'''simple docstring'''

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







class 				_lowercase     (				UpperCAmelCase__			):


 '''simple docstring'''






 def __init__(      self   :	Any							)  ->    Optional[Any]:
  # test for the above condition
  self.test()
 def a					(      self   :	str							)  ->    Any:
  __lowerCAmelCase											=						0
  __lowerCAmelCase											=						False
  while not completed:
   if counter == 1:
    self.reset()
   __lowerCAmelCase											=						self.advance()
   if not self.does_advance(SCREAMING_SNAKE_CASE__							):
    raise Exception(
        """Custom Constraint is not defined correctly. self.does_advance(self.advance()) must be true."""							)

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





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







class 				_lowercase     (				UpperCAmelCase__			):


 '''simple docstring'''






 def __init__(      self   :	Union[str, Any]      ,       SCREAMING_SNAKE_CASE__   :	List[int]							)  ->    Any:
  super(SCREAMING_SNAKE_CASE__      ,       self							).__init__()

  if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							) or len(SCREAMING_SNAKE_CASE__							) == 0:
   raise ValueError(f"""`token_ids` has to be a non-empty list, but is {token_ids}."""							)
  if any((not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							) 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 a					(      self   :	Any							)  ->    List[str]:
  if self.completed:
   return None
  return self.token_ids[self.fulfilled_idx + 1]
 def a					(      self   :	List[Any]      ,       SCREAMING_SNAKE_CASE__   :	int							)  ->    int:
  if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
   raise ValueError(f"""`token_id` has to be an `int`, but is {token_id} of type {type(SCREAMING_SNAKE_CASE__							)}"""							)

  if self.completed:
   return False

  return token_id == self.token_ids[self.fulfilled_idx + 1]
 def a					(      self   :	Any      ,       SCREAMING_SNAKE_CASE__   :	int							)  ->    Union[str, Any]:
  if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
   raise ValueError(f"""`token_id` has to be an `int`, but is {token_id} of type {type(SCREAMING_SNAKE_CASE__							)}"""							)

  __lowerCAmelCase											=						False
  __lowerCAmelCase											=						False
  __lowerCAmelCase											=						False

  if self.does_advance(SCREAMING_SNAKE_CASE__							):
   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 a					(      self   :	Optional[int]							)  ->    Any:
  __lowerCAmelCase											=						False
  __lowerCAmelCase											=						0
 def a					(      self   :	str							)  ->    Optional[Any]:
  return self.seqlen - (self.fulfilled_idx + 1)





 def a					(      self   :	Optional[Any]      ,       SCREAMING_SNAKE_CASE__   :	Optional[Any]=False							)  ->    str:
  __lowerCAmelCase											=						PhrasalConstraint(self.token_ids							)

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

  return new_constraint







class 				_lowercase     :


 '''simple docstring'''






 def __init__(      self   :	List[str]      ,       SCREAMING_SNAKE_CASE__   :	List[List[int]]      ,       SCREAMING_SNAKE_CASE__   :	Any=True							)  ->    Union[str, Any]:
  __lowerCAmelCase											=						max([len(SCREAMING_SNAKE_CASE__							) for one in nested_token_ids]							)

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

    __lowerCAmelCase											=						level[token_id]

  if no_subsets and self.has_subsets(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
   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 a					(      self   :	str      ,       SCREAMING_SNAKE_CASE__   :	Union[str, Any]							)  ->    Optional[int]:
  __lowerCAmelCase											=						self.trie

  for current_token in current_seq:
   __lowerCAmelCase											=						start[current_token]

  __lowerCAmelCase											=						list(start.keys()							)

  return next_tokens
 def a					(      self   :	List[str]      ,       SCREAMING_SNAKE_CASE__   :	Optional[int]							)  ->    List[Any]:
  __lowerCAmelCase											=						self.next_tokens(SCREAMING_SNAKE_CASE__							)

  return len(SCREAMING_SNAKE_CASE__							) == 0
 def a					(      self   :	Tuple      ,       SCREAMING_SNAKE_CASE__   :	List[Any]							)  ->    int:
  __lowerCAmelCase											=						list(root.values()							)
  if len(SCREAMING_SNAKE_CASE__							) == 0:
   return 1
  else:
   return sum([self.count_leaves(SCREAMING_SNAKE_CASE__							) for nn in next_nodes]							)





 def a					(      self   :	Optional[int]      ,       SCREAMING_SNAKE_CASE__   :	str      ,       SCREAMING_SNAKE_CASE__   :	List[str]							)  ->    Union[str, Any]:
  __lowerCAmelCase											=						self.count_leaves(SCREAMING_SNAKE_CASE__							)
  return len(SCREAMING_SNAKE_CASE__							) != leaf_count







class 				_lowercase     (				UpperCAmelCase__			):


