






from abc import ABC, abstractmethod
from typing import List, Optional


class 					_snake_case						(			_A ):






	def __init__(		self       )						->    str:
					# test for the above condition
					self.test()






	def    lowerCAmelCase_							(		self       )						->    List[str]:
					snake_case__      :List[str]         =   0
					snake_case__      :str         =   False
					while not completed:
									if counter == 1:
													self.reset()
									snake_case__      :Optional[int]         =   self.advance()
									if not self.does_advance(UpperCamelCase       ):
													raise Exception(
													    "Custom Constraint is not defined correctly. self.does_advance(self.advance()) must be true."       )

									snake_case__    ,						snake_case__    ,						snake_case__      :Union[str, Any]         =   self.update(UpperCamelCase       )
									counter += 1

									if counter > 10_000:
													raise Exception("update() does not fulfill the constraint."       )

					if self.remaining() != 0:
									raise Exception("Custom Constraint is not defined correctly."       )






	@abstractmethod
	def    lowerCAmelCase_							(		self       )						->    Dict:
					raise NotImplementedError(
					    f'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'       )






	@abstractmethod
	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    Optional[int]:
					raise NotImplementedError(
					    f'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'       )






	@abstractmethod
	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    Union[str, Any]:
					raise NotImplementedError(
					    f'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'       )






	@abstractmethod
	def    lowerCAmelCase_							(		self       )						->    Tuple:
					raise NotImplementedError(
					    f'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'       )






	@abstractmethod
	def    lowerCAmelCase_							(		self       )						->    str:
					raise NotImplementedError(
					    f'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'       )






	@abstractmethod
	def    lowerCAmelCase_							(		self					,UpperCamelCase=False       )						->    Any:
					raise NotImplementedError(
					    f'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'       )




class 					_snake_case						(			_A ):






	def __init__(		self					,UpperCamelCase       )						->    str:
					super(UpperCamelCase					,self       ).__init__()

					if not isinstance(UpperCamelCase					,UpperCamelCase       ) or len(UpperCamelCase       ) == 0:
									raise ValueError(f'`token_ids` has to be a non-empty list, but is {token_ids}.'       )
					if any((not isinstance(UpperCamelCase					,UpperCamelCase       ) or token_id < 0) for token_id in token_ids       ):
									raise ValueError(f'Each list in `token_ids` has to be a list of positive integers, but is {token_ids}.'       )

					snake_case__      :List[Any]         =   token_ids

					snake_case__      :List[str]         =   len(self.token_ids       )
					snake_case__      :Optional[Any]         =   -1  # the index of the currently fulfilled step
					snake_case__      :Dict         =   False






	def    lowerCAmelCase_							(		self       )						->    List[str]:
					if self.completed:
									return None
					return self.token_ids[self.fulfilled_idx + 1]






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    Optional[int]:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									raise ValueError(f'`token_id` has to be an `int`, but is {token_id} of type {type(UpperCamelCase       )}'       )

					if self.completed:
									return False

					return token_id == self.token_ids[self.fulfilled_idx + 1]






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    List[str]:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									raise ValueError(f'`token_id` has to be an `int`, but is {token_id} of type {type(UpperCamelCase       )}'       )

					snake_case__      :Tuple         =   False
					snake_case__      :str         =   False
					snake_case__      :Tuple         =   False

					if self.does_advance(UpperCamelCase       ):
									self.fulfilled_idx += 1
									snake_case__      :int         =   True
									if self.fulfilled_idx == (self.seqlen - 1):
													snake_case__      :List[Any]         =   True
									snake_case__      :Tuple         =   completed
					else:
									# failed to make progress.
									snake_case__      :List[Any]         =   True
									self.reset()
					return stepped, completed, reset






	def    lowerCAmelCase_							(		self       )						->    Union[str, Any]:
					snake_case__      :Union[str, Any]         =   False
					snake_case__      :Union[str, Any]         =   0






