Fix merge sort comparable clean (#15259)

* updating DIRECTORY.md

* sorts: support comparable items in merge sort

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* sorts: use type parameters in merge sort

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Fix grammar in merge sort docstring

Corrected minor grammatical errors in docstring.

* Update DIRECTORY.md with new algorithms and functions

* updating DIRECTORY.md

* updating DIRECTORY.md

---------

Co-authored-by: kadubhumika <kadubhumika@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

DIRECTORY.md

@@ -1354,11 +1354,13 @@
   * [Ternary Search](searches/ternary_search.py)
 
 ## [Sorts](sorts)
+  * [Adaptive Merge Sort](sorts/adaptive_merge_sort.py)
   * [Bead Sort](sorts/bead_sort.py)
   * [Binary Insertion Sort](sorts/binary_insertion_sort.py)
   * [Bitonic Sort](sorts/bitonic_sort.py)
   * [Bogo Sort](sorts/bogo_sort.py)
   * [Bubble Sort](sorts/bubble_sort.py)
+  * [Bubble Sort Recursive](sorts/bubble_sort_recursive.py)
   * [Bucket Sort](sorts/bucket_sort.py)
   * [Circle Sort](sorts/circle_sort.py)
   * [Cocktail Shaker Sort](sorts/cocktail_shaker_sort.py)
@@ -1376,6 +1378,7 @@
   * [Insertion Sort](sorts/insertion_sort.py)
   * [Intro Sort](sorts/intro_sort.py)
   * [Iterative Merge Sort](sorts/iterative_merge_sort.py)
+  * [Kirkpatrick Reisch Sort](sorts/kirkpatrick_reisch_sort.py)
   * [Merge Insertion Sort](sorts/merge_insertion_sort.py)
   * [Merge Sort](sorts/merge_sort.py)
   * [Msd Radix Sort](sorts/msd_radix_sort.py)
@@ -1387,16 +1390,20 @@
   * [Patience Sort](sorts/patience_sort.py)
   * [Pigeon Sort](sorts/pigeon_sort.py)
   * [Pigeonhole Sort](sorts/pigeonhole_sort.py)
+  * [Power Sort](sorts/power_sort.py)
   * [Quick Sort](sorts/quick_sort.py)
   * [Quick Sort 3 Partition](sorts/quick_sort_3_partition.py)
   * [Radix Sort](sorts/radix_sort.py)
   * [Recursive Insertion Sort](sorts/recursive_insertion_sort.py)
   * [Recursive Mergesort Array](sorts/recursive_mergesort_array.py)
   * [Recursive Quick Sort](sorts/recursive_quick_sort.py)
+  * [Reverse Selection](sorts/reverse_selection.py)
+  * [Reversort](sorts/reversort.py)
   * [Selection Sort](sorts/selection_sort.py)
   * [Shell Sort](sorts/shell_sort.py)
   * [Shrink Shell Sort](sorts/shrink_shell_sort.py)
   * [Slowsort](sorts/slowsort.py)
+  * [Smoothsort](sorts/smoothsort.py)
   * [Stalin Sort](sorts/stalin_sort.py)
   * [Stooge Sort](sorts/stooge_sort.py)
   * [Strand Sort](sorts/strand_sort.py)

sorts/merge_sort.py

@@ -1,21 +1,27 @@
 """
-This is a pure Python implementation of the merge sort algorithm.
+The merge sort algorithm.
 
-For doctests run following command:
+For doctests, run the following command:
 python -m doctest -v merge_sort.py
 or
 python3 -m doctest -v merge_sort.py
-For manual testing run:
+For manual testing, run:
 python merge_sort.py
 """
 
+from typing import Protocol
 
-def merge_sort(collection: list) -> list:
+
+class Comparable(Protocol):
+    def __lt__(self, other: object, /) -> bool: ...
+
+
+def merge_sort[T: Comparable](collection: list[T]) -> list[T]:
     """
     Sorts a list using the merge sort algorithm.
 
-    :param collection: A mutable ordered collection with comparable items.
-    :return: The same collection ordered in ascending order.
+    :param collection: A collection with comparable items.
+    :return: The collection ordered in ascending order.
 
     Time Complexity: O(n log n)
     Space Complexity: O(n)
@@ -23,13 +29,15 @@ def merge_sort(collection: list) -> list:
     Examples:
     >>> merge_sort([0, 5, 3, 2, 2])
     [0, 2, 2, 3, 5]
+
     >>> merge_sort([])
     []
-    >>> merge_sort([-2, -5, -45])
+
+    >>> merge_sort([-2, -45, -5])
     [-45, -5, -2]
     """
 
-    def merge(left: list, right: list) -> list:
+    def merge(left: list[T], right: list[T]) -> list[T]:
         """
         Merge two sorted lists into a single sorted list.
 
@@ -37,9 +45,12 @@ def merge_sort(collection: list) -> list:
         :param right: Right collection
         :return: Merged result
         """
-        result = []
+        result: list[T] = []
         while left and right:
-            result.append(left.pop(0) if left[0] <= right[0] else right.pop(0))
+            if right[0] < left[0]:
+                result.append(right.pop(0))
+            else:
+                result.append(left.pop(0))
         result.extend(left)
         result.extend(right)
         return result