Python/maths/automorphic_number.py

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"""
== Automorphic Numbers ==
A number n is said to be a Automorphic number if
the square of n "ends" in the same digits as n itself.
Examples of Automorphic Numbers: 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, ...
https://en.wikipedia.org/wiki/Automorphic_number
"""
# Author : Akshay Dubey (https://github.com/itsAkshayDubey)
# Time Complexity : O(log10n)
def is_automorphic_number(number: int) -> bool:
"""
# doctest: +NORMALIZE_WHITESPACE
This functions takes an integer number as input.
returns True if the number is automorphic.
>>> is_automorphic_number(-1)
False
>>> is_automorphic_number(0)
True
>>> is_automorphic_number(5)
True
>>> is_automorphic_number(6)
True
>>> is_automorphic_number(7)
False
>>> is_automorphic_number(25)
True
>>> is_automorphic_number(259918212890625)
True
>>> is_automorphic_number(259918212890636)
False
>>> is_automorphic_number(740081787109376)
True
>>> is_automorphic_number(5.0)
Traceback (most recent call last):
...
TypeError: Input value of [number=5.0] must be an integer
"""
if not isinstance(number, int):
raise TypeError(f"Input value of [number={number}] must be an integer")
if number < 0:
return False
number_square = number * number
while number > 0:
if number % 10 != number_square % 10:
return False
number //= 10
number_square //= 10
return True
if __name__ == "__main__":
import doctest
doctest.testmod()