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* feat: Add liouville lambda function * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor: Refactor if-else block * refactor: Refactor error handling for -ve numbers * refactor: Remove # doctest: +NORMALIZE_WHITESPACE Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
46 lines
1.3 KiB
Python
46 lines
1.3 KiB
Python
"""
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== Liouville Lambda Function ==
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The Liouville Lambda function, denoted by λ(n)
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and λ(n) is 1 if n is the product of an even number of prime numbers,
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and -1 if it is the product of an odd number of primes.
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https://en.wikipedia.org/wiki/Liouville_function
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"""
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# Author : Akshay Dubey (https://github.com/itsAkshayDubey)
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from maths.prime_factors import prime_factors
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def liouville_lambda(number: int) -> int:
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"""
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This functions takes an integer number as input.
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returns 1 if n has even number of prime factors and -1 otherwise.
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>>> liouville_lambda(10)
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1
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>>> liouville_lambda(11)
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-1
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>>> liouville_lambda(0)
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Traceback (most recent call last):
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...
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ValueError: Input must be a positive integer
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>>> liouville_lambda(-1)
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Traceback (most recent call last):
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...
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ValueError: Input must be a positive integer
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>>> liouville_lambda(11.0)
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Traceback (most recent call last):
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...
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TypeError: Input value of [number=11.0] must be an integer
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"""
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if not isinstance(number, int):
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raise TypeError(f"Input value of [number={number}] must be an integer")
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if number < 1:
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raise ValueError("Input must be a positive integer")
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return -1 if len(prime_factors(number)) % 2 else 1
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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