



"""simple docstring"""


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







class       A_			(     __snake_case				):



						"""simple docstring"""






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






						def 	UpperCAmelCase__     (					self :Optional[int]					)				->			str:
												UpperCAmelCase             = 0
												UpperCAmelCase             = False
												while not completed:
																		if counter == 1:
																								self.reset()
																		UpperCAmelCase             = self.advance()
																		if not self.does_advance(a_					):
																								raise Exception(
																								    'Custom Constraint is not defined correctly. self.does_advance(self.advance()) must be true.'					)

																		UpperCAmelCase             = self.update(a_					)
																		counter += 1

																		if counter > 1_00_00:
																								raise Exception('update() does not fulfill the constraint.'					)

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






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






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






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






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






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






						@abstractmethod
						def 	UpperCAmelCase__     (					self :List[str]   ,  lowercase_ :Optional[int]=False					)				->			Tuple:
												raise NotImplementedError(
												    f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""					)







class       A_			(     __snake_case				):



						"""simple docstring"""






						def __init__(					self :List[Any]   ,  lowercase_ :Optional[int]					)				->			List[Any]:
												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}."""					)

												UpperCAmelCase             = token_ids

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






						def 	UpperCAmelCase__     (					self :List[str]					)				->			Optional[int]:

												if self.completed:
																		return None
												return self.token_ids[self.fulfilled_idx + 1]






						def 	UpperCAmelCase__     (					self :Dict   ,  lowercase_ :Dict					)				->			Optional[Any]:

												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 	UpperCAmelCase__     (					self :List[str]   ,  lowercase_ :int					)				->			Optional[int]:

												if not isinstance(a_   ,  a_					):
																		raise ValueError(f"""`token_id` has to be an `int`, but is {token_id} of type {type(a_					)}"""					)

												UpperCAmelCase             = False
												UpperCAmelCase             = False
												UpperCAmelCase             = False

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






						def 	UpperCAmelCase__     (					self :str					)				->			List[Any]:
												UpperCAmelCase             = False
												UpperCAmelCase             = 0






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






						def 	UpperCAmelCase__     (					self :List[Any]   ,  lowercase_ :Any=False					)				->			List[str]:
												UpperCAmelCase             = PhrasalConstraint(self.token_ids					)

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

												return new_constraint







class       A_			:



						"""simple docstring"""






						def __init__(					self :Tuple   ,  lowercase_ :Optional[int]   ,  lowercase_ :Optional[int]=True					)				->			Union[str, Any]:
												UpperCAmelCase             = max([len(a_					) for one in nested_token_ids]					)

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

																								UpperCAmelCase             = 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}."""					)

												UpperCAmelCase             = root






						def 	UpperCAmelCase__     (					self :Any   ,  lowercase_ :Union[str, Any]					)				->			List[str]:
												UpperCAmelCase             = self.trie

												for current_token in current_seq:
																		UpperCAmelCase             = start[current_token]

												UpperCAmelCase             = list(start.keys()					)

												return next_tokens






						def 	UpperCAmelCase__     (					self :Union[str, Any]   ,  lowercase_ :int					)				->			str:
												UpperCAmelCase             = self.next_tokens(a_					)

												return len(a_					) == 0






						def 	UpperCAmelCase__     (					self :List[Any]   ,  lowercase_ :str					)				->			List[Any]:
												UpperCAmelCase             = list(root.values()					)
												if len(a_					) == 0:
																		return 1
												else:
																		return sum([self.count_leaves(a_					) for nn in next_nodes]					)






						def 	UpperCAmelCase__     (					self :int   ,  lowercase_ :List[Any]   ,  lowercase_ :Tuple					)				->			Dict:
												UpperCAmelCase             = self.count_leaves(a_					)
												return len(a_					) != leaf_count







class       A_			(     __snake_case				):



						"""simple docstring"""






						def __init__(					self :List[Any]   ,  lowercase_ :Dict					)				->			Optional[int]:
												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}."""					)

												UpperCAmelCase             = DisjunctiveTrie(a_					)
												UpperCAmelCase             = nested_token_ids

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






						def 	UpperCAmelCase__     (					self :Dict					)				->			Union[str, Any]:
												UpperCAmelCase             = self.trie.next_tokens(self.current_seq					)

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






						def 	UpperCAmelCase__     (					self :int   ,  lowercase_ :Dict					)				->			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_					)}"""					)

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

												return token_id in next_tokens






						def 	UpperCAmelCase__     (					self :Dict   ,  lowercase_ :List[Any]					)				->			Union[str, Any]:

												if not isinstance(a_   ,  a_					):
																		raise ValueError(f"""`token_id` is supposed to be type `int`, but is {token_id} of type {type(a_					)}"""					)

												UpperCAmelCase             = False
												UpperCAmelCase             = False
												UpperCAmelCase             = False

												if self.does_advance(a_					):
																		self.current_seq.append(a_					)
																		UpperCAmelCase             = True
												else:
																		UpperCAmelCase             = True
																		self.reset()