	def    lowerCAmelCase_							(		self       )						->    List[Any]:
					return self.seqlen - (self.fulfilled_idx + 1)






	def    lowerCAmelCase_							(		self					,UpperCamelCase=False       )						->    Optional[Any]:
					snake_case__      :Tuple         =   PhrasalConstraint(self.token_ids       )

					if stateful:
									snake_case__      :str         =   self.seqlen
									snake_case__      :Optional[Any]         =   self.fulfilled_idx
									snake_case__      :List[str]         =   self.completed

					return new_constraint




class 					_snake_case						:






	def __init__(		self					,UpperCamelCase					,UpperCamelCase=True       )						->    Tuple:
					snake_case__      :Optional[int]         =   max([len(UpperCamelCase       ) for one in nested_token_ids]       )

					snake_case__      :Union[str, Any]         =   {}
					for token_ids in nested_token_ids:
									snake_case__      :Tuple         =   root
									for tidx, token_id in enumerate(UpperCamelCase       ):
													if token_id not in level:
																	snake_case__      :Tuple         =   {}

													snake_case__      :List[str]         =   level[token_id]

					if no_subsets and self.has_subsets(UpperCamelCase					,UpperCamelCase       ):
									raise ValueError(
									    "Each list in `nested_token_ids` can't be a complete subset of another list, but is"
									    f' {nested_token_ids}.'       )

					snake_case__      :List[Any]         =   root






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    Union[str, Any]:
					snake_case__      :str         =   self.trie

					for current_token in current_seq:
									snake_case__      :Any         =   start[current_token]

					snake_case__      :Union[str, Any]         =   list(start.keys()       )

					return next_tokens






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    List[Any]:
					snake_case__      :str         =   self.next_tokens(UpperCamelCase       )

					return len(UpperCamelCase       ) == 0






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    str:
					snake_case__      :int         =   list(root.values()       )
					if len(UpperCamelCase       ) == 0:
									return 1
					else:
									return sum([self.count_leaves(UpperCamelCase       ) for nn in next_nodes]       )






	def    lowerCAmelCase_							(		self					,UpperCamelCase					,UpperCamelCase       )						->    Dict:
					snake_case__      :Any         =   self.count_leaves(UpperCamelCase       )
					return len(UpperCamelCase       ) != leaf_count




class 					_snake_case						(			_A ):






	def __init__(		self					,UpperCamelCase       )						->    int:
					super(UpperCamelCase					,self       ).__init__()

					if not isinstance(UpperCamelCase					,UpperCamelCase       ) or len(UpperCamelCase       ) == 0:
									raise ValueError(f'`nested_token_ids` has to be a non-empty list, but is {nested_token_ids}.'       )
					if any(not isinstance(UpperCamelCase					,UpperCamelCase       ) for token_ids in nested_token_ids       ):
									raise ValueError(f'`nested_token_ids` has to be a list of lists, but is {nested_token_ids}.'       )
					if any(
					    any((not isinstance(UpperCamelCase					,UpperCamelCase       ) or token_id < 0) for token_id in token_ids       )
					    for token_ids in nested_token_ids       ):
									raise ValueError(
									    f'Each list in `nested_token_ids` has to be a list of positive integers, but is {nested_token_ids}.'       )

					snake_case__      :Dict         =   DisjunctiveTrie(UpperCamelCase       )
					snake_case__      :List[Any]         =   nested_token_ids

					snake_case__      :Tuple         =   self.trie.max_height
					snake_case__      :Tuple         =   []
					snake_case__      :str         =   False






	def    lowerCAmelCase_							(		self       )						->    Dict:
					snake_case__      :List[Any]         =   self.trie.next_tokens(self.current_seq       )

					if len(UpperCamelCase       ) == 0:
									return None
					else:
									return token_list






