Pyupgrade to Python 3.9 (#4718)

* Pyupgrade to Python 3.9

* updating DIRECTORY.md

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

searches/binary_search.py

@@ -9,12 +9,13 @@ python3 -m doctest -v binary_search.py
 For manual testing run:
 python3 binary_search.py
 """
+from __future__ import annotations
+
 import bisect
-from typing import List, Optional
 
 
 def bisect_left(
-    sorted_collection: List[int], item: int, lo: int = 0, hi: int = -1
+    sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
 ) -> int:
     """
     Locates the first element in a sorted array that is larger or equal to a given
@@ -60,7 +61,7 @@ def bisect_left(
 
 
 def bisect_right(
-    sorted_collection: List[int], item: int, lo: int = 0, hi: int = -1
+    sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
 ) -> int:
     """
     Locates the first element in a sorted array that is larger than a given value.
@@ -105,7 +106,7 @@ def bisect_right(
 
 
 def insort_left(
-    sorted_collection: List[int], item: int, lo: int = 0, hi: int = -1
+    sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
 ) -> None:
     """
     Inserts a given value into a sorted array before other values with the same value.
@@ -148,7 +149,7 @@ def insort_left(
 
 
 def insort_right(
-    sorted_collection: List[int], item: int, lo: int = 0, hi: int = -1
+    sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
 ) -> None:
     """
     Inserts a given value into a sorted array after other values with the same value.
@@ -190,7 +191,7 @@ def insort_right(
     sorted_collection.insert(bisect_right(sorted_collection, item, lo, hi), item)
 
 
-def binary_search(sorted_collection: List[int], item: int) -> Optional[int]:
+def binary_search(sorted_collection: list[int], item: int) -> int | None:
     """Pure implementation of binary search algorithm in Python
 
     Be careful collection must be ascending sorted, otherwise result will be
@@ -228,7 +229,7 @@ def binary_search(sorted_collection: List[int], item: int) -> Optional[int]:
     return None
 
 
-def binary_search_std_lib(sorted_collection: List[int], item: int) -> Optional[int]:
+def binary_search_std_lib(sorted_collection: list[int], item: int) -> int | None:
     """Pure implementation of binary search algorithm in Python using stdlib
 
     Be careful collection must be ascending sorted, otherwise result will be
@@ -258,8 +259,8 @@ def binary_search_std_lib(sorted_collection: List[int], item: int) -> Optional[i
 
 
 def binary_search_by_recursion(
-    sorted_collection: List[int], item: int, left: int, right: int
-) -> Optional[int]:
+    sorted_collection: list[int], item: int, left: int, right: int
+) -> int | None:
 
     """Pure implementation of binary search algorithm in Python by recursion
 

searches/fibonacci_search.py

@@ -13,7 +13,7 @@ python3 fibonacci_search.py
 from functools import lru_cache
 
 
-@lru_cache()
+@lru_cache
 def fibonacci(k: int) -> int:
     """Finds fibonacci number in index k.
 

searches/ternary_search.py

@@ -6,7 +6,7 @@ This is a type of divide and conquer algorithm which divides the search space in
 Time Complexity  : O(log3 N)
 Space Complexity : O(1)
 """
-from typing import List
+from __future__ import annotations
 
 # This is the precision for this function which can be altered.
 # It is recommended for users to keep this number greater than or equal to 10.
@@ -16,7 +16,7 @@ precision = 10
 # This is the linear search that will occur after the search space has become smaller.
 
 
-def lin_search(left: int, right: int, array: List[int], target: int) -> int:
+def lin_search(left: int, right: int, array: list[int], target: int) -> int:
     """Perform linear search in list. Returns -1 if element is not found.
 
     Parameters
@@ -58,7 +58,7 @@ def lin_search(left: int, right: int, array: List[int], target: int) -> int:
     return -1
 
 
-def ite_ternary_search(array: List[int], target: int) -> int:
+def ite_ternary_search(array: list[int], target: int) -> int:
     """Iterative method of the ternary search algorithm.
     >>> test_list = [0, 1, 2, 8, 13, 17, 19, 32, 42]
     >>> ite_ternary_search(test_list, 3)
@@ -110,7 +110,7 @@ def ite_ternary_search(array: List[int], target: int) -> int:
         return -1
 
 
-def rec_ternary_search(left: int, right: int, array: List[int], target: int) -> int:
+def rec_ternary_search(left: int, right: int, array: list[int], target: int) -> int:
     """Recursive method of the ternary search algorithm.
 
     >>> test_list = [0, 1, 2, 8, 13, 17, 19, 32, 42]