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import math

from timeit import timeit

def num_digits(n: int) -> int:

"""

Find the number of digits in a number.

>>> num_digits(12345)

>>> num_digits(123)

>>> num_digits(0)

>>> num_digits(-1)

>>> num_digits(-123456)

"""

digits = 0

n = abs(n)

while True:

n = n // 10

digits += 1

if n == 0:

break

return digits

def num_digits_fast(n: int) -> int:

"""

Find the number of digits in a number.

abs() is used as logarithm for negative numbers is not defined.

>>> num_digits_fast(12345)

>>> num_digits_fast(123)

>>> num_digits_fast(0)

>>> num_digits_fast(-1)

>>> num_digits_fast(-123456)

"""

return 1 if n == 0 else math.floor(math.log(abs(n), 10) + 1)

def num_digits_faster(n: int) -> int:

"""

Find the number of digits in a number.

abs() is used for negative numbers

>>> num_digits_faster(12345)

>>> num_digits_faster(123)

>>> num_digits_faster(0)

>>> num_digits_faster(-1)

>>> num_digits_faster(-123456)

"""

return len(str(abs(n)))

def benchmark() -> None:

"""

Benchmark code for comparing 3 functions,

with 3 different length int values.

"""

print("\nFor small_num = ", small_num, ":")

print(

"> num_digits()",

"\t\tans =",

num_digits(small_num),

"\ttime =",

timeit("z.num_digits(z.small_num)", setup="import __main__ as z"),

"seconds",

)

print(

"> num_digits_fast()",

"\tans =",

num_digits_fast(small_num),

"\ttime =",

timeit("z.num_digits_fast(z.small_num)", setup="import __main__ as z"),

"seconds",

)

print(

"> num_digits_faster()",

"\tans =",

num_digits_faster(small_num),

"\ttime =",

timeit("z.num_digits_faster(z.small_num)", setup="import __main__ as z"),

"seconds",

)

print("\nFor medium_num = ", medium_num, ":")

print(

"> num_digits()",

"\t\tans =",

num_digits(medium_num),

"\ttime =",

timeit("z.num_digits(z.medium_num)", setup="import __main__ as z"),

"seconds",

)

print(

"> num_digits_fast()",

"\tans =",

num_digits_fast(medium_num),

"\ttime =",

timeit("z.num_digits_fast(z.medium_num)", setup="import __main__ as z"),

"seconds",

)

print(

"> num_digits_faster()",

"\tans =",

num_digits_faster(medium_num),

"\ttime =",

timeit("z.num_digits_faster(z.medium_num)", setup="import __main__ as z"),

"seconds",

)

print("\nFor large_num = ", large_num, ":")

print(

"> num_digits()",

"\t\tans =",

num_digits(large_num),

"\ttime =",

timeit("z.num_digits(z.large_num)", setup="import __main__ as z"),

"seconds",

)

print(

"> num_digits_fast()",

"\tans =",

num_digits_fast(large_num),

"\ttime =",

timeit("z.num_digits_fast(z.large_num)", setup="import __main__ as z"),

"seconds",

)

print(

"> num_digits_faster()",

"\tans =",

num_digits_faster(large_num),

"\ttime =",

timeit("z.num_digits_faster(z.large_num)", setup="import __main__ as z"),

"seconds",

)

if __name__ == "__main__":

small_num = 262144

medium_num = 1125899906842624

large_num = 1267650600228229401496703205376

benchmark()

import doctest

doctest.testmod()

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