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

												return stepped, completed, reset






						def 	UpperCAmelCase__     (					self :int					)				->			Optional[int]:
												UpperCAmelCase             = False
												UpperCAmelCase             = []






						def 	UpperCAmelCase__     (					self :Any					)				->			Optional[Any]:

												if self.completed:
																		# since this can be completed without reaching max height
																		return 0
												else:
																		return self.seqlen - len(self.current_seq					)






						def 	UpperCAmelCase__     (					self :int   ,  lowercase_ :Optional[Any]=False					)				->			List[Any]:
												UpperCAmelCase             = DisjunctiveConstraint(self.token_ids					)

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

												return new_constraint







class       A_			:



						"""simple docstring"""






						def __init__(					self :int   ,  lowercase_ :Union[str, Any]					)				->			Tuple:
												UpperCAmelCase             = constraints

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

												self.init_state()






						def 	UpperCAmelCase__     (					self :Dict					)				->			List[Any]:
												UpperCAmelCase             = []
												UpperCAmelCase             = None
												UpperCAmelCase             = [constraint.copy(stateful=a_					) for constraint in self.constraints]






						def 	UpperCAmelCase__     (					self :List[Any]					)				->			str:
												UpperCAmelCase             = 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 	UpperCAmelCase__     (					self :Tuple					)				->			Dict:
												UpperCAmelCase             = []
												if self.inprogress_constraint is None:
																		for constraint in self.pending_constraints:  # "pending" == "unfulfilled yet"
																								UpperCAmelCase             = constraint.advance()
																								if isinstance(a_   ,  a_					):
																														token_list.append(a_					)
																								elif isinstance(a_   ,  a_					):
																														token_list.extend(a_					)
												else:
																		UpperCAmelCase             = 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 	UpperCAmelCase__     (					self :List[str]   ,  lowercase_ :Dict					)				->			Union[str, Any]:
												self.init_state()

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

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






						def 	UpperCAmelCase__     (					self :int   ,  lowercase_ :Tuple					)				->			Optional[Any]:

												if not isinstance(a_   ,  a_					):
																		raise ValueError(f"""`token_id` should be an `int`, but is `{token_id}`."""					)

												UpperCAmelCase             = False, False

												if self.completed:
																		UpperCAmelCase             = True
																		UpperCAmelCase             = 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

																		UpperCAmelCase             = 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_					)					)
																								UpperCAmelCase             = 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					)
																								UpperCAmelCase             = None

																								if len(self.pending_constraints					) == 0:
																														# we're done!
																														UpperCAmelCase             = 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_					):
																														UpperCAmelCase             = 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_					)
																																				UpperCAmelCase             = None

																														if not complete and stepped:
																																				UpperCAmelCase             = pending_constraint

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

																																				UpperCAmelCase             = (
																																				    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.

																																										UpperCAmelCase             = True

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

												return complete, stepped






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

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

												return new_state









"""simple docstring"""
from __future__ import annotations

from scipy.special import comb  # type: ignore



class 			_UpperCAmelCase :






		'''simple docstring'''

		def __init__(self				,       a_					):





			'''simple docstring'''

			__snake_case	:						List[str]						=				list_of_points
			# Degree determines the flexibility of the curve.
			# Degree = 1 will produce a straight line.
			__snake_case	:						Optional[Any]						=				len(a_					) - 1



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			assert 0 <= t <= 1, "Time t must be between 0 and 1."
			__snake_case	:						list[float]						=				[]
			for i in range(len(self.list_of_points					)					):
				# basis function for each i
				output_values.append(
				    comb(self.degree				,       a_					) * ((1 - t) ** (self.degree - i)) * (t**i)					)
			# the basis must sum up to 1 for it to produce a valid Bezier curve.
			assert round(sum(a_					)				,       5					) == 1
			return output_values



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			assert 0 <= t <= 1, "Time t must be between 0 and 1."

			__snake_case	:						List[str]						=				self.basis_function(a_					)
			__snake_case	:						str						=				0.0
			__snake_case	:						Union[str, Any]						=				0.0
			for i in range(len(self.list_of_points					)					):
				# For all points, sum up the product of i-th basis function and i-th point.
				x += basis_function[i] * self.list_of_points[i][0]
				y += basis_function[i] * self.list_of_points[i][1]
			return (x, y)



		def 				SCREAMING_SNAKE_CASE  (self				,       a_ = 0.01					):





			'''simple docstring'''

			from matplotlib import pyplot as plt  # type: ignore

			__snake_case	:						list[float]						=				[]  # x coordinates of points to plot
			__snake_case	:						list[float]						=				[]  # y coordinates of points to plot

			__snake_case	:						int						=				0.0
			while t <= 1:
				__snake_case	:						Union[str, Any]						=				self.bezier_curve_function(a_					)
				to_plot_x.append(value[0]					)
				to_plot_y.append(value[1]					)
				t += step_size

			__snake_case	:						List[Any]						=				[i[0] for i in self.list_of_points]
			__snake_case	:						Any						=				[i[1] for i in self.list_of_points]

			plt.plot(
			    a_				,       a_				,       color='''blue'''				,       label='''Curve of Degree ''' + str(self.degree					)				,       )
			plt.scatter(a_				,       a_				,       color='''red'''				,       label='''Control Points'''					)
			plt.legend()
			plt.show()


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
			BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
			BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3