 '''simple docstring'''






 def __init__(      self   :	int      ,       SCREAMING_SNAKE_CASE__   :	List[List[int]]							)  ->    str:
  super(SCREAMING_SNAKE_CASE__      ,       self							).__init__()

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

  __lowerCAmelCase											=						self.trie.max_height
  __lowerCAmelCase											=						[]
  __lowerCAmelCase											=						False
 def a					(      self   :	Optional[int]							)  ->    int:
  __lowerCAmelCase											=						self.trie.next_tokens(self.current_seq							)

  if len(SCREAMING_SNAKE_CASE__							) == 0:
   return None
  else:
   return token_list
 def a					(      self   :	Tuple      ,       SCREAMING_SNAKE_CASE__   :	int							)  ->    Tuple:
  if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
   raise ValueError(f"""`token_id` is supposed to be type `int`, but is {token_id} of type {type(SCREAMING_SNAKE_CASE__							)}"""							)

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

  return token_id in next_tokens
 def a					(      self   :	str      ,       SCREAMING_SNAKE_CASE__   :	int							)  ->    Union[str, Any]:
  if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
   raise ValueError(f"""`token_id` is supposed to be type `int`, but is {token_id} of type {type(SCREAMING_SNAKE_CASE__							)}"""							)

  __lowerCAmelCase											=						False
  __lowerCAmelCase											=						False
  __lowerCAmelCase											=						False

  if self.does_advance(SCREAMING_SNAKE_CASE__							):
   self.current_seq.append(SCREAMING_SNAKE_CASE__							)
   __lowerCAmelCase											=						True
  else:
   __lowerCAmelCase											=						True
   self.reset()

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

  return stepped, completed, reset
 def a					(      self   :	str							)  ->    Tuple:
  __lowerCAmelCase											=						False
  __lowerCAmelCase											=						[]
 def a					(      self   :	List[Any]							)  ->    Optional[int]:
  if self.completed:
   # since this can be completed without reaching max height
   return 0
  else:
   return self.seqlen - len(self.current_seq							)





 def a					(      self   :	Dict      ,       SCREAMING_SNAKE_CASE__   :	Any=False							)  ->    int:
  __lowerCAmelCase											=						DisjunctiveConstraint(self.token_ids							)

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

  return new_constraint







class 				_lowercase     :


 '''simple docstring'''






 def __init__(      self   :	str      ,       SCREAMING_SNAKE_CASE__   :	List[Constraint]							)  ->    str:
  __lowerCAmelCase											=						constraints

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

  self.init_state()
 def a					(      self   :	List[str]							)  ->    Any:
  __lowerCAmelCase											=						[]
  __lowerCAmelCase											=						None
  __lowerCAmelCase											=						[constraint.copy(stateful=SCREAMING_SNAKE_CASE__							) for constraint in self.constraints]
 def a					(      self   :	Dict							)  ->    List[Any]:
  __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 a					(      self   :	Optional[int]							)  ->    Any:
  __lowerCAmelCase											=						[]
  if self.inprogress_constraint is None:
   for constraint in self.pending_constraints:  # "pending" == "unfulfilled yet"
    __lowerCAmelCase											=						constraint.advance()
    if isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
     token_list.append(SCREAMING_SNAKE_CASE__							)
    elif isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
     token_list.extend(SCREAMING_SNAKE_CASE__							)
  else:
   __lowerCAmelCase											=						self.inprogress_constraint.advance()
   if isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
    token_list.append(SCREAMING_SNAKE_CASE__							)
   elif isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
    token_list.extend(SCREAMING_SNAKE_CASE__							)

  if len(SCREAMING_SNAKE_CASE__							) == 0:
   return None
  else:
   return token_list
 def a					(      self   :	Dict      ,       SCREAMING_SNAKE_CASE__   :	Optional[List[int]]							)  ->    List[str]:
  self.init_state()

