text: import abc
  from typing import Any
  from typing import Dict
  from typing import Optional
  from typing import Sequence
  
  from optuna.distributions import BaseDistribution
  from optuna.study import Study
  from optuna.trial import FrozenTrial
  from optuna.trial import TrialState
  
  
  class BaseSampler(object, metaclass=abc.ABCMeta):
      """Base class for samplers.
  
      Optuna combines two types of sampling strategies, which are called *relative sampling* and
      *independent sampling*.
  
      *The relative sampling* determines values of multiple parameters simultaneously so that
      sampling algorithms can use relationship between parameters (e.g., correlation).
      Target parameters of the relative sampling are described in a relative search space, which
      is determined by :func:`~optuna.samplers.BaseSampler.infer_relative_search_space`.
  
      *The independent sampling* determines a value of a single parameter without considering any
      relationship between parameters. Target parameters of the independent sampling are the
      parameters not described in the relative search space.
  
      More specifically, parameters are sampled by the following procedure.
      At the beginning of a trial, :meth:`~optuna.samplers.BaseSampler.infer_relative_search_space`
      is called to determine the relative search space for the trial. Then,
      :meth:`~optuna.samplers.BaseSampler.sample_relative` is invoked to sample parameters
      from the relative search space. During the execution of the objective function,
      :meth:`~optuna.samplers.BaseSampler.sample_independent` is used to sample
      parameters that don't belong to the relative search space.
  
      The following figure depicts the lifetime of a trial and how the above three methods are
      called in the trial.
  
      .. image:: ../../../../image/sampling-sequence.png
  
      |
  
      """
  
      def __str__(self) -> str:
          return self.__class__.__name__
  
      @abc.abstractmethod
      def infer_relative_search_space(
          self, study: Study, trial: FrozenTrial
      ) -> Dict[str, BaseDistribution]:
          """Infer the search space that will be used by relative sampling in the target trial.
  
          This method is called right before :func:`~optuna.samplers.BaseSampler.sample_relative`
          method, and the search space returned by this method is passed to it. The parameters not
          contained in the search space will be sampled by using
          :func:`~optuna.samplers.BaseSampler.sample_independent` method.
  
          Args:
              study:
                  Target study object.
              trial:
                  Target trial object.
                  Take a copy before modifying this object.
  
          Returns:
              A dictionary containing the parameter names and parameter's distributions.
  
          .. seealso::
              Please refer to :func:`~optuna.samplers.intersection_search_space` as an
              implementation of :func:`~optuna.samplers.BaseSampler.infer_relative_search_space`.
          """
  
          raise NotImplementedError
  
      @abc.abstractmethod
      def sample_relative(
          self, study: Study, trial: FrozenTrial, search_space: Dict[str, BaseDistribution]
      ) -> Dict[str, Any]:
          """Sample parameters in a given search space.
  
          This method is called once at the beginning of each trial, i.e., right before the
          evaluation of the objective function. This method is suitable for sampling algorithms
          that use relationship between parameters such as Gaussian Process and CMA-ES.
  
          .. note::
                  The failed trials are ignored by any build-in samplers when they sample new
                  parameters. Thus, failed trials are regarded as deleted in the samplers'
                  perspective.
  
          Args:
              study:
                  Target study object.
              trial:
                  Target trial object.
                  Take a copy before modifying this object.
              search_space:
                  The search space returned by
                  :func:`~optuna.samplers.BaseSampler.infer_relative_search_space`.
  
          Returns:
              A dictionary containing the parameter names and the values.
  
          """
  
          raise NotImplementedError
  
      @abc.abstractmethod
      def sample_independent(
          self,
          study: Study,
          trial: FrozenTrial,
          param_name: str,
          param_distribution: BaseDistribution,
      ) -> Any:
          """Sample a parameter for a given distribution.
  
          This method is called only for the parameters not contained in the search space returned
          by :func:`~optuna.samplers.BaseSampler.sample_relative` method. This method is suitable
          for sampling algorithms that do not use relationship between parameters such as random
          sampling and TPE.
  
          .. note::
                  The failed trials are ignored by any build-in samplers when they sample new
                  parameters. Thus, failed trials are regarded as deleted in the samplers'
                  perspective.
  
          Args:
              study:
                  Target study object.
              trial:
                  Target trial object.
                  Take a copy before modifying this object.
              param_name:
                  Name of the sampled parameter.
              param_distribution:
                  Distribution object that specifies a prior and/or scale of the sampling algorithm.
  
          Returns:
              A parameter value.
  
          """
  
          raise NotImplementedError
  
      def after_trial(
          self,
          study: Study,
          trial: FrozenTrial,
          state: TrialState,
          values: Optional[Sequence[float]],
      ) -> None:
          """Trial post-processing.
  
          This method is called after the objective function returns and right before the trials is
          finished and its state is stored.
  
          .. note::
              Added in v2.4.0 as an experimental feature. The interface may change in newer versions
              without prior notice. See https://github.com/optuna/optuna/releases/tag/v2.4.0.
  
          Args:
              study:
                  Target study object.
              trial:
                  Target trial object.
                  Take a copy before modifying this object.
              state:
                  Resulting trial state.
              values:
                  Resulting trial values. Guaranteed to not be :obj:`None` if trial succeeded.
  
          """
  
          pass
  
      def reseed_rng(self) -> None:
          """Reseed sampler's random number generator.
  
          This method is called by the :class:`~optuna.study.Study` instance if trials are executed
          in parallel with the option ``n_jobs>1``. In that case, the sampler instance will be
          replicated including the state of the random number generator, and they may suggest the
          same values. To prevent this issue, this method assigns a different seed to each random
          number generator.
          """
  
          pass
  
      def _raise_error_if_multi_objective(self, study: Study) -> None:
  
          if study._is_multi_objective():
              raise ValueError(
                  "If the study is being used for multi-objective optimization, "
                  f"{self.__class__.__name__} cannot be used."
              )
  