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41 lines
1.1 KiB
Python
41 lines
1.1 KiB
Python
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from math import gcd
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def proper_fractions(denominator: int) -> list[str]:
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"""
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this algorithm returns a list of proper fractions, in the
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range between 0 and 1, which can be formed with the given denominator
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https://en.wikipedia.org/wiki/Fraction#Proper_and_improper_fractions
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>>> proper_fractions(10)
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['1/10', '3/10', '7/10', '9/10']
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>>> proper_fractions(5)
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['1/5', '2/5', '3/5', '4/5']
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>>> proper_fractions(-15)
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Traceback (most recent call last):
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...
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ValueError: The Denominator Cannot be less than 0
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>>> proper_fractions(0)
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[]
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>>> proper_fractions(1.2)
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Traceback (most recent call last):
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...
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ValueError: The Denominator must be an integer
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"""
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if denominator < 0:
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raise ValueError("The Denominator Cannot be less than 0")
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elif isinstance(denominator, float):
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raise ValueError("The Denominator must be an integer")
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return [
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f"{numerator}/{denominator}"
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for numerator in range(1, denominator)
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if gcd(numerator, denominator) == 1
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]
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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