





'''simple docstring'''


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

class       lowerCAmelCase_						(						UpperCAmelCase__						):




 def __init__(		self						)			->							List[Any]:
     self.test()




 def 							_snake_case      (		self						)			->							Union[str, Any]:
     _lowerCAmelCase			=					0
     _lowerCAmelCase			=					False
     while not completed:
         if counter == 1:
             self.reset()
         _lowerCAmelCase			=					self.advance()
         if not self.does_advance(_a						):
             raise Exception(
                 "Custom Constraint is not defined correctly. self.does_advance(self.advance()) must be true."						)

         _lowerCAmelCase	,	_lowerCAmelCase	,	_lowerCAmelCase			=					self.update(_a						)
         counter += 1

         if counter > 10000:
             raise Exception("update() does not fulfill the constraint."						)

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




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




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




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




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




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





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







class       lowerCAmelCase_						(						UpperCAmelCase__						):




 def __init__(		self	,   _lowerCAmelCase						)			->							List[str]:
     super(_a	,   self						).__init__()

     if not isinstance(_a	,   _a						) or len(_a						) == 0:
         raise ValueError(f'''`token_ids` has to be a non-empty list, but is {token_ids}.'''						)
     if any((not isinstance(_a	,   _a						) 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}.'''						)

     _lowerCAmelCase			=					token_ids

     _lowerCAmelCase			=					len(self.token_ids						)
     _lowerCAmelCase			=					-1  # the index of the currently fulfilled step
     _lowerCAmelCase			=					False




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




 def 							_snake_case      (		self	,   _lowerCAmelCase						)			->							Tuple:
     if not isinstance(_a	,   _a						):
         raise ValueError(f'''`token_id` has to be an `int`, but is {token_id} of type {type(_a						)}'''						)

     if self.completed:
         return False

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




 def 							_snake_case      (		self	,   _lowerCAmelCase						)			->							Dict:
     if not isinstance(_a	,   _a						):
         raise ValueError(f'''`token_id` has to be an `int`, but is {token_id} of type {type(_a						)}'''						)

     _lowerCAmelCase			=					False
     _lowerCAmelCase			=					False
     _lowerCAmelCase			=					False

     if self.does_advance(_a						):
         self.fulfilled_idx += 1
         _lowerCAmelCase			=					True
         if self.fulfilled_idx == (self.seqlen - 1):
             _lowerCAmelCase			=					True
         _lowerCAmelCase			=					completed
     else:
         # failed to make progress.
         _lowerCAmelCase			=					True
         self.reset()
     return stepped, completed, reset




 def 							_snake_case      (		self						)			->							List[Any]:
     _lowerCAmelCase			=					False
     _lowerCAmelCase			=					0




 def 							_snake_case      (		self						)			->							int:
     return self.seqlen - (self.fulfilled_idx + 1)





 def 							_snake_case      (		self	,   _lowerCAmelCase=False						)			->							Tuple:
     _lowerCAmelCase			=					PhrasalConstraint(self.token_ids						)

     if stateful:
         _lowerCAmelCase			=					self.seqlen
         _lowerCAmelCase			=					self.fulfilled_idx
         _lowerCAmelCase			=					self.completed

     return new_constraint







class       lowerCAmelCase_						:




 def __init__(		self	,   _lowerCAmelCase	,   _lowerCAmelCase=True						)			->							Dict:
     _lowerCAmelCase			=					max([len(_a						) for one in nested_token_ids]						)

     _lowerCAmelCase			=					{}
     for token_ids in nested_token_ids:
         _lowerCAmelCase			=					root
         for tidx, token_id in enumerate(_a						):
             if token_id not in level:
                 _lowerCAmelCase			=					{}

             _lowerCAmelCase			=					level[token_id]

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

     _lowerCAmelCase			=					root




 def 							_snake_case      (		self	,   _lowerCAmelCase						)			->							Union[str, Any]:
     _lowerCAmelCase			=					self.trie

     for current_token in current_seq:
         _lowerCAmelCase			=					start[current_token]

     _lowerCAmelCase			=					list(start.keys()						)

     return next_tokens




 def 							_snake_case      (		self	,   _lowerCAmelCase						)			->							Tuple:
     _lowerCAmelCase			=					self.next_tokens(_a						)

     return len(_a						) == 0




 def 							_snake_case      (		self	,   _lowerCAmelCase						)			->							Dict:
     _lowerCAmelCase			=					list(root.values()						)
     if len(_a						) == 0:
         return 1
     else:
         return sum([self.count_leaves(_a						) for nn in next_nodes]						)





 def 							_snake_case      (		self	,   _lowerCAmelCase	,   _lowerCAmelCase						)			->							Dict:
     _lowerCAmelCase			=					self.count_leaves(_a						)
     return len(_a						) != leaf_count







class       lowerCAmelCase_						(						UpperCAmelCase__						):




 def __init__(		self	,   _lowerCAmelCase						)			->							Tuple:
     super(_a	,   self						).__init__()

     if not isinstance(_a	,   _a						) or len(_a						) == 0:
         raise ValueError(f'''`nested_token_ids` has to be a non-empty list, but is {nested_token_ids}.'''						)
     if any(not isinstance(_a	,   _a						) 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(_a	,   _a						) 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}.'''						)

