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>

backtracking/knight_tour.py

@@ -1,9 +1,9 @@
 # Knight Tour Intro: https://www.youtube.com/watch?v=ab_dY3dZFHM
 
-from typing import List, Tuple
+from __future__ import annotations
 
 
-def get_valid_pos(position: Tuple[int, int], n: int) -> List[Tuple[int, int]]:
+def get_valid_pos(position: tuple[int, int], n: int) -> list[tuple[int, int]]:
     """
     Find all the valid positions a knight can move to from the current position.
 
@@ -32,7 +32,7 @@ def get_valid_pos(position: Tuple[int, int], n: int) -> List[Tuple[int, int]]:
     return permissible_positions
 
 
-def is_complete(board: List[List[int]]) -> bool:
+def is_complete(board: list[list[int]]) -> bool:
     """
     Check if the board (matrix) has been completely filled with non-zero values.
 
@@ -47,7 +47,7 @@ def is_complete(board: List[List[int]]) -> bool:
 
 
 def open_knight_tour_helper(
-    board: List[List[int]], pos: Tuple[int, int], curr: int
+    board: list[list[int]], pos: tuple[int, int], curr: int
 ) -> bool:
     """
     Helper function to solve knight tour problem.
@@ -68,7 +68,7 @@ def open_knight_tour_helper(
     return False
 
 
-def open_knight_tour(n: int) -> List[List[int]]:
+def open_knight_tour(n: int) -> list[list[int]]:
     """
     Find the solution for the knight tour problem for a board of size n. Raises
     ValueError if the tour cannot be performed for the given size.