text: import math
  from typing import List
  from typing import Optional
  from typing import Union
  
  import optuna
  from optuna._study_direction import StudyDirection
  from optuna.pruners._base import BasePruner
  from optuna.trial._state import TrialState
  
  
  class SuccessiveHalvingPruner(BasePruner):
      """Pruner using Asynchronous Successive Halving Algorithm.
  
      `Successive Halving <https://arxiv.org/abs/1502.07943>`_ is a bandit-based algorithm to
      identify the best one among multiple configurations. This class implements an asynchronous
      version of Successive Halving. Please refer to the paper of
      `Asynchronous Successive Halving <http://arxiv.org/abs/1810.05934>`_ for detailed descriptions.
  
      Note that, this class does not take care of the parameter for the maximum
      resource, referred to as :math:`R` in the paper. The maximum resource allocated to a trial is
      typically limited inside the objective function (e.g., ``step`` number in `simple_pruning.py
      <https://github.com/optuna/optuna/blob/master/examples/simple_pruning.py#L35>`_,
      ``EPOCH`` number in `chainer_integration.py
      <https://github.com/optuna/optuna/blob/master/examples/chainer/chainer_integration.py#L77>`_).
  
      .. seealso::
          Please refer to :meth:`~optuna.trial.Trial.report`.
  
      Example:
  
          We minimize an objective function with ``SuccessiveHalvingPruner``.
  
          .. testcode::
  
              import numpy as np
              from sklearn.datasets import load_iris
              from sklearn.linear_model import SGDClassifier
              from sklearn.model_selection import train_test_split
  
              import optuna
  
              X, y = load_iris(return_X_y=True)
              X_train, X_valid, y_train, y_valid = train_test_split(X, y)
              classes = np.unique(y)
  
  
              def objective(trial):
                  alpha = trial.suggest_float("alpha", 0.0, 1.0)
                  clf = SGDClassifier(alpha=alpha)
                  n_train_iter = 100
  
                  for step in range(n_train_iter):
                      clf.partial_fit(X_train, y_train, classes=classes)
  
                      intermediate_value = clf.score(X_valid, y_valid)
                      trial.report(intermediate_value, step)
  
                      if trial.should_prune():
                          raise optuna.TrialPruned()
  
                  return clf.score(X_valid, y_valid)
  
  
              study = optuna.create_study(
                  direction="maximize", pruner=optuna.pruners.SuccessiveHalvingPruner()
              )
              study.optimize(objective, n_trials=20)
  
      Args:
          min_resource:
              A parameter for specifying the minimum resource allocated to a trial
              (in the `paper <http://arxiv.org/abs/1810.05934>`_ this parameter is
              referred to as :math:`r`).
              This parameter defaults to 'auto' where the value is determined based on a heuristic
              that looks at the number of required steps for the first trial to complete.
  
              A trial is never pruned until it executes
              :math:`\\mathsf{min}\\_\\mathsf{resource} \\times
              \\mathsf{reduction}\\_\\mathsf{factor}^{
              \\mathsf{min}\\_\\mathsf{early}\\_\\mathsf{stopping}\\_\\mathsf{rate}}`
              steps (i.e., the completion point of the first rung). When the trial completes
              the first rung, it will be promoted to the next rung only
              if the value of the trial is placed in the top
              :math:`{1 \\over \\mathsf{reduction}\\_\\mathsf{factor}}` fraction of
              the all trials that already have reached the point (otherwise it will be pruned there).
              If the trial won the competition, it runs until the next completion point (i.e.,
              :math:`\\mathsf{min}\\_\\mathsf{resource} \\times
              \\mathsf{reduction}\\_\\mathsf{factor}^{
              (\\mathsf{min}\\_\\mathsf{early}\\_\\mathsf{stopping}\\_\\mathsf{rate}
              + \\mathsf{rung})}` steps)
              and repeats the same procedure.
  
              .. note::
                  If the step of the last intermediate value may change with each trial, please
                  manually specify the minimum possible step to ``min_resource``.
          reduction_factor:
              A parameter for specifying reduction factor of promotable trials
              (in the `paper <http://arxiv.org/abs/1810.05934>`_ this parameter is
              referred to as :math:`\\eta`).  At the completion point of each rung,
              about :math:`{1 \\over \\mathsf{reduction}\\_\\mathsf{factor}}`
              trials will be promoted.
          min_early_stopping_rate:
              A parameter for specifying the minimum early-stopping rate
              (in the `paper <http://arxiv.org/abs/1810.05934>`_ this parameter is
              referred to as :math:`s`).
          bootstrap_count:
              Minimum number of trials that need to complete a rung before any trial
              is considered for promotion into the next rung.
      """
  
      def __init__(
          self,
          min_resource: Union[str, int] = "auto",
          reduction_factor: int = 4,
          min_early_stopping_rate: int = 0,
          bootstrap_count: int = 0,
      ) -> None:
  