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

    # the entire list of constraints are fulfilled
    if self.completed:
     break
 def a					(      self   :	str      ,       SCREAMING_SNAKE_CASE__   :	int							)  ->    str:
  if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							):
   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(SCREAMING_SNAKE_CASE__							)
   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=SCREAMING_SNAKE_CASE__							)							)
    __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(SCREAMING_SNAKE_CASE__							):
     __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						pending_constraint.update(SCREAMING_SNAKE_CASE__							)

     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(SCREAMING_SNAKE_CASE__							)
      __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 a					(      self   :	Tuple      ,       SCREAMING_SNAKE_CASE__   :	Union[str, Any]=True							)  ->    Optional[int]:
  __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=SCREAMING_SNAKE_CASE__							) for constraint in self.complete_constraints
   ]
   if self.inprogress_constraint is not None:
    __lowerCAmelCase											=						self.inprogress_constraint.copy(stateful=SCREAMING_SNAKE_CASE__							)
   __lowerCAmelCase											=						[constraint.copy() for constraint in self.pending_constraints]

  return new_state







'''simple docstring'''

import numpy as np
import qiskit







def      UpperCamelCase_						(					snake_case_       :       int = 8						,		snake_case_       :       int | None = None      )					->     str:






 '''simple docstring'''

 __lowerCAmelCase											=						np.random.default_rng(seed=snake_case_      )

 # Roughly 25% of the qubits will contribute to the key.
 # So we take more than we need.
 __lowerCAmelCase											=						6 * key_len
 # Measurement basis for Alice's qubits.
 __lowerCAmelCase											=						rng.integers(2						,		size=snake_case_      )
 # The set of states Alice will prepare.
 __lowerCAmelCase											=						rng.integers(2						,		size=snake_case_      )
 # Measurement basis for Bob's qubits.
 __lowerCAmelCase											=						rng.integers(2						,		size=snake_case_      )

 # Quantum Circuit to simulate BB84
 __lowerCAmelCase											=						qiskit.QuantumCircuit(snake_case_						,		name="""BB84"""      )

 # Alice prepares her qubits according to rules above.
 for index, _ in enumerate(snake_case_      ):
  if alice_state[index] == 1:
   bbaa_circ.x(snake_case_      )
  if alice_basis[index] == 1:
   bbaa_circ.h(snake_case_      )
 bbaa_circ.barrier()

 # Bob measures the received qubits according to rules above.
 for index, _ in enumerate(snake_case_      ):
  if bob_basis[index] == 1:
   bbaa_circ.h(snake_case_      )

 bbaa_circ.barrier()
 bbaa_circ.measure_all()

 # Simulate the quantum circuit.
 __lowerCAmelCase											=						qiskit.Aer.get_backend("""aer_simulator"""      )
 # We only need to run one shot because the key is unique.
 # Multiple shots will produce the same key.
 __lowerCAmelCase											=						qiskit.execute(snake_case_						,		snake_case_						,		shots=1						,		seed_simulator=snake_case_      )
 # Returns the result of measurement.
 __lowerCAmelCase											=						job.result().get_counts(snake_case_      ).most_frequent()

 # Extracting the generated key from the simulation results.
 # Only keep measurement results where Alice and Bob chose the same basis.
 __lowerCAmelCase											=						"""""".join(
     [
         result_bit
         for alice_basis_bit, bob_basis_bit, result_bit in zip(
             snake_case_						,		snake_case_						,		snake_case_      )
         if alice_basis_bit == bob_basis_bit
     ]      )

 # Get final key. Pad with 0 if too short, otherwise truncate.
 __lowerCAmelCase											=						gen_key[:key_len] if len(snake_case_      ) >= key_len else gen_key.ljust(snake_case_						,		"""0"""      )
 return key


if __name__ == "__main__":
 print(f'The generated key is : {bbaa(8, seed=0)}')
 from doctest import testmod

 testmod()






