Optimization and fix bug (#2342)

* * optimization aliquot_sum
* fix bug in average_median

* fixup! Format Python code with psf/black push

* Update maths/average_median.py

* updating DIRECTORY.md

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

DIRECTORY.md

@@ -138,6 +138,7 @@
     * [Queue On Pseudo Stack](https://github.com/TheAlgorithms/Python/blob/master/data_structures/queue/queue_on_pseudo_stack.py)
   * Stacks
     * [Balanced Parentheses](https://github.com/TheAlgorithms/Python/blob/master/data_structures/stacks/balanced_parentheses.py)
+    * [Dijkstras Two Stack Algorithm](https://github.com/TheAlgorithms/Python/blob/master/data_structures/stacks/dijkstras_two_stack_algorithm.py)
     * [Infix To Postfix Conversion](https://github.com/TheAlgorithms/Python/blob/master/data_structures/stacks/infix_to_postfix_conversion.py)
     * [Infix To Prefix Conversion](https://github.com/TheAlgorithms/Python/blob/master/data_structures/stacks/infix_to_prefix_conversion.py)
     * [Linked Stack](https://github.com/TheAlgorithms/Python/blob/master/data_structures/stacks/linked_stack.py)
@@ -587,10 +588,18 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_35/sol1.py)
   * Problem 36
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_36/sol1.py)
+  * Problem 37
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_37/sol1.py)
+  * Problem 39
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_39/sol1.py)
   * Problem 40
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_40/sol1.py)
+  * Problem 41
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_41/sol1.py)
   * Problem 42
     * [Solution42](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_42/solution42.py)
+  * Problem 43
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_43/sol1.py)
   * Problem 47
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_47/sol1.py)
   * Problem 48
@@ -676,6 +685,7 @@
 ## Strings
   * [Aho-Corasick](https://github.com/TheAlgorithms/Python/blob/master/strings/aho-corasick.py)
   * [Boyer Moore Search](https://github.com/TheAlgorithms/Python/blob/master/strings/boyer_moore_search.py)
+  * [Check Anagrams](https://github.com/TheAlgorithms/Python/blob/master/strings/check_anagrams.py)
   * [Check Pangram](https://github.com/TheAlgorithms/Python/blob/master/strings/check_pangram.py)
   * [Is Palindrome](https://github.com/TheAlgorithms/Python/blob/master/strings/is_palindrome.py)
   * [Jaro Winkler](https://github.com/TheAlgorithms/Python/blob/master/strings/jaro_winkler.py)

data_structures/stacks/dijkstras_two_stack_algorithm.py

@@ -31,10 +31,10 @@ NOTE:   It only works with whole numbers.
 """
 __author__ = "Alexander Joslin"
 
-from .stack import Stack
-
 import operator as op
 
+from .stack import Stack
+
 
 def dijkstras_two_stack_algorithm(equation: str) -> int:
     """

maths/aliquot_sum.py

@@ -37,7 +37,9 @@ def aliquot_sum(input_num: int) -> int:
         raise ValueError("Input must be an integer")
     if input_num <= 0:
         raise ValueError("Input must be positive")
-    return sum(divisor for divisor in range(1, input_num) if input_num % divisor == 0)
+    return sum(
+        divisor for divisor in range(1, input_num // 2 + 1) if input_num % divisor == 0
+    )
 
 
 if __name__ == "__main__":

maths/average_median.py

@@ -6,6 +6,8 @@ def median(nums):
     0
     >>> median([4,1,3,2])
     2.5
+    >>> median([2, 70, 6, 50, 20, 8, 4])
+    8
 
     Args:
         nums: List of nums
@@ -14,22 +16,19 @@ def median(nums):
         Median.
     """
     sorted_list = sorted(nums)
-    med = None
-    if len(sorted_list) % 2 == 0:
-        mid_index_1 = len(sorted_list) // 2
-        mid_index_2 = (len(sorted_list) // 2) - 1
-        med = (sorted_list[mid_index_1] + sorted_list[mid_index_2]) / float(2)
-    else:
-        mid_index = (len(sorted_list) - 1) // 2
-        med = sorted_list[mid_index]
-    return med
+    length = len(sorted_list)
+    mid_index = length >> 1
+    return (
+        (sorted_list[mid_index] + sorted_list[mid_index - 1]) / 2
+        if length % 2 == 0
+        else sorted_list[mid_index]
+    )
 
 
 def main():
-    print("Odd number of numbers:")
-    print(median([2, 4, 6, 8, 20, 50, 70]))
-    print("Even number of numbers:")
-    print(median([2, 4, 6, 8, 20, 50]))
+    import doctest
+
+    doctest.testmod()
 
 
 if __name__ == "__main__":

project_euler/problem_39/sol1.py

@@ -6,8 +6,8 @@ If p is the perimeter of a right angle triangle with integral length sides,
 For which value of p ≤ 1000, is the number of solutions maximised?
 """
 
-from typing import Dict
 from collections import Counter
+from typing import Dict
 
 
 def pythagorean_triple(max_perimeter: int) -> Dict:

project_euler/problem_41/sol1.py

@@ -1,6 +1,6 @@
+from itertools import permutations
 from math import sqrt
 from typing import List
-from itertools import permutations
 
 """
 We shall say that an n-digit number is pandigital if it makes use of all the digits

strings/check_anagrams.py

@@ -17,6 +17,4 @@ if __name__ == "__main__":
     input_B = input("Enter the second string ").strip()
 
     status = check_anagrams(input_A, input_B)
-    print(
-        f"{input_A} and {input_B} are {'' if status else 'not '}anagrams."
-    )
+    print(f"{input_A} and {input_B} are {'' if status else 'not '}anagrams.")