diff --git a/maths/continued_fraction.py b/maths/continued_fraction.py new file mode 100644 index 000000000..e3e47a500 --- /dev/null +++ b/maths/continued_fraction.py @@ -0,0 +1,52 @@ +""" +Finding the continuous fraction for a rational number using python + +https://en.wikipedia.org/wiki/Continued_fraction +""" + + +from fractions import Fraction + + +def continued_fraction(num: Fraction) -> list[int]: + """ + :param num: + Fraction of the number whose continued fractions to be found. + Use Fraction(str(number)) for more accurate results due to + float inaccuracies. + + :return: + The continued fraction of rational number. + It is the all commas in the (n + 1)-tuple notation. + + >>> continued_fraction(Fraction(2)) + [2] + >>> continued_fraction(Fraction("3.245")) + [3, 4, 12, 4] + >>> continued_fraction(Fraction("2.25")) + [2, 4] + >>> continued_fraction(1/Fraction("2.25")) + [0, 2, 4] + >>> continued_fraction(Fraction("415/93")) + [4, 2, 6, 7] + """ + numerator, denominator = num.as_integer_ratio() + continued_fraction_list: list[int] = [] + while True: + integer_part = int(numerator / denominator) + continued_fraction_list.append(integer_part) + numerator = numerator - integer_part * denominator + if numerator == 0: + break + numerator, denominator = denominator, numerator + + return continued_fraction_list + + +if __name__ == "__main__": + + import doctest + + doctest.testmod() + + print("Continued Fraction of 0.84375 is: ", continued_fraction(Fraction("0.84375")))