mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 21:41:08 +00:00
bc8df6de31
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
58 lines
1.5 KiB
Python
58 lines
1.5 KiB
Python
"""
|
|
Finding the continuous fraction for a rational number using python
|
|
|
|
https://en.wikipedia.org/wiki/Continued_fraction
|
|
"""
|
|
|
|
from fractions import Fraction
|
|
from math import floor
|
|
|
|
|
|
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]
|
|
>>> continued_fraction(Fraction(0))
|
|
[0]
|
|
>>> continued_fraction(Fraction(0.75))
|
|
[0, 1, 3]
|
|
>>> continued_fraction(Fraction("-2.25")) # -2.25 = -3 + 0.75
|
|
[-3, 1, 3]
|
|
"""
|
|
numerator, denominator = num.as_integer_ratio()
|
|
continued_fraction_list: list[int] = []
|
|
while True:
|
|
integer_part = floor(numerator / denominator)
|
|
continued_fraction_list.append(integer_part)
|
|
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")))
|