     _lowerCAmelCase			=					DisjunctiveTrie(_a						)
     _lowerCAmelCase			=					nested_token_ids

     _lowerCAmelCase			=					self.trie.max_height
     _lowerCAmelCase			=					[]
     _lowerCAmelCase			=					False




 def 							_snake_case      (		self						)			->							List[Any]:
     _lowerCAmelCase			=					self.trie.next_tokens(self.current_seq						)

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




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

     _lowerCAmelCase			=					self.trie.next_tokens(self.current_seq						)

     return token_id in next_tokens




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

     _lowerCAmelCase			=					False
     _lowerCAmelCase			=					False
     _lowerCAmelCase			=					False

     if self.does_advance(_a						):
         self.current_seq.append(_a						)
         _lowerCAmelCase			=					True
     else:
         _lowerCAmelCase			=					True
         self.reset()

     _lowerCAmelCase			=					self.trie.reached_leaf(self.current_seq						)
     _lowerCAmelCase			=					completed

     return stepped, completed, reset




 def 							_snake_case      (		self						)			->							int:
     _lowerCAmelCase			=					False
     _lowerCAmelCase			=					[]




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





 def 							_snake_case      (		self	,   _lowerCAmelCase=False						)			->							str:
     _lowerCAmelCase			=					DisjunctiveConstraint(self.token_ids						)

     if stateful:
         _lowerCAmelCase			=					self.seqlen
         _lowerCAmelCase			=					self.current_seq
         _lowerCAmelCase			=					self.completed

     return new_constraint







class       lowerCAmelCase_						:




 def __init__(		self	,   _lowerCAmelCase						)			->							Optional[Any]:
     _lowerCAmelCase			=					constraints

     # max # of steps required to fulfill a given constraint
     _lowerCAmelCase			=					max([c.seqlen for c in constraints]						)
     _lowerCAmelCase			=					len(_a						)
     _lowerCAmelCase			=					False

     self.init_state()




 def 							_snake_case      (		self						)			->							List[Any]:
     _lowerCAmelCase			=					[]
     _lowerCAmelCase			=					None
     _lowerCAmelCase			=					[constraint.copy(stateful=_a						) for constraint in self.constraints]




 def 							_snake_case      (		self						)			->							Optional[int]:
     _lowerCAmelCase			=					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 							_snake_case      (		self						)			->							Optional[Any]:
     _lowerCAmelCase			=					[]
     if self.inprogress_constraint is None:
         for constraint in self.pending_constraints:  # "pending" == "unfulfilled yet"
             _lowerCAmelCase			=					constraint.advance()
             if isinstance(_a	,   _a						):
                 token_list.append(_a						)
             elif isinstance(_a	,   _a						):
                 token_list.extend(_a						)
     else:
         _lowerCAmelCase			=					self.inprogress_constraint.advance()
         if isinstance(_a	,   _a						):
             token_list.append(_a						)
         elif isinstance(_a	,   _a						):
             token_list.extend(_a						)

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




 def 							_snake_case      (		self	,   _lowerCAmelCase						)			->							int:
     self.init_state()

     if token_ids is not None:
         for token in token_ids:
             # completes or steps **one** constraint
             _lowerCAmelCase	,	_lowerCAmelCase			=					self.add(_a						)

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




 def 							_snake_case      (		self	,   _lowerCAmelCase						)			->							Union[str, Any]:
     if not isinstance(_a	,   _a						):
         raise ValueError(f'''`token_id` should be an `int`, but is `{token_id}`.'''						)

     _lowerCAmelCase	,	_lowerCAmelCase			=					False, False

     if self.completed:
         _lowerCAmelCase			=					True
         _lowerCAmelCase			=					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

         _lowerCAmelCase	,	_lowerCAmelCase	,	_lowerCAmelCase			=					self.inprogress_constraint.update(_a						)
         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=_a						)						)
             _lowerCAmelCase			=					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						)
             _lowerCAmelCase			=					None

             if len(self.pending_constraints						) == 0:
                 # we're done!
                 _lowerCAmelCase			=					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(_a						):
                 _lowerCAmelCase	,	_lowerCAmelCase	,	_lowerCAmelCase			=					pending_constraint.update(_a						)

                 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(_a						)
                     _lowerCAmelCase			=					None

                 if not complete and stepped:
                     _lowerCAmelCase			=					pending_constraint

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

                     _lowerCAmelCase			=					(
                         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.

                         _lowerCAmelCase			=					True

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

     return complete, stepped





 def 							_snake_case      (		self	,   _lowerCAmelCase=True						)			->							Union[str, Any]:
     _lowerCAmelCase			=					ConstraintListState(self.constraints						)  # we actually never though self.constraints objects
     # throughout this process. So it's at initialization state.

     if stateful:
         _lowerCAmelCase			=					[
             constraint.copy(stateful=_a						) for constraint in self.complete_constraints
         ]
         if self.inprogress_constraint is not None:
             _lowerCAmelCase			=					self.inprogress_constraint.copy(stateful=_a						)
         _lowerCAmelCase			=					[constraint.copy() for constraint in self.pending_constraints]

     return new_state








"""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()



