Added Continued fractions (TheAlgorithms#6846)

* updating DIRECTORY.md * added continued fractions * updating DIRECTORY.md * Update maths/continued_fraction.py Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com> * Update maths/continued_fraction.py Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com> --------- Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com> Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

Author: 4 people

DIRECTORY.md

@@ -555,6 +555,7 @@
  * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
  * [Collatz Sequence](maths/collatz_sequence.py)
  * [Combinations](maths/combinations.py)
+ * [Continued Fraction](maths/continued_fraction.py)
  * [Decimal Isolate](maths/decimal_isolate.py)
  * [Decimal To Fraction](maths/decimal_to_fraction.py)
  * [Dodecahedron](maths/dodecahedron.py)

maths/continued_fraction.py

@@ -0,0 +1,51 @@
+"""
+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 -= 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")))