


'''simple docstring'''
class        lowercase     :

		"""simple docstring"""

		def __init__(		self							):

							'''simple docstring'''


							UpperCamelCase__       :dict[str, TrieNode]							 =			{}  # Mapping from char to TrieNode
							UpperCamelCase__       :int							 =			False




		def    lowerCAmelCase__    (		self   ,       UpperCamelCase_							):

							'''simple docstring'''


							for word in words:
												self.insert(UpperCamelCase_							)




		def    lowerCAmelCase__    (		self   ,       UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__       :str							 =			self
							for char in word:
												if char not in curr.nodes:
																	UpperCamelCase__       :Union[str, Any]							 =			TrieNode()
												UpperCamelCase__       :Any							 =			curr.nodes[char]
							UpperCamelCase__       :Any							 =			True




		def    lowerCAmelCase__    (		self   ,       UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__       :Dict							 =			self
							for char in word:
												if char not in curr.nodes:
																	return False
												UpperCamelCase__       :List[Any]							 =			curr.nodes[char]
							return curr.is_leaf




		def    lowerCAmelCase__    (		self   ,       UpperCamelCase_							):

							'''simple docstring'''


							def _delete(UpperCamelCase_   ,       UpperCamelCase_   ,       UpperCamelCase_							) -> bool:
												if index == len(UpperCamelCase_							):
																	# If word does not exist
																	if not curr.is_leaf:
																						return False
																	UpperCamelCase__       :Tuple							 =			False
																	return len(curr.nodes							) == 0
												UpperCamelCase__       :int							 =			word[index]
												UpperCamelCase__       :int							 =			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
												UpperCamelCase__       :List[str]							 =			_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       a				(      __a			, __a       )  ->     None:



					'''simple docstring'''






					if node.is_leaf:
										print(__a			, end=''' '''       )

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


def       a				(      )  ->     bool:



					'''simple docstring'''






					UpperCamelCase__       :List[Any]							 =			'''banana bananas bandana band apple all beast'''.split()
					UpperCamelCase__       :str							 =			TrieNode()
					root.insert_many(__a       )
					# print_words(root, "")
					assert all(root.find(__a       ) 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       a				(      __a			, __a       )  ->     None:



					'''simple docstring'''






					print(str(__a       )			, '''works!''' if passes else '''doesn\'t work :('''       )


def       a				(      )  ->     None:



					'''simple docstring'''






					assert test_trie()


def       a				(      )  ->     None:



					'''simple docstring'''






					print_results('''Testing trie functionality'''			, test_trie()       )


if __name__ == "__main__":
		main()



'''simple docstring'''
from __future__ import annotations

__snake_case											=					list[list[int]]

# assigning initial values to the grid
__snake_case											=					[
    [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
__snake_case											=					[
    [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       a				(      __a			, __a			, __a			, __a       )  ->     bool:



					'''simple docstring'''






					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       a				(      __a       )  ->     tuple[int, int] | None:



					'''simple docstring'''






					for i in range(9       ):
										for j in range(9       ):
															if grid[i][j] == 0:
																				return i, j
					return None


def       a				(      __a       )  ->     Matrix | None:



					'''simple docstring'''






					if location := find_empty_location(__a       ):
										UpperCamelCase__ ,    UpperCamelCase__       :Optional[int]							 =			location
					else:
										# If the location is ``None``, then the grid is solved.
										return grid

					for digit in range(1			, 10       ):
										if is_safe(__a			, __a			, __a			, __a       ):
															UpperCamelCase__       :Tuple							 =			digit

															if sudoku(__a       ) is not None:
																				return grid

															UpperCamelCase__       :Union[str, Any]							 =			0

					return None


def       a				(      __a       )  ->     None:



					'''simple docstring'''






					for row in grid:
										for cell in row:
															print(__a			, 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:''')
				__snake_case											=					sudoku(example_grid)
				if solution is not None:
						print_solution(solution)
				else:
						print('''Cannot find a solution.''')