          if isinstance(min_resource, str) and min_resource != "auto":
              raise ValueError(
                  "The value of `min_resource` is {}, "
                  "but must be either `min_resource` >= 1 or 'auto'".format(min_resource)
              )
  
          if isinstance(min_resource, int) and min_resource < 1:
              raise ValueError(
                  "The value of `min_resource` is {}, "
                  "but must be either `min_resource >= 1` or 'auto'".format(min_resource)
              )
  
          if reduction_factor < 2:
              raise ValueError(
                  "The value of `reduction_factor` is {}, "
                  "but must be `reduction_factor >= 2`".format(reduction_factor)
              )
  
          if min_early_stopping_rate < 0:
              raise ValueError(
                  "The value of `min_early_stopping_rate` is {}, "
                  "but must be `min_early_stopping_rate >= 0`".format(min_early_stopping_rate)
              )
  
          if bootstrap_count < 0:
              raise ValueError(
                  "The value of `bootstrap_count` is {}, "
                  "but must be `bootstrap_count >= 0`".format(bootstrap_count)
              )
  
          if bootstrap_count > 0 and min_resource == "auto":
              raise ValueError(
                  "bootstrap_count > 0 and min_resource == 'auto' "
                  "are mutually incompatible, bootstrap_count is {}".format(bootstrap_count)
              )
  
          self._min_resource: Optional[int] = None
          if isinstance(min_resource, int):
              self._min_resource = min_resource
          self._reduction_factor = reduction_factor
          self._min_early_stopping_rate = min_early_stopping_rate
          self._bootstrap_count = bootstrap_count
  
      def prune(self, study: "optuna.study.Study", trial: "optuna.trial.FrozenTrial") -> bool:
  
          step = trial.last_step
          if step is None:
              return False
  
          rung = _get_current_rung(trial)
          value = trial.intermediate_values[step]
          trials: Optional[List["optuna.trial.FrozenTrial"]] = None
  
          while True:
              if self._min_resource is None:
                  if trials is None:
                      trials = study.get_trials(deepcopy=False)
                  self._min_resource = _estimate_min_resource(trials)
                  if self._min_resource is None:
                      return False
  
              assert self._min_resource is not None
              rung_promotion_step = self._min_resource * (
                  self._reduction_factor ** (self._min_early_stopping_rate + rung)
              )
              if step < rung_promotion_step:
                  return False
  
              if math.isnan(value):
                  return True
  
              if trials is None:
                  trials = study.get_trials(deepcopy=False)
  
              rung_key = _completed_rung_key(rung)
  
              study._storage.set_trial_system_attr(trial._trial_id, rung_key, value)
  
              competing = _get_competing_values(trials, value, rung_key)
  
              # 'competing' already includes the current trial
              # Therefore, we need to use the '<=' operator here
              if len(competing) <= self._bootstrap_count:
                  return True
  
              if not _is_trial_promotable_to_next_rung(
                  value,
                  competing,
                  self._reduction_factor,
                  study.direction,
              ):
                  return True
  
              rung += 1
  
  
  def _estimate_min_resource(trials: List["optuna.trial.FrozenTrial"]) -> Optional[int]:
  
      n_steps = [
          t.last_step for t in trials if t.state == TrialState.COMPLETE and t.last_step is not None
      ]
  
      if not n_steps:
          return None
  
      # Get the maximum number of steps and divide it by 100.
      last_step = max(n_steps)
      return max(last_step // 100, 1)
  
  
  def _get_current_rung(trial: "optuna.trial.FrozenTrial") -> int:
  
      # The following loop takes `O(log step)` iterations.
      rung = 0
      while _completed_rung_key(rung) in trial.system_attrs:
          rung += 1
      return rung
  
  
  def _completed_rung_key(rung: int) -> str:
  
      return "completed_rung_{}".format(rung)
  
  
  def _get_competing_values(
      trials: List["optuna.trial.FrozenTrial"], value: float, rung_key: str
  ) -> List[float]:
  
      competing_values = [t.system_attrs[rung_key] for t in trials if rung_key in t.system_attrs]
      competing_values.append(value)
      return competing_values
  
  
  def _is_trial_promotable_to_next_rung(
      value: float,
      competing_values: List[float],
      reduction_factor: int,
      study_direction: StudyDirection,
  ) -> bool:
  
      promotable_idx = (len(competing_values) // reduction_factor) - 1
  
      if promotable_idx == -1:
          # Optuna does not support suspending or resuming ongoing trials. Therefore, for the first
          # `eta - 1` trials, this implementation instead promotes the trial if its value is the
          # smallest one among the competing values.
          promotable_idx = 0
  
      competing_values.sort()
      if study_direction == StudyDirection.MAXIMIZE:
          return value >= competing_values[-(promotable_idx + 1)]
      return value <= competing_values[promotable_idx]
  