task: Add type hints to inversions.py (#14262)

* task: Add type hints to inversions.py

* fixed formatting error

* style: Fix RUF037 in hash_table_with_linked_list

* Initialize deque with empty list for None values

---------

Co-authored-by: Christian Clauss <cclauss@me.com>

Author: nupurvavhal

divide_and_conquer/inversions.py

@@ -9,7 +9,7 @@
 """
 
 
-def count_inversions_bf(arr):
+def count_inversions_bf(arr: list[int]) -> int:
     """
     Counts the number of inversions using a naive brute-force algorithm
     Parameters
@@ -40,7 +40,7 @@ def count_inversions_bf(arr):
     return num_inversions
 
 
-def count_inversions_recursive(arr):
+def count_inversions_recursive(arr: list[int]) -> tuple[list[int], int]:
     """
     Counts the number of inversions using a divide-and-conquer algorithm
     Parameters
@@ -74,7 +74,7 @@ def count_inversions_recursive(arr):
     return c, num_inversions
 
 
-def _count_cross_inversions(p, q):
+def _count_cross_inversions(p: list[int], q: list[int]) -> tuple[list[int], int]:
     """
     Counts the inversions across two sorted arrays.
     And combine the two arrays into one sorted array