Added Continued fractions

DIRECTORY.md

@@ -9,6 +9,7 @@
   * [Newton Forward Interpolation](arithmetic_analysis/newton_forward_interpolation.py)
   * [Newton Method](arithmetic_analysis/newton_method.py)
   * [Newton Raphson](arithmetic_analysis/newton_raphson.py)
+  * [Newton Raphson New](arithmetic_analysis/newton_raphson_new.py)
   * [Secant Method](arithmetic_analysis/secant_method.py)
 
 ## Audio Filters
@@ -107,6 +108,7 @@
   * [Lempel Ziv](compression/lempel_ziv.py)
   * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py)
   * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py)
+  * [Run Length Encoding](compression/run_length_encoding.py)
 
 ## Computer Vision
   * [Cnn Classification](computer_vision/cnn_classification.py)
@@ -478,6 +480,7 @@
   * [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)
   * [Double Factorial Iterative](maths/double_factorial_iterative.py)
   * [Double Factorial Recursive](maths/double_factorial_recursive.py)
@@ -621,6 +624,7 @@
   * [Linear Congruential Generator](other/linear_congruential_generator.py)
   * [Lru Cache](other/lru_cache.py)
   * [Magicdiamondpattern](other/magicdiamondpattern.py)
+  * [Maximum Subarray](other/maximum_subarray.py)
   * [Nested Brackets](other/nested_brackets.py)
   * [Password Generator](other/password_generator.py)
   * [Scoring Algorithm](other/scoring_algorithm.py)
@@ -1053,6 +1057,7 @@
   * [Fetch Bbc News](web_programming/fetch_bbc_news.py)
   * [Fetch Github Info](web_programming/fetch_github_info.py)
   * [Fetch Jobs](web_programming/fetch_jobs.py)
+  * [Fetch Quotes](web_programming/fetch_quotes.py)
   * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
   * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
   * [Get Imdbtop](web_programming/get_imdbtop.py)

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")))