




"""simple docstring"""




class    UpperCAmelCase_  :
		def __init__(		self    )		->    Dict:
					__lowercase       :   dict[str, TrieNode]        =    {}  # Mapping from char to TrieNode
					__lowercase       :   List[Any]        =    False
		def      _lowerCamelCase				(		self							,		UpperCamelCase_    )		->    Tuple:







					for word in words:
								self.insert(UpperCamelCase_    )
		def      _lowerCamelCase				(		self							,		UpperCamelCase_    )		->    Union[str, Any]:
					__lowercase       :   int        =    self
					for char in word:
								if char not in curr.nodes:
											__lowercase       :   int        =    TrieNode()
								__lowercase       :   Tuple        =    curr.nodes[char]
					__lowercase       :   Tuple        =    True
		def      _lowerCamelCase				(		self							,		UpperCamelCase_    )		->    List[Any]:
					__lowercase       :   Dict        =    self
					for char in word:
								if char not in curr.nodes:
											return False
								__lowercase       :   Optional[Any]        =    curr.nodes[char]
					return curr.is_leaf
		def      _lowerCamelCase				(		self							,		UpperCamelCase_    )		->    str:







					def _delete(UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_    ) -> bool:
								if index == len(UpperCamelCase_    ):
											# If word does not exist
											if not curr.is_leaf:
														return False
											__lowercase       :   Optional[Any]        =    False
											return len(curr.nodes    ) == 0
								__lowercase       :   Optional[Any]        =    word[index]
								__lowercase       :   Union[str, Any]        =    curr.nodes.get(UpperCamelCase_    )
								# If char not in current trie node
								if not char_node:
											return False
								# Flag to check if node can be deleted
								__lowercase       :   Any        =    _delete(UpperCamelCase_							,		UpperCamelCase_							,		index + 1    )
								if delete_curr:
											del curr.nodes[char]
											return len(curr.nodes    ) == 0
								return delete_curr

					_delete(self							,		UpperCamelCase_							,		0    )







def 			__UpperCAmelCase			(      __UpperCamelCase     ,							__UpperCamelCase     ):
			if node.is_leaf:
						print(SCREAMING_SNAKE_CASE_     ,							end=''' '''     )

			for key, value in node.nodes.items():
						print_words(SCREAMING_SNAKE_CASE_     ,							word + key     )







def 			__UpperCAmelCase			(      ):
			__lowercase       :   Optional[int]        =    'banana bananas bandana band apple all beast'.split()
			__lowercase       :   Optional[Any]        =    TrieNode()
			root.insert_many(SCREAMING_SNAKE_CASE_     )
			# print_words(root, "")
			assert all(root.find(SCREAMING_SNAKE_CASE_     ) for word in words     )
			assert root.find('''banana'''     )
			assert not root.find('''bandanas'''     )
			assert not root.find('''apps'''     )
			assert root.find('''apple'''     )
			assert root.find('''all'''     )
			root.delete('''all'''     )
			assert not root.find('''all'''     )
			root.delete('''banana'''     )
			assert not root.find('''banana'''     )
			assert root.find('''bananas'''     )
			return True







def 			__UpperCAmelCase			(      __UpperCamelCase     ,							__UpperCamelCase     ):
			print(str(SCREAMING_SNAKE_CASE_     )     ,							'''works!''' if passes else '''doesn\'t work :('''     )







def 			__UpperCAmelCase			(      ):
			assert test_trie()







def 			__UpperCAmelCase			(      ):
			print_results('''Testing trie functionality'''     ,							test_trie()     )


if __name__ == "__main__":
			main()





from __future__ import annotations

lowerCamelCase__          =		list[list[int]]

# assigning initial values to the grid
lowerCamelCase__          =		[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
lowerCamelCase__          =		[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		bool:
			for i in range(9     ):
						if grid[row][i] == n or grid[i][column] == n:
									return False

			for i in range(3     ):
						for j in range(3     ):
									if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
												return False

			return True
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		tuple[int, int] | None:
			for i in range(9     ):
						for j in range(9     ):
									if grid[i][j] == 0:
												return i, j
			return None
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		Matrix | None:
			if location := find_empty_location(SCREAMING_SNAKE_CASE_     ):
						lowerCAmelCase__      ,				lowerCAmelCase__      :      Any         =		location
			else:
						# If the location is ``None``, then the grid is solved.
						return grid

			for digit in range(1       ,							10     ):
						if is_safe(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     ):
									lowerCAmelCase__      :      Optional[Any]         =		digit

									if sudoku(SCREAMING_SNAKE_CASE_     ) is not None:
												return grid

									lowerCAmelCase__      :      List[Any]         =		0

			return None
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		None:
			for row in grid:
						for cell in row:
									print(SCREAMING_SNAKE_CASE_       ,							end=' '     )
						print()


if __name__ == "__main__":
					# make a copy of grid so that you can compare with the unmodified grid
					for example_grid in (initial_grid, no_solution):
										print("""\nExample grid:\n""" + """=""" * 20)
										print_solution(example_grid)
										print("""\nExample grid solution:""")
										lowerCamelCase__          =		sudoku(example_grid)
										if solution is not None:
															print_solution(solution)
										else:
															print("""Cannot find a solution.""")