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    int:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									raise ValueError(f'`token_id` is supposed to be type `int`, but is {token_id} of type {type(UpperCamelCase       )}'       )

					snake_case__      :Optional[Any]         =   self.trie.next_tokens(self.current_seq       )

					return token_id in next_tokens






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    str:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									raise ValueError(f'`token_id` is supposed to be type `int`, but is {token_id} of type {type(UpperCamelCase       )}'       )

					snake_case__      :Optional[int]         =   False
					snake_case__      :Tuple         =   False
					snake_case__      :Dict         =   False

					if self.does_advance(UpperCamelCase       ):
									self.current_seq.append(UpperCamelCase       )
									snake_case__      :Optional[Any]         =   True
					else:
									snake_case__      :Optional[int]         =   True
									self.reset()

					snake_case__      :Dict         =   self.trie.reached_leaf(self.current_seq       )
					snake_case__      :Any         =   completed

					return stepped, completed, reset






	def    lowerCAmelCase_							(		self       )						->    Optional[Any]:
					snake_case__      :Optional[Any]         =   False
					snake_case__      :Optional[int]         =   []






	def    lowerCAmelCase_							(		self       )						->    List[str]:
					if self.completed:
									# since this can be completed without reaching max height
									return 0
					else:
									return self.seqlen - len(self.current_seq       )






	def    lowerCAmelCase_							(		self					,UpperCamelCase=False       )						->    Optional[Any]:
					snake_case__      :Tuple         =   DisjunctiveConstraint(self.token_ids       )

					if stateful:
									snake_case__      :str         =   self.seqlen
									snake_case__      :Tuple         =   self.current_seq
									snake_case__      :Optional[Any]         =   self.completed

					return new_constraint




class 					_snake_case						:






	def __init__(		self					,UpperCamelCase       )						->    Union[str, Any]:
					snake_case__      :Dict         =   constraints

					# max # of steps required to fulfill a given constraint
					snake_case__      :Any         =   max([c.seqlen for c in constraints]       )
					snake_case__      :Dict         =   len(UpperCamelCase       )
					snake_case__      :int         =   False

					self.init_state()






	def    lowerCAmelCase_							(		self       )						->    int:
					snake_case__      :Optional[int]         =   []
					snake_case__      :Tuple         =   None
					snake_case__      :Any         =   [constraint.copy(stateful=UpperCamelCase       ) for constraint in self.constraints]






	def    lowerCAmelCase_							(		self       )						->    str:
					snake_case__      :List[str]         =   0
					if self.inprogress_constraint:
									# extra points for having a constraint mid-fulfilled
									add += self.max_seqlen - self.inprogress_constraint.remaining()

					return (len(self.complete_constraints       ) * self.max_seqlen) + add






	def    lowerCAmelCase_							(		self       )						->    List[str]:
					snake_case__      :Any         =   []
					if self.inprogress_constraint is None:
									for constraint in self.pending_constraints:  # "pending" == "unfulfilled yet"
													snake_case__      :int         =   constraint.advance()
													if isinstance(UpperCamelCase					,UpperCamelCase       ):
																	token_list.append(UpperCamelCase       )
													elif isinstance(UpperCamelCase					,UpperCamelCase       ):
																	token_list.extend(UpperCamelCase       )
					else:
									snake_case__      :List[Any]         =   self.inprogress_constraint.advance()
									if isinstance(UpperCamelCase					,UpperCamelCase       ):
													token_list.append(UpperCamelCase       )
									elif isinstance(UpperCamelCase					,UpperCamelCase       ):
													token_list.extend(UpperCamelCase       )

					if len(UpperCamelCase       ) == 0:
									return None
					else:
									return token_list






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    List[str]:
					self.init_state()

					if token_ids is not None:
									for token in token_ids:
													# completes or steps **one** constraint
													snake_case__    ,						snake_case__      :Optional[Any]         =   self.add(UpperCamelCase       )

