




'''simple docstring'''






import timeit

import numpy as np

import datasets
from datasets.arrow_writer import ArrowWriter
from datasets.features.features import _ArrayXD

def 			__lowerCAmelCase					(    snake_case__						):



			def wrapper(*snake_case__					,      **snake_case__						):
						__UpperCamelCase      :			List[Any]									=   timeit.default_timer()
						__UpperCamelCase      :			Optional[Any]									=   func(*A__					,      **A__						)
						__UpperCamelCase      :			List[Any]									=   timeit.default_timer() - starttime
						return delta

			__UpperCamelCase      :			Optional[int]									=   func.__name__

			return wrapper

def 			__lowerCAmelCase					(    snake_case__					,      snake_case__=100					,      snake_case__=None						):
			__UpperCamelCase      :			str									=   []
			__UpperCamelCase      :			Dict									=   seq_shapes or {}
			for i in range(A__						):
						__UpperCamelCase      :			int									=   {}
						for col_id, (k, v) in enumerate(features.items()						):
									if isinstance(A__					,      _ArrayXD						):
												__UpperCamelCase      :			Dict									=   np.random.rand(*v.shape						).astype(v.dtype						)
									elif isinstance(A__					,      datasets.Value						):
												if v.dtype == "string":
															__UpperCamelCase      :			Optional[Any]									=   "The small grey turtle was surprisingly fast when challenged."
												else:
															__UpperCamelCase      :			List[Any]									=   np.random.randint(10					,      size=1						).astype(v.dtype						).item()
									elif isinstance(A__					,      datasets.Sequence						):
												while isinstance(A__					,      datasets.Sequence						):
															__UpperCamelCase      :			int									=   v.feature
												__UpperCamelCase      :			Union[str, Any]									=   seq_shapes[k]
												__UpperCamelCase      :			Dict									=   np.random.rand(*A__						).astype(v.dtype						)
									__UpperCamelCase      :			Any									=   data

						dummy_data.append((i, example)						)

			return dummy_data




def 			__lowerCAmelCase					(    snake_case__					,      snake_case__					,      snake_case__=100					,      snake_case__=None						):
			__UpperCamelCase      :			Dict									=   generate_examples(A__					,      num_examples=A__					,      seq_shapes=A__						)

			with ArrowWriter(features=A__					,      path=A__						) as writer:
						for key, record in dummy_data:
									__UpperCamelCase      :			Union[str, Any]									=   features.encode_example(A__						)
									writer.write(A__						)

						__UpperCamelCase		,					__UpperCamelCase      :			Optional[Any]									=   writer.finalize()

			if not num_final_examples == num_examples:
						raise ValueError(
						    F"Error writing the dataset, wrote {num_final_examples} examples but should have written {num_examples}."						)

			__UpperCamelCase      :			int									=   datasets.Dataset.from_file(filename=A__					,      info=datasets.DatasetInfo(features=A__						)						)

			return dataset









from __future__ import annotations




def 					lowerCamelCase__       (						A__       :					list[int]  ,			A__       :					list[int]  ,			A__       :					list[int]  ,			A__       :					list[list[str]]  ,			A__       :					int  ,			):





       '''simple docstring'''



       __lowerCamelCase   =						len(A__	)

       # If row is equal to the size of the board it means there are a queen in each row in
       # the current board (possible_board)
       if row == n:
              # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
              # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
              boards.append([""". """ * i + """Q """ + """. """ * (n - 1 - i) for i in possible_board]	)
              return

       # We iterate each column in the row to find all possible results in each row
       for col in range(A__	):
              # We apply that we learned previously. First we check that in the current board
              # (possible_board) there are not other same value because if there is it means
              # that there are a collision in vertical. Then we apply the two formulas we
              # learned before:
              #
              # 45º: y - x = b or 45: row - col = b
              # 135º: y + x = b or row + col = b.
              #
              # And we verify if the results of this two formulas not exist in their variables
              # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
              #
              # If any or these are True it means there is a collision so we continue to the
              # next value in the for loop.
              if (
                  col in possible_board
                  or row - col in diagonal_right_collisions
                  or row + col in diagonal_left_collisions
              ):
                     continue

              # If it is False we call dfs function again and we update the inputs
              depth_first_search(
                  [*possible_board, col]  ,			[*diagonal_right_collisions, row - col]  ,			[*diagonal_left_collisions, row + col]  ,			A__  ,			A__  ,			)




def 					lowerCamelCase__       (						A__       :					int	):





       '''simple docstring'''



       __lowerCamelCase   =						[]
       depth_first_search([]  ,			[]  ,			[]  ,			A__  ,			A__	)

       # Print all the boards
       for board in boards:
              for column in board:
                     print(A__	)
              print(""""""	)

       print(len(A__	)  ,			"""solutions were found."""	)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       n_queens_solution(4)

