




"""simple docstring"""




def     a__ (				snake_case__				)						->					str:
			if number > 0:
						raise ValueError("""input must be a negative integer"""				)
			lowerCamelCase			      =					len(bin(snake_case__				)[3:]				)
			lowerCamelCase			      =					bin(abs(snake_case__				) - (1 << binary_number_length)				)[3:]
			lowerCamelCase			      =					(
			    (
			        """1"""
			        + """0""" * (binary_number_length - len(snake_case__				))
			        + twos_complement_number
			    )
			    if number < 0
			    else """0"""
			)
			return "0b" + twos_complement_number


if __name__ == "__main__":
					import doctest

					doctest.testmod()









"""simple docstring"""




from typing import Any



def     a__ (				snake_case__       , snake_case__       , snake_case__       , snake_case__       , snake_case__       , )						->					list:
			_validation(
			    snake_case__       , snake_case__       , snake_case__       , snake_case__       , snake_case__       , )
			# Creates data structures and fill initial step
			lowerCamelCase			      =					{}
			lowerCamelCase			      =					{}
			for state in states_space:
						lowerCamelCase			      =					observations_space[0]
						lowerCamelCase			      =					(
						    initial_probabilities[state] * emission_probabilities[state][observation]
						)
						lowerCamelCase			      =					None

			# Fills the data structure with the probabilities of
			# different transitions and pointers to previous states
			for o in range(1       , len(snake_case__				)				):
						lowerCamelCase			      =					observations_space[o]
						lowerCamelCase			      =					observations_space[o - 1]
						for state in states_space:
									# Calculates the argmax for probability function
									lowerCamelCase			      =					""""""
									lowerCamelCase			      =					-1
									for k_state in states_space:
												lowerCamelCase			      =					(
												    probabilities[(k_state, prior_observation)]
												    * transition_probabilities[k_state][state]
												    * emission_probabilities[state][observation]
												)
												if probability > max_probability:
															lowerCamelCase			      =					probability
															lowerCamelCase			      =					k_state

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

									lowerCamelCase			      =					arg_max

    # The final observation
			lowerCamelCase			      =					observations_space[len(snake_case__				) - 1]

			# argmax for given final observation
			lowerCamelCase			      =					""""""
			lowerCamelCase			      =					-1
			for k_state in states_space:
						lowerCamelCase			      =					probabilities[(k_state, final_observation)]
						if probability > max_probability:
									lowerCamelCase			      =					probability
									lowerCamelCase			      =					k_state
			lowerCamelCase			      =					arg_max

			# Process pointers backwards
			lowerCamelCase			      =					last_state
			lowerCamelCase			      =					[]
			for o in range(len(snake_case__				) - 1       , -1       , -1				):
						result.append(snake_case__				)
						lowerCamelCase			      =					pointers[previous, observations_space[o]]
			result.reverse()

			return result



def     a__ (				snake_case__       , snake_case__       , snake_case__       , snake_case__       , snake_case__       , )						->					None:
			_validate_not_empty(
			    snake_case__       , snake_case__       , snake_case__       , snake_case__       , snake_case__       , )
			_validate_lists(snake_case__       , snake_case__				)
			_validate_dicts(
			    snake_case__       , snake_case__       , snake_case__				)



def     a__ (				snake_case__       , snake_case__       , snake_case__       , snake_case__       , snake_case__       , )						->					None:
			if not all(
			    [
			        observations_space,
			        states_space,
			        initial_probabilities,
			        transition_probabilities,
			        emission_probabilities,
			    ]				):
						raise ValueError("""There's an empty parameter"""				)



def     a__ (				snake_case__       , snake_case__				)						->					None:
			_validate_list(snake_case__       , """observations_space"""				)
			_validate_list(snake_case__       , """states_space"""				)



def     a__ (				snake_case__       , snake_case__				)						->					None:
			if not isinstance(_object       , snake_case__				):
						lowerCamelCase			      =					F'{var_name} must be a list'
						raise ValueError(snake_case__				)
			else:
						for x in _object:
									if not isinstance(snake_case__       , snake_case__				):
												lowerCamelCase			      =					F'{var_name} must be a list of strings'
												raise ValueError(snake_case__				)



def     a__ (				snake_case__       , snake_case__       , snake_case__       , )						->					None:
			_validate_dict(snake_case__       , """initial_probabilities"""       , snake_case__				)
			_validate_nested_dict(snake_case__       , """transition_probabilities"""				)
			_validate_nested_dict(snake_case__       , """emission_probabilities"""				)



def     a__ (				snake_case__       , snake_case__				)						->					None:
			_validate_dict(_object       , snake_case__       , snake_case__				)
			for x in _object.values():
						_validate_dict(snake_case__       , snake_case__       , snake_case__       , snake_case__				)



def     a__ (				snake_case__       , snake_case__       , snake_case__       , snake_case__ = False				)						->					None:
			if not isinstance(_object       , snake_case__				):
						lowerCamelCase			      =					F'{var_name} must be a dict'
						raise ValueError(snake_case__				)
			if not all(isinstance(snake_case__       , snake_case__				) for x in _object				):
						lowerCamelCase			      =					F'{var_name} all keys must be strings'
						raise ValueError(snake_case__				)
			if not all(isinstance(snake_case__       , snake_case__				) for x in _object.values()				):
						lowerCamelCase			      =					"""nested dictionary """ if nested else """"""
						lowerCamelCase			      =					F'{var_name} {nested_text}all values must be {value_type.__name__}'
						raise ValueError(snake_case__				)


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

					testmod()



