code: def _correct_predecessor(
      reachability_plot, predecessor_plot, ordering, s, e
  ):
      """Correct for predecessors.
  
      Applies Algorithm 2 of [1]_.
  
      Input parameters are ordered by the computer OPTICS ordering.
  
      .. [1] Schubert, Erich, Michael Gertz.
         "Improving the Cluster Structure Extracted from OPTICS Plots." Proc. of
         the Conference "Lernen, Wissen, Daten, Analysen" (LWDA) (2018): 318-329.
      """
      while s < e:
          if reachability_plot[s] > reachability_plot[e]:
              return s, e
          p_e = ordering[predecessor_plot[e]]
          for i in range(s, e):
              if p_e == ordering[i]:
                  return s, e
          e -= 1
      return None, None
  
imports: import warnings
  from numbers import Integral, Real
  import numpy
  from scipy.sparse import SparseEfficiencyWarning, issparse
  from ..base import BaseEstimator, ClusterMixin, _fit_context
  from ..exceptions import DataConversionWarning
  from ..metrics import pairwise_distances
  from ..metrics.pairwise import _VALID_METRICS, PAIRWISE_BOOLEAN_FUNCTIONS
  from ..neighbors import NearestNeighbors
  from ..utils import gen_batches, get_chunk_n_rows
  from ..utils._param_validation import HasMethods, Interval, RealNotInt, StrOptions, validate_params
  from ..utils.validation import check_memory
label_desc: Use image node_id 9 for calling a global function with example usage: _correct_predecessor(reachability_plot, predecessor_plot, ordering, s, e) and returns: None,  None, s,  e, s,  e