code: def get_group_index_sorter(
      group_index: npt.NDArray[np.intp], ngroups: int | None = None
  ) -> npt.NDArray[np.intp]:
      """
      algos.groupsort_indexer implements `counting sort` and it is at least
      O(ngroups), where
          ngroups = prod(shape)
          shape = map(len, keys)
      that is, linear in the number of combinations (cartesian product) of unique
      values of groupby keys. This can be huge when doing multi-key groupby.
      np.argsort(kind='mergesort') is O(count x log(count)) where count is the
      length of the data-frame;
      Both algorithms are `stable` sort and that is necessary for correctness of
      groupby operations. e.g. consider:
          df.groupby(key)[col].transform('first')
  
      Parameters
      ----------
      group_index : np.ndarray[np.intp]
          signed integer dtype
      ngroups : int or None, default None
  
      Returns
      -------
      np.ndarray[np.intp]
      """
      if ngroups is None:
          ngroups = 1 + group_index.max()
      count = len(group_index)
      alpha = 0.0  # taking complexities literally; there may be
      beta = 1.0  # some room for fine-tuning these parameters
      do_groupsort = count > 0 and (
          (alpha + beta * ngroups) < (count * np.log(count))
      )
      if do_groupsort:
          sorter, _ = algos.groupsort_indexer(
              ensure_platform_int(group_index),
              ngroups,
          )
          # sorter _should_ already be intp, but mypy is not yet able to verify
      else:
          sorter = group_index.argsort(kind="mergesort")
      return ensure_platform_int(sorter)
  
imports: from __future__ import annotations
  from collections import defaultdict
  from typing import TYPE_CHECKING, Callable, DefaultDict, cast
  import numpy
  from pandas._libs import algos, hashtable, lib
  from pandas._libs.hashtable import unique_label_indices
  from pandas.core.dtypes.common import ensure_int64, ensure_platform_int
  from pandas.core.dtypes.generic import ABCMultiIndex, ABCRangeIndex
  from pandas.core.dtypes.missing import isna
  from pandas.core.construction import extract_array
label_desc: Use image node_id 15 for calling a global function with example usage: get_group_index_sorter(group_index, ngroups) and returns: ensure_platform_int