added continued fractions

Author: Saksham1970

Diff for: 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")))