Added sudoku type hints [Hacktober Fest] (#3124)

* chore(sudoku): added type hints [HACKTOBER-FEST]

* updating DIRECTORY.md

* chore: added matrix type alias

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

backtracking/sudoku.py

@@ -1,3 +1,7 @@
+from typing import List, Tuple, Union
+
+Matrix = List[List[int]]
+
 """
     Given a partially filled 9×9 2D array, the objective is to fill a 9×9
     square grid with digits numbered 1 to 9, so that every row, column, and
@@ -36,7 +40,7 @@ no_solution = [
 ]
 
 
-def is_safe(grid, row, column, n):
+def is_safe(grid: Matrix, row: int, column: int, n: int) -> bool:
     """
     This function checks the grid to see if each row,
     column, and the 3x3 subgrids contain the digit 'n'.
@@ -55,7 +59,7 @@ def is_safe(grid, row, column, n):
     return True
 
 
-def is_completed(grid):
+def is_completed(grid: Matrix) -> bool:
     """
     This function checks if the puzzle is completed or not.
     it is completed when all the cells are assigned with a non-zero number.
@@ -76,7 +80,7 @@ def is_completed(grid):
     return all(all(cell != 0 for cell in row) for row in grid)
 
 
-def find_empty_location(grid):
+def find_empty_location(grid: Matrix) -> Tuple[int, int]:
     """
     This function finds an empty location so that we can assign a number
     for that particular row and column.
@@ -87,7 +91,7 @@ def find_empty_location(grid):
                 return i, j
 
 
-def sudoku(grid):
+def sudoku(grid: Matrix) -> Union[Matrix, bool]:
     """
     Takes a partially filled-in grid and attempts to assign values to
     all unassigned locations in such a way to meet the requirements
@@ -124,7 +128,7 @@ def sudoku(grid):
     return False
 
 
-def print_solution(grid):
+def print_solution(grid: Matrix) -> None:
     """
     A function to print the solution in the form
     of a 9x9 grid