code: def duplicated(
      values: ArrayLike, keep: Literal["first", "last", False] = "first"
  ) -> npt.NDArray[np.bool_]:
      """
      Return boolean ndarray denoting duplicate values.
  
      Parameters
      ----------
      values : nd.array, ExtensionArray or Series
          Array over which to check for duplicate values.
      keep : {'first', 'last', False}, default 'first'
          - ``first`` : Mark duplicates as ``True`` except for the first
            occurrence.
          - ``last`` : Mark duplicates as ``True`` except for the last
            occurrence.
          - False : Mark all duplicates as ``True``.
  
      Returns
      -------
      duplicated : ndarray[bool]
      """
      if hasattr(values, "dtype") and isinstance(
          values.dtype, BaseMaskedDtype
      ):
          values = cast("BaseMaskedArray", values)
          return htable.duplicated(
              values._data, keep=keep, mask=values._mask
          )
  
      values = _ensure_data(values)
      return htable.duplicated(values, keep=keep)
  
imports: from __future__ import annotations
  import operator
  from textwrap import dedent
  from typing import TYPE_CHECKING, Literal, cast
  import warnings
  import numpy
  from pandas._libs import algos, hashtable, iNaT, lib
  from pandas._typing import AnyArrayLike, ArrayLike, AxisInt, DtypeObj, TakeIndexer, npt
  from pandas.util._decorators import doc
  from pandas.util._exceptions import find_stack_level
  from pandas.core.dtypes.cast import construct_1d_object_array_from_listlike, infer_dtype_from_array, np_find_common_type
  from pandas.core.dtypes.common import ensure_float64, ensure_object, ensure_platform_int, is_array_like, is_bool_dtype, is_categorical_dtype, is_complex_dtype, is_extension_array_dtype, is_float_dtype, is_integer, is_integer_dtype, is_list_like, is_numeric_dtype, is_object_dtype, is_scalar, is_signed_integer_dtype, needs_i8_conversion
  from pandas.core.dtypes.concat import concat_compat
  from pandas.core.dtypes.dtypes import BaseMaskedDtype, ExtensionDtype, PandasDtype
  from pandas.core.dtypes.generic import ABCDatetimeArray, ABCExtensionArray, ABCIndex, ABCMultiIndex, ABCSeries, ABCTimedeltaArray
  from pandas.core.dtypes.missing import isna, na_value_for_dtype
  from pandas.core.array_algos.take import take_nd
  from pandas.core.construction import array, ensure_wrapped_if_datetimelike, extract_array
  from pandas.core.indexers import validate_indices
label_desc: Use image node_id 14 for calling a global function with example usage: duplicated(values, keep) and returns: htable, htable