





def 							_lowerCAmelCase (  _a   :					int					,   _a   :					int					,   _a   :					list[list[int]]			)	->			int:

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

          lowerCAmelCase_					:       Optional[int]    =		update_area_of_max_square(_a					,   col + 1			)
          lowerCAmelCase_					:       List[Any]    =		update_area_of_max_square(row + 1					,   col + 1			)
          lowerCAmelCase_					:       Any    =		update_area_of_max_square(row + 1					,   _a			)

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

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






def 							_lowerCAmelCase (  _a   :					int					,   _a   :					int					,   _a   :					list[list[int]]			)	->			int:

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

          lowerCAmelCase_					:       Optional[Any]    =		update_area_of_max_square_using_dp_array(_a					,   col + 1					,   _a			)
          lowerCAmelCase_					:       Optional[Any]    =		update_area_of_max_square_using_dp_array(row + 1					,   col + 1					,   _a			)
          lowerCAmelCase_					:       int    =		update_area_of_max_square_using_dp_array(row + 1					,   _a					,   _a			)

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

     lowerCAmelCase_					:       Tuple    =		[0]
     lowerCAmelCase_					:       str    =		[[-1] * cols for _ in range(_a			)]
     update_area_of_max_square_using_dp_array(0					,   0					,   _a			)

     return largest_square_area[0]






def 							_lowerCAmelCase (  _a   :					int					,   _a   :					int					,   _a   :					list[list[int]]			)	->			int:
     lowerCAmelCase_					:       Any    =		[[0] * (cols + 1) for _ in range(rows + 1			)]
     lowerCAmelCase_					:       int    =		0
     for row in range(rows - 1					,   -1					,   -1			):
          for col in range(cols - 1					,   -1					,   -1			):
               lowerCAmelCase_					:       Optional[int]    =		dp_array[row][col + 1]
               lowerCAmelCase_					:       int    =		dp_array[row + 1][col + 1]
               lowerCAmelCase_					:       List[str]    =		dp_array[row + 1][col]

               if mat[row][col] == 1:
                    lowerCAmelCase_					:       int    =		1 + min(_a					,   _a					,   _a			)
                    lowerCAmelCase_					:       Tuple    =		max(dp_array[row][col]					,   _a			)
               else:
                    lowerCAmelCase_					:       Union[str, Any]    =		0

     return largest_square_area






def 							_lowerCAmelCase (  _a   :					int					,   _a   :					int					,   _a   :					list[list[int]]			)	->			int:
     lowerCAmelCase_					:       Dict    =		[0] * (cols + 1)
     lowerCAmelCase_					:       int    =		[0] * (cols + 1)
     lowerCAmelCase_					:       Optional[int]    =		0
     for row in range(rows - 1					,   -1					,   -1			):
          for col in range(cols - 1					,   -1					,   -1			):
               lowerCAmelCase_					:       List[str]    =		current_row[col + 1]
               lowerCAmelCase_					:       Any    =		next_row[col + 1]
               lowerCAmelCase_					:       Dict    =		next_row[col]

               if mat[row][col] == 1:
                    lowerCAmelCase_					:       str    =		1 + min(_a					,   _a					,   _a			)
                    lowerCAmelCase_					:       Optional[Any]    =		max(current_row[col]					,   _a			)
               else:
                    lowerCAmelCase_					:       Optional[int]    =		0
          lowerCAmelCase_					:       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 dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin





@dataclass
class      lowercase__    (							__A  ):
  __UpperCamelCase	     =  42
  __UpperCamelCase	     =  42
  __UpperCamelCase	     =  None





class      lowercase__    (							__A     ,					__A  ):
  __UpperCamelCase	     =  2







  @register_to_config
  def __init__(	self    ,						_lowercase = 0.02    ,						_lowercase = 100    ,						_lowercase = 1.007    ,						_lowercase = 80    ,						_lowercase = 0.05    ,						_lowercase = 50    ,						):
       # standard deviation of the initial noise distribution
       lowerCAmelCase_					:       int    =		sigma_max

       # setable values
       lowerCAmelCase_					:       int    =		None
       lowerCAmelCase_					:       np.IntTensor    =		None
       lowerCAmelCase_					:       torch.FloatTensor    =		None  # sigma(t_i)







  def 	UpperCAmelCase__		(	self    ,						_lowercase    ,						_lowercase = None						):
       return sample







  def 	UpperCAmelCase__		(	self    ,						_lowercase    ,						_lowercase = None						):
       lowerCAmelCase_					:       int    =		num_inference_steps
       lowerCAmelCase_					:       int    =		np.arange(0    ,						self.num_inference_steps						)[::-1].copy()
       lowerCAmelCase_					:       List[Any]    =		torch.from_numpy(_lowercase						).to(_lowercase						)
       lowerCAmelCase_					:       List[str]    =		[
           (
               self.config.sigma_max**2
               * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
           )
           for i in self.timesteps
       ]
       lowerCAmelCase_					:       Optional[int]    =		torch.tensor(_lowercase    ,						dtype=torch.floataa    ,						device=_lowercase						)







  def 	UpperCAmelCase__		(	self    ,						_lowercase    ,						_lowercase    ,						_lowercase = None						):
       if self.config.s_min <= sigma <= self.config.s_max:
            lowerCAmelCase_					:       List[Any]    =		min(self.config.s_churn / self.num_inference_steps    ,						2**0.5 - 1						)
       else:
            lowerCAmelCase_					:       List[str]    =		0

       # sample eps ~ N(0, S_noise^2 * I)
       lowerCAmelCase_					:       List[Any]    =		self.config.s_noise * randn_tensor(sample.shape    ,						generator=_lowercase						).to(sample.device						)
       lowerCAmelCase_					:       Optional[int]    =		sigma + gamma * sigma
       lowerCAmelCase_					:       int    =		sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

       return sample_hat, sigma_hat







  def 	UpperCAmelCase__		(	self    ,						_lowercase    ,						_lowercase    ,						_lowercase    ,						_lowercase    ,						_lowercase = True    ,						):
       lowerCAmelCase_					:       Union[str, Any]    =		sample_hat + sigma_hat * model_output
       lowerCAmelCase_					:       Dict    =		(sample_hat - pred_original_sample) / sigma_hat
       lowerCAmelCase_					:       List[Any]    =		sample_hat + (sigma_prev - sigma_hat) * derivative

       if not return_dict:
            return (sample_prev, derivative)

       return KarrasVeOutput(
           prev_sample=_lowercase    ,						derivative=_lowercase    ,						pred_original_sample=_lowercase						)







  def 	UpperCAmelCase__		(	self    ,						_lowercase    ,						_lowercase    ,						_lowercase    ,						_lowercase    ,						_lowercase    ,						_lowercase    ,						_lowercase = True    ,						):
       lowerCAmelCase_					:       str    =		sample_prev + sigma_prev * model_output
       lowerCAmelCase_					:       List[Any]    =		(sample_prev - pred_original_sample) / sigma_prev
       lowerCAmelCase_					:       Tuple    =		sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

       if not return_dict:
            return (sample_prev, derivative)

       return KarrasVeOutput(
           prev_sample=_lowercase    ,						derivative=_lowercase    ,						pred_original_sample=_lowercase						)







  def 	UpperCAmelCase__		(	self    ,						_lowercase    ,						_lowercase    ,						_lowercase						):
       raise NotImplementedError()