													# the entire list of constraints are fulfilled
													if self.completed:
																	break






	def    lowerCAmelCase_							(		self					,UpperCamelCase       )						->    Any:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									raise ValueError(f'`token_id` should be an `int`, but is `{token_id}`.'       )

					snake_case__    ,						snake_case__      :Optional[Any]         =   False, False

					if self.completed:
									snake_case__      :List[Any]         =   True
									snake_case__      :str         =   False
									return complete, stepped

					if self.inprogress_constraint is not None:
									# In the middle of fulfilling a constraint. If the `token_id` *does* makes an incremental progress to current
									# job, simply update the state

									snake_case__    ,						snake_case__    ,						snake_case__      :Dict         =   self.inprogress_constraint.update(UpperCamelCase       )
									if reset:
													# 1. If the next token breaks the progress, then we must restart.
													#     e.g. constraint = "I love pies" and sequence so far is "I love" but `token_id` == "books".

													#     But that doesn't mean we self.init_state(), since we only reset the state for this particular
													#     constraint, not the full list of constraints.

													self.pending_constraints.append(self.inprogress_constraint.copy(stateful=UpperCamelCase       )       )
													snake_case__      :Any         =   None

									if complete:
													# 2. If the next token completes the constraint, move it to completed list, set
													#     inprogress to None. If there are no pending constraints either, then this full list of constraints
													#     is complete.

													self.complete_constraints.append(self.inprogress_constraint       )
													snake_case__      :str         =   None

													if len(self.pending_constraints       ) == 0:
																	# we're done!
																	snake_case__      :int         =   True

					else:
									# Not in the middle of fulfilling a constraint. So does this `token_id` helps us step towards any of our list
									# of constraints?

									for cidx, pending_constraint in enumerate(self.pending_constraints       ):
													if pending_constraint.does_advance(UpperCamelCase       ):
																	snake_case__    ,						snake_case__    ,						snake_case__      :Union[str, Any]         =   pending_constraint.update(UpperCamelCase       )

																	if not stepped:
																					raise Exception(
																					    "`constraint.update(token_id)` is not yielding incremental progress, "
																					    "even though `constraint.does_advance(token_id)` is true."       )

																	if complete:
																					self.complete_constraints.append(UpperCamelCase       )
																					snake_case__      :Union[str, Any]         =   None

																	if not complete and stepped:
																					snake_case__      :Union[str, Any]         =   pending_constraint

																	if complete or stepped:
																					# If we made any progress at all, then it's at least not a "pending constraint".

																					snake_case__      :List[str]         =   (
																					    self.pending_constraints[:cidx] + self.pending_constraints[cidx + 1 :]
																					)

																					if len(self.pending_constraints       ) == 0 and self.inprogress_constraint is None:
																									# If there's no longer any pending after this and no inprogress either, then we must be
																									# complete.

																									snake_case__      :int         =   True

																					break  # prevent accidentally stepping through multiple constraints with just one token.

					return complete, stepped






	def    lowerCAmelCase_							(		self					,UpperCamelCase=True       )						->    Optional[int]:
					snake_case__      :List[str]         =   ConstraintListState(self.constraints       )  # we actually never though self.constraints objects
					# throughout this process. So it's at initialization state.

					if stateful:
									snake_case__      :Optional[Any]         =   [
									    constraint.copy(stateful=UpperCamelCase       ) for constraint in self.complete_constraints
									]
									if self.inprogress_constraint is not None:
													snake_case__      :List[Any]         =   self.inprogress_constraint.copy(stateful=UpperCamelCase       )
									snake_case__      :str         =   [constraint.copy() for constraint in self.pending_constraints]

					return new_state







from typing import Any





def 					lowercase_ (    __snake_case     :							list	,	__snake_case     :							list	,	__snake_case     :							dict	,	__snake_case     :							dict	,	__snake_case     :							dict	,	)     -> list:





				'''simple docstring'''


