code: def test_value_counts_sort_categorical(sort, vc_sort, normalize):
      # GH#55951
      df = DataFrame(
          {"a": [2, 1, 1, 1], 0: [3, 4, 3, 3]}, dtype="category"
      )
      gb = df.groupby("a", sort=sort, observed=True)
      result = gb.value_counts(sort=vc_sort, normalize=normalize)
  
      if normalize:
          values = [2 / 3, 1 / 3, 1.0, 0.0]
      else:
          values = [2, 1, 1, 0]
      name = "proportion" if normalize else "count"
      expected = DataFrame(
          {
              "a": Categorical([1, 1, 2, 2]),
              0: Categorical([3, 4, 3, 4]),
              name: values,
          }
      ).set_index(["a", 0])[name]
      if sort and vc_sort:
          taker = [0, 1, 2, 3]
      elif sort and not vc_sort:
          taker = [0, 1, 2, 3]
      elif not sort and vc_sort:
          taker = [0, 2, 1, 3]
      else:
          taker = [2, 3, 0, 1]
      expected = expected.take(taker)
  
      tm.assert_series_equal(result, expected)
  
imports: import numpy
  import pytest
  import pandas.util._test_decorators
  from pandas import Categorical, CategoricalIndex, DataFrame, Grouper, Index, MultiIndex, Series, date_range, to_datetime
  import pandas._testing
  from pandas.util.version import Version
label_desc: Use image node_id 36 for calling a global function with example usage: test_value_counts_sort_categorical(sort, vc_sort, normalize) without return types