Replace typing.optional with new annotations syntax (TheAlgorithms#5829)

* Replace typing.optional with new annotations syntax

* updating DIRECTORY.md

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

DIRECTORY.md

@@ -525,6 +525,7 @@
   * [Perfect Cube](https://github.com/TheAlgorithms/Python/blob/master/maths/perfect_cube.py)
   * [Perfect Number](https://github.com/TheAlgorithms/Python/blob/master/maths/perfect_number.py)
   * [Perfect Square](https://github.com/TheAlgorithms/Python/blob/master/maths/perfect_square.py)
+  * [Persistence](https://github.com/TheAlgorithms/Python/blob/master/maths/persistence.py)
   * [Pi Monte Carlo Estimation](https://github.com/TheAlgorithms/Python/blob/master/maths/pi_monte_carlo_estimation.py)
   * [Pollard Rho](https://github.com/TheAlgorithms/Python/blob/master/maths/pollard_rho.py)
   * [Polynomial Evaluation](https://github.com/TheAlgorithms/Python/blob/master/maths/polynomial_evaluation.py)

data_structures/linked_list/__init__.py

@@ -5,8 +5,9 @@
                  head node gives us access of the complete list
     - Last node: points to null
 """
+from __future__ import annotations
 
-from typing import Any, Optional
+from typing import Any
 
 
 class Node:
@@ -17,7 +18,7 @@ def __init__(self, item: Any, next: Any) -> None:
 
 class LinkedList:
     def __init__(self) -> None:
-        self.head: Optional[Node] = None
+        self.head: Node | None = None
         self.size = 0
 
     def add(self, item: Any) -> None:

data_structures/linked_list/circular_linked_list.py

@@ -1,10 +1,12 @@
-from typing import Any, Iterator, Optional
+from __future__ import annotations
+
+from typing import Any, Iterator
 
 
 class Node:
     def __init__(self, data: Any):
         self.data: Any = data
-        self.next: Optional[Node] = None
+        self.next: Node | None = None
 
 
 class CircularLinkedList:

data_structures/linked_list/has_loop.py

@@ -1,4 +1,6 @@
-from typing import Any, Optional
+from __future__ import annotations
+
+from typing import Any
 
 
 class ContainsLoopError(Exception):
@@ -8,7 +10,7 @@ class ContainsLoopError(Exception):
 class Node:
     def __init__(self, data: Any) -> None:
         self.data: Any = data
-        self.next_node: Optional[Node] = None
+        self.next_node: Node | None = None
 
     def __iter__(self):
         node = self

data_structures/linked_list/middle_element_of_linked_list.py

@@ -1,4 +1,4 @@
-from typing import Optional
+from __future__ import annotations
 
 
 class Node:
@@ -17,7 +17,7 @@ def push(self, new_data: int) -> int:
         self.head = new_node
         return self.head.data
 
-    def middle_element(self) -> Optional[int]:
+    def middle_element(self) -> int | None:
         """
         >>> link = LinkedList()
         >>> link.middle_element()

maths/pollard_rho.py

@@ -1,13 +1,14 @@
+from __future__ import annotations
+
 from math import gcd
-from typing import Union
 
 
 def pollard_rho(
     num: int,
     seed: int = 2,
     step: int = 1,
     attempts: int = 3,
-) -> Union[int, None]:
+) -> int | None:
     """
     Use Pollard's Rho algorithm to return a nontrivial factor of ``num``.
     The returned factor may be composite and require further factorization.