Optimized recursive_bubble_sort (#2410)

* optimized recursive_bubble_sort

* Fixed doctest error due whitespace

* reduce loop times for optimization

* fixup! Format Python code with psf/black push

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

Author: realDuYuanChao

arithmetic_analysis/newton_method.py

@@ -7,7 +7,11 @@
 
 
 # function is the f(x) and derivative is the f'(x)
-def newton(function: RealFunc, derivative: RealFunc, starting_int: int,) -> float:
+def newton(
+    function: RealFunc,
+    derivative: RealFunc,
+    starting_int: int,
+) -> float:
     """
     >>> newton(lambda x: x ** 3 - 2 * x - 5, lambda x: 3 * x ** 2 - 2, 3)
     2.0945514815423474

arithmetic_analysis/newton_raphson.py

@@ -9,7 +9,7 @@
 
 
 def newton_raphson(func: str, a: int, precision: int = 10 ** -10) -> float:
-    """ Finds root from the point 'a' onwards by Newton-Raphson method
+    """Finds root from the point 'a' onwards by Newton-Raphson method
     >>> newton_raphson("sin(x)", 2)
     3.1415926536808043
     >>> newton_raphson("x**2 - 5*x +2", 0.4)