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>

project_euler/problem_09/sol2.py

@@ -23,8 +23,7 @@ def solution(n):
     product = -1
     d = 0
     for a in range(1, n // 3):
-        """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
-        """
+        """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c"""
         b = (n * n - 2 * a * n) // (2 * n - 2 * a)
         c = n - a - b
         if c * c == (a * a + b * b):

project_euler/problem_10/sol3.py

@@ -12,7 +12,7 @@ smaller than n when n is smaller than 10 million.  Only for positive numbers.
 
 
 def prime_sum(n: int) -> int:
-    """ Returns the sum of all the primes below n.
+    """Returns the sum of all the primes below n.
 
     >>> prime_sum(2_000_000)
     142913828922

project_euler/problem_15/sol1.py

@@ -8,31 +8,31 @@ from math import factorial
 
 def lattice_paths(n):
     """
-    Returns the number of paths possible in a n x n grid starting at top left
-    corner going to bottom right corner and being able to move right and down
-    only.
+        Returns the number of paths possible in a n x n grid starting at top left
+        corner going to bottom right corner and being able to move right and down
+        only.
 
-bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 50
-1.008913445455642e+29
-bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 25
-126410606437752.0
-bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 23
-8233430727600.0
-bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 15
-155117520.0
-bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 1
-2.0
+    bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 50
+    1.008913445455642e+29
+    bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 25
+    126410606437752.0
+    bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 23
+    8233430727600.0
+    bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 15
+    155117520.0
+    bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 1
+    2.0
 
-    >>> lattice_paths(25)
-    126410606437752
-    >>> lattice_paths(23)
-    8233430727600
-    >>> lattice_paths(20)
-    137846528820
-    >>> lattice_paths(15)
-    155117520
-    >>> lattice_paths(1)
-    2
+        >>> lattice_paths(25)
+        126410606437752
+        >>> lattice_paths(23)
+        8233430727600
+        >>> lattice_paths(20)
+        137846528820
+        >>> lattice_paths(15)
+        155117520
+        >>> lattice_paths(1)
+        2
 
     """
     n = 2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,

project_euler/problem_27/problem_27_sol1.py

@@ -39,17 +39,17 @@ def is_prime(k: int) -> bool:
 
 def solution(a_limit: int, b_limit: int) -> int:
     """
-        >>> solution(1000, 1000)
-        -59231
-        >>> solution(200, 1000)
-        -59231
-        >>> solution(200, 200)
-        -4925
-        >>> solution(-1000, 1000)
-        0
-        >>> solution(-1000, -1000)
-        0
-        """
+    >>> solution(1000, 1000)
+    -59231
+    >>> solution(200, 1000)
+    -59231
+    >>> solution(200, 200)
+    -4925
+    >>> solution(-1000, 1000)
+    0
+    >>> solution(-1000, -1000)
+    0
+    """
     longest = [0, 0, 0]  # length, a, b
     for a in range((a_limit * -1) + 1, a_limit):
         for b in range(2, b_limit):

project_euler/problem_56/sol1.py

@@ -1,18 +1,18 @@
 def maximum_digital_sum(a: int, b: int) -> int:
     """
-        Considering natural numbers of the form, a**b, where a, b < 100,
-        what is the maximum digital sum?
-        :param a:
-        :param b:
-        :return:
-        >>> maximum_digital_sum(10,10)
-        45
+    Considering natural numbers of the form, a**b, where a, b < 100,
+    what is the maximum digital sum?
+    :param a:
+    :param b:
+    :return:
+    >>> maximum_digital_sum(10,10)
+    45
 
-        >>> maximum_digital_sum(100,100)
-        972
+    >>> maximum_digital_sum(100,100)
+    972
 
-        >>> maximum_digital_sum(100,200)
-        1872
+    >>> maximum_digital_sum(100,200)
+    1872
     """
 
     # RETURN the MAXIMUM from the list of SUMs of the list of INT converted from STR of