				_validation(
				    __snake_case	,	__snake_case	,	__snake_case	,	__snake_case	,	__snake_case	,	)
				# Creates data structures and fill initial step
				snake_case__      :dict         =   {}
				snake_case__      :dict         =   {}
				for state in states_space:
								snake_case__      :List[Any]         =   observations_space[0]
								snake_case__      :str         =   (
								    initial_probabilities[state] * emission_probabilities[state][observation]
								)
								snake_case__      :str         =   None

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

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

												snake_case__      :List[str]         =   arg_max

    # The final observation
				snake_case__      :str         =   observations_space[len(__snake_case      ) - 1]

				# argmax for given final observation
				snake_case__      :Optional[int]         =   ""
				snake_case__      :List[str]         =   -1
				for k_state in states_space:
								snake_case__      :List[str]         =   probabilities[(k_state, final_observation)]
								if probability > max_probability:
												snake_case__      :List[str]         =   probability
												snake_case__      :int         =   k_state
				snake_case__      :Any         =   arg_max

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

				return result





def 					lowercase_ (    __snake_case     :							Any	,	__snake_case     :							Any	,	__snake_case     :							Any	,	__snake_case     :							Any	,	__snake_case     :							Any	,	)     -> None:





				'''simple docstring'''


				_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 					lowercase_ (    __snake_case     :							Any	,	__snake_case     :							Any	,	__snake_case     :							Any	,	__snake_case     :							Any	,	__snake_case     :							Any	,	)     -> None:





				'''simple docstring'''


				if not all(
				    [
				        observations_space,
				        states_space,
				        initial_probabilities,
				        transition_probabilities,
				        emission_probabilities,
				    ]      ):
								raise ValueError("There's an empty parameter"      )





def 					lowercase_ (    __snake_case     :							Any	,	__snake_case     :							Any      )     -> None:





				'''simple docstring'''


				_validate_list(__snake_case	,	"observations_space"      )
				_validate_list(__snake_case	,	"states_space"      )





def 					lowercase_ (    __snake_case     :							Any	,	__snake_case     :							str      )     -> None:





				'''simple docstring'''


				if not isinstance(_object	,	__snake_case      ):
								snake_case__      :Optional[int]         =   F'{var_name} must be a list'
								raise ValueError(__snake_case      )
				else:
								for x in _object:
												if not isinstance(__snake_case	,	__snake_case      ):
																snake_case__      :Any         =   F'{var_name} must be a list of strings'
																raise ValueError(__snake_case      )





def 					lowercase_ (    __snake_case     :							Any	,	__snake_case     :							Any	,	__snake_case     :							Any	,	)     -> None:





				'''simple docstring'''


				_validate_dict(__snake_case	,	"initial_probabilities"	,	__snake_case      )
				_validate_nested_dict(__snake_case	,	"transition_probabilities"      )
				_validate_nested_dict(__snake_case	,	"emission_probabilities"      )





def 					lowercase_ (    __snake_case     :							Any	,	__snake_case     :							str      )     -> None:





				'''simple docstring'''


				_validate_dict(_object	,	__snake_case	,	__snake_case      )
				for x in _object.values():
								_validate_dict(__snake_case	,	__snake_case	,	__snake_case	,	__snake_case      )





def 					lowercase_ (    __snake_case     :							Any	,	__snake_case     :							str	,	__snake_case     :							type	,	__snake_case     :							bool = False      )     -> None:





				'''simple docstring'''


				if not isinstance(_object	,	__snake_case      ):
								snake_case__      :str         =   F'{var_name} must be a dict'
								raise ValueError(__snake_case      )
				if not all(isinstance(__snake_case	,	__snake_case      ) for x in _object      ):
								snake_case__      :List[Any]         =   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()      ):
								snake_case__      :Optional[int]         =   "nested dictionary " if nested else ""
								snake_case__      :int         =   F'{var_name} {nested_text}all values must be {value_type.__name__}'
								raise ValueError(__snake_case      )


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

	testmod()