>> num_digits(12)

2

>>> num_digits(0)

1

>>> num_digits(-254)

3

"""

n = abs(n)

if n == 0:

return 1

return int(math.log10(n)) + 1