





"""simple docstring"""






from typing import Any

def       __A (     a_  :list				,    a_  :list				,    a_  :dict				,    a_  :dict				,    a_  :dict				,    )						->						list:
				_validation(
				    a_				,    a_				,    a_				,    a_				,    a_				,    )
				# Creates data structures and fill initial step
				__a	:  dict         =					{}
				__a	:  dict         =					{}
				for state in states_space:
								__a	:  int         =					observations_space[0]
								__a	:  List[Any]         =					(
								    initial_probabilities[state] * emission_probabilities[state][observation]
								)
								__a	:  int         =					None

				# Fills the data structure with the probabilities of
				# different transitions and pointers to previous states
				for o in range(1				,    len(a_)):
								__a	:  Dict         =					observations_space[o]
								__a	:  Union[str, Any]         =					observations_space[o - 1]
								for state in states_space:
												# Calculates the argmax for probability function
												__a	:  Union[str, Any]         =					''''''
												__a	:  Optional[Any]         =					-1
												for k_state in states_space:
																__a	:  List[str]         =					(
																    probabilities[(k_state, prior_observation)]
																    * transition_probabilities[k_state][state]
																    * emission_probabilities[state][observation]
																)
																if probability > max_probability:
																				__a	:  List[Any]         =					probability
																				__a	:  Any         =					k_state

            # Update probabilities and pointers dicts
												__a	:  Any         =					(
												    probabilities[(arg_max, prior_observation)]
												    * transition_probabilities[arg_max][state]
												    * emission_probabilities[state][observation]
												)

												__a	:  Optional[int]         =					arg_max

    # The final observation
				__a	:  Optional[int]         =					observations_space[len(a_) - 1]

				# argmax for given final observation
				__a	:  str         =					''''''
				__a	:  List[Any]         =					-1
				for k_state in states_space:
								__a	:  List[str]         =					probabilities[(k_state, final_observation)]
								if probability > max_probability:
												__a	:  Union[str, Any]         =					probability
												__a	:  Any         =					k_state
				__a	:  Dict         =					arg_max

				# Process pointers backwards
				__a	:  Tuple         =					last_state
				__a	:  Tuple         =					[]
				for o in range(len(a_) - 1				,    -1				,    -1):
								result.append(a_)
								__a	:  List[str]         =					pointers[previous, observations_space[o]]
				result.reverse()

				return result

def       __A (     a_  :Any				,    a_  :Any				,    a_  :Any				,    a_  :Any				,    a_  :Any				,    )						->						None:
				_validate_not_empty(
				    a_				,    a_				,    a_				,    a_				,    a_				,    )
				_validate_lists(a_				,    a_)
				_validate_dicts(
				    a_				,    a_				,    a_)

def       __A (     a_  :Any				,    a_  :Any				,    a_  :Any				,    a_  :Any				,    a_  :Any				,    )						->						None:
				if not all(
				    [
				        observations_space,
				        states_space,
				        initial_probabilities,
				        transition_probabilities,
				        emission_probabilities,
				    ]):
								raise ValueError('''There\'s an empty parameter''')

def       __A (     a_  :Any				,    a_  :Any)						->						None:
				_validate_list(a_				,    '''observations_space''')
				_validate_list(a_				,    '''states_space''')

def       __A (     a_  :Any				,    a_  :str)						->						None:
				if not isinstance(_object				,    a_):
								__a	:  Optional[int]         =					F"""{var_name} must be a list"""
								raise ValueError(a_)
				else:
								for x in _object:
												if not isinstance(a_				,    a_):
																__a	:  Any         =					F"""{var_name} must be a list of strings"""
																raise ValueError(a_)

def       __A (     a_  :Any				,    a_  :Any				,    a_  :Any				,    )						->						None:
				_validate_dict(a_				,    '''initial_probabilities'''				,    a_)
				_validate_nested_dict(a_				,    '''transition_probabilities''')
				_validate_nested_dict(a_				,    '''emission_probabilities''')

def       __A (     a_  :Any				,    a_  :str)						->						None:
				_validate_dict(_object				,    a_				,    a_)
				for x in _object.values():
								_validate_dict(a_				,    a_				,    a_				,    a_)

def       __A (     a_  :Any				,    a_  :str				,    a_  :type				,    a_  :bool = False)						->						None:
				if not isinstance(_object				,    a_):
								__a	:  int         =					F"""{var_name} must be a dict"""
								raise ValueError(a_)
				if not all(isinstance(a_				,    a_) for x in _object):
								__a	:  Any         =					F"""{var_name} all keys must be strings"""
								raise ValueError(a_)
				if not all(isinstance(a_				,    a_) for x in _object.values()):
								__a	:  Dict         =					'''nested dictionary ''' if nested else ''''''
								__a	:  Optional[Any]         =					F"""{var_name} {nested_text}all values must be {value_type.__name__}"""
								raise ValueError(a_)


if __name__ == "__main__":
		from doctest import testmod

		testmod()






"""simple docstring"""






from pathlib import Path

import numpy as np
from PIL import Image

def       __A (     a_  :np.ndarray)						->						np.ndarray:
				__a    ,  __a    ,  __a	:  Union[str, Any]         =					rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
				return 0.2_9_8_9 * r + 0.5_8_7_0 * g + 0.1_1_4_0 * b

def       __A (     a_  :np.ndarray)						->						np.ndarray:
				return (gray > 1_27) & (gray <= 2_55)

def       __A (     a_  :np.ndarray				,    a_  :np.ndarray)						->						np.ndarray:
				__a	:  Optional[int]         =					np.zeros_like(a_)
				__a	:  Dict         =					np.zeros(
				    (image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1))

				# Copy image to padded image
				__a	:  int         =					image

				# Iterate over image & apply kernel
				for x in range(image.shape[1]):
								for y in range(image.shape[0]):
												__a	:  Optional[Any]         =					(
												    kernel * image_padded[y : y + kernel.shape[0], x : x + kernel.shape[1]]
												).sum()
												__a	:  Any         =					int(summation > 0)
				return output


if __name__ == "__main__":
		# read original image
		A	     =					Path(__file__).resolve().parent / '''image_data''' / '''lena.jpg'''
		A	     =					np.array(Image.open(lena_path))
		# kernel to be applied
		A	     =					np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])
		A	     =					dilation(gray_to_binary(rgb_to_gray(lena)), structuring_element)
		# Save the output image
		A	     =					Image.fromarray(output).convert('''RGB''')
		pil_img.save('''result_dilation.png''')