




def        __UpperCAmelCase						(							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     list[list[int]]  )       ->  int:







			"""simple docstring"""





			def update_area_of_max_square(lowerCamelCase_ :     int  ,							lowerCamelCase_ :     int  ) -> int:
						# BASE CASE
						if row >= rows or col >= cols:
									return 0

						SCREAMING_SNAKE_CASE_   : Optional[int]					  =      update_area_of_max_square(lowerCamelCase_  ,							col + 1  )
						SCREAMING_SNAKE_CASE_   : int					  =      update_area_of_max_square(row + 1  ,							col + 1  )
						SCREAMING_SNAKE_CASE_   : Optional[int]					  =      update_area_of_max_square(row + 1  ,							lowerCamelCase_  )

						if mat[row][col]:
									SCREAMING_SNAKE_CASE_   : Dict					  =      1 + min([right, diagonal, down]  )
									SCREAMING_SNAKE_CASE_   : int					  =      max(largest_square_area[0]  ,							lowerCamelCase_  )
									return sub_problem_sol
						else:
									return 0

			SCREAMING_SNAKE_CASE_   : int					  =      [0]
			update_area_of_max_square(0  ,							0  )
			return largest_square_area[0]





def        __UpperCAmelCase						(							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     list[list[int]]  )       ->  int:







			"""simple docstring"""





			def update_area_of_max_square_using_dp_array(
			    lowerCamelCase_ :     int  ,							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     list[list[int]]  ) -> int:
						if row >= rows or col >= cols:
									return 0
						if dp_array[row][col] != -1:
									return dp_array[row][col]

						SCREAMING_SNAKE_CASE_   : List[str]					  =      update_area_of_max_square_using_dp_array(lowerCamelCase_  ,							col + 1  ,							lowerCamelCase_  )
						SCREAMING_SNAKE_CASE_   : str					  =      update_area_of_max_square_using_dp_array(row + 1  ,							col + 1  ,							lowerCamelCase_  )
						SCREAMING_SNAKE_CASE_   : Any					  =      update_area_of_max_square_using_dp_array(row + 1  ,							lowerCamelCase_  ,							lowerCamelCase_  )

						if mat[row][col]:
									SCREAMING_SNAKE_CASE_   : List[Any]					  =      1 + min([right, diagonal, down]  )
									SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      max(largest_square_area[0]  ,							lowerCamelCase_  )
									SCREAMING_SNAKE_CASE_   : List[Any]					  =      sub_problem_sol
									return sub_problem_sol
						else:
									return 0

			SCREAMING_SNAKE_CASE_   : str					  =      [0]
			SCREAMING_SNAKE_CASE_   : str					  =      [[-1] * cols for _ in range(lowerCamelCase_  )]
			update_area_of_max_square_using_dp_array(0  ,							0  ,							lowerCamelCase_  )

			return largest_square_area[0]





def        __UpperCAmelCase						(							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     list[list[int]]  )       ->  int:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : int					  =      [[0] * (cols + 1) for _ in range(rows + 1  )]
			SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      0
			for row in range(rows - 1  ,							-1  ,							-1  ):
						for col in range(cols - 1  ,							-1  ,							-1  ):
									SCREAMING_SNAKE_CASE_   : Optional[int]					  =      dp_array[row][col + 1]
									SCREAMING_SNAKE_CASE_   : List[Any]					  =      dp_array[row + 1][col + 1]
									SCREAMING_SNAKE_CASE_   : int					  =      dp_array[row + 1][col]

									if mat[row][col] == 1:
												SCREAMING_SNAKE_CASE_   : Dict					  =      1 + min(lowerCamelCase_  ,							lowerCamelCase_  ,							lowerCamelCase_  )
												SCREAMING_SNAKE_CASE_   : int					  =      max(dp_array[row][col]  ,							lowerCamelCase_  )
									else:
												SCREAMING_SNAKE_CASE_   : List[str]					  =      0

			return largest_square_area





def        __UpperCAmelCase						(							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     int  ,							lowerCamelCase_ :     list[list[int]]  )       ->  int:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      [0] * (cols + 1)
			SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      [0] * (cols + 1)
			SCREAMING_SNAKE_CASE_   : int					  =      0
			for row in range(rows - 1  ,							-1  ,							-1  ):
						for col in range(cols - 1  ,							-1  ,							-1  ):
									SCREAMING_SNAKE_CASE_   : Optional[int]					  =      current_row[col + 1]
									SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      next_row[col + 1]
									SCREAMING_SNAKE_CASE_   : str					  =      next_row[col]

									if mat[row][col] == 1:
												SCREAMING_SNAKE_CASE_   : Dict					  =      1 + min(lowerCamelCase_  ,							lowerCamelCase_  ,							lowerCamelCase_  )
												SCREAMING_SNAKE_CASE_   : List[Any]					  =      max(current_row[col]  ,							lowerCamelCase_  )
									else:
												SCREAMING_SNAKE_CASE_   : Tuple					  =      0
						SCREAMING_SNAKE_CASE_   : Tuple					  =      current_row

			return largest_square_area


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))









from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm





def        __UpperCAmelCase						(							lowerCamelCase_ :     np.ndarray  ,							lowerCamelCase_ :     np.ndarray  )       ->  float:







			"""simple docstring"""





			return math.sqrt(sum(pow(a - b  ,							2  ) for a, b in zip(lowerCamelCase_  ,							lowerCamelCase_  )  )  )





def        __UpperCAmelCase						(							lowerCamelCase_ :     np.ndarray  ,							lowerCamelCase_ :     np.ndarray  )       ->  list[list[list[float] | float]]:







			"""simple docstring"""





			if dataset.ndim != value_array.ndim:
						SCREAMING_SNAKE_CASE_   : Optional[int]					  =      (
						    'Wrong input data\'s dimensions... '
						    F'dataset : {dataset.ndim}, value_array : {value_array.ndim}'
						)
						raise ValueError(lowerCamelCase_  )

			try:
						if dataset.shape[1] != value_array.shape[1]:
									SCREAMING_SNAKE_CASE_   : List[Any]					  =      (
									    'Wrong input data\'s shape... '
									    F'dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}'
									)
									raise ValueError(lowerCamelCase_  )
			except IndexError:
						if dataset.ndim != value_array.ndim:
									raise TypeError('Wrong shape'  )

			if dataset.dtype != value_array.dtype:
						SCREAMING_SNAKE_CASE_   : Tuple					  =      (
						    'Input data have different datatype... '
						    F'dataset : {dataset.dtype}, value_array : {value_array.dtype}'
						)
						raise TypeError(lowerCamelCase_  )

			SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      []

			for value in value_array:
						SCREAMING_SNAKE_CASE_   : str					  =      euclidean(lowerCamelCase_  ,							dataset[0]  )
						SCREAMING_SNAKE_CASE_   : List[Any]					  =      dataset[0].tolist()

						for dataset_value in dataset[1:]:
									SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      euclidean(lowerCamelCase_  ,							lowerCamelCase_  )

									if dist > temp_dist:
												SCREAMING_SNAKE_CASE_   : Optional[int]					  =      temp_dist
												SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      dataset_value.tolist()

						answer.append([vector, dist]  )

			return answer





def        __UpperCAmelCase						(							lowerCamelCase_ :     np.ndarray  ,							lowerCamelCase_ :     np.ndarray  )       ->  float:







			"""simple docstring"""





			return np.dot(lowerCamelCase_  ,							lowerCamelCase_  ) / (norm(lowerCamelCase_  ) * norm(lowerCamelCase_  ))


if __name__ == "__main__":
						import doctest

						doctest.testmod()



