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58 lines
1.5 KiB
Python
58 lines
1.5 KiB
Python
"""
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Finding the continuous fraction for a rational number using python
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https://en.wikipedia.org/wiki/Continued_fraction
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"""
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from fractions import Fraction
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from math import floor
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def continued_fraction(num: Fraction) -> list[int]:
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"""
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:param num:
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Fraction of the number whose continued fractions to be found.
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Use Fraction(str(number)) for more accurate results due to
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float inaccuracies.
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:return:
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The continued fraction of rational number.
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It is the all commas in the (n + 1)-tuple notation.
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>>> continued_fraction(Fraction(2))
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[2]
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>>> continued_fraction(Fraction("3.245"))
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[3, 4, 12, 4]
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>>> continued_fraction(Fraction("2.25"))
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[2, 4]
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>>> continued_fraction(1/Fraction("2.25"))
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[0, 2, 4]
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>>> continued_fraction(Fraction("415/93"))
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[4, 2, 6, 7]
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>>> continued_fraction(Fraction(0))
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[0]
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>>> continued_fraction(Fraction(0.75))
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[0, 1, 3]
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>>> continued_fraction(Fraction("-2.25")) # -2.25 = -3 + 0.75
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[-3, 1, 3]
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"""
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numerator, denominator = num.as_integer_ratio()
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continued_fraction_list: list[int] = []
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while True:
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integer_part = floor(numerator / denominator)
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continued_fraction_list.append(integer_part)
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numerator -= integer_part * denominator
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if numerator == 0:
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break
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numerator, denominator = denominator, numerator
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return continued_fraction_list
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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print("Continued Fraction of 0.84375 is: ", continued_fraction(Fraction("0.84375")))
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