code: def factorize(
      values,
      sort: bool = False,
      use_na_sentinel: bool = True,
      size_hint: int | None = None,
  ) -> tuple[np.ndarray, np.ndarray | Index]:
      """
      Encode the object as an enumerated type or categorical variable.
  
      This method is useful for obtaining a numeric representation of an
      array when all that matters is identifying distinct values. `factorize`
      is available as both a top-level function :func:`pandas.factorize`,
      and as a method :meth:`Series.factorize` and :meth:`Index.factorize`.
  
      Parameters
      ----------
      {values}{sort}
      use_na_sentinel : bool, default True
          If True, the sentinel -1 will be used for NaN values. If False,
          NaN values will be encoded as non-negative integers and will not drop the
          NaN from the uniques of the values.
  
          .. versionadded:: 1.5.0
      {size_hint}\
  
      Returns
      -------
      codes : ndarray
          An integer ndarray that's an indexer into `uniques`.
          ``uniques.take(codes)`` will have the same values as `values`.
      uniques : ndarray, Index, or Categorical
          The unique valid values. When `values` is Categorical, `uniques`
          is a Categorical. When `values` is some other pandas object, an
          `Index` is returned. Otherwise, a 1-D ndarray is returned.
  
          .. note::
  
             Even if there's a missing value in `values`, `uniques` will
             *not* contain an entry for it.
  
      See Also
      --------
      cut : Discretize continuous-valued array.
      unique : Find the unique value in an array.
  
      Notes
      -----
      Reference :ref:`the user guide <reshaping.factorize>` for more examples.
  
      Examples
      --------
      These examples all show factorize as a top-level method like
      ``pd.factorize(values)``. The results are identical for methods like
      :meth:`Series.factorize`.
  
      >>> codes, uniques = pd.factorize(np.array(['b', 'b', 'a', 'c', 'b'], dtype="O"))
      >>> codes
      array([0, 0, 1, 2, 0])
      >>> uniques
      array(['b', 'a', 'c'], dtype=object)
  
      With ``sort=True``, the `uniques` will be sorted, and `codes` will be
      shuffled so that the relationship is the maintained.
  
      >>> codes, uniques = pd.factorize(np.array(['b', 'b', 'a', 'c', 'b'], dtype="O"),
      ...                               sort=True)
      >>> codes
      array([1, 1, 0, 2, 1])
      >>> uniques
      array(['a', 'b', 'c'], dtype=object)
  
      When ``use_na_sentinel=True`` (the default), missing values are indicated in
      the `codes` with the sentinel value ``-1`` and missing values are not
      included in `uniques`.
  
      >>> codes, uniques = pd.factorize(np.array(['b', None, 'a', 'c', 'b'], dtype="O"))
      >>> codes
      array([ 0, -1,  1,  2,  0])
      >>> uniques
      array(['b', 'a', 'c'], dtype=object)
  
      Thus far, we've only factorized lists (which are internally coerced to
      NumPy arrays). When factorizing pandas objects, the type of `uniques`
      will differ. For Categoricals, a `Categorical` is returned.
  
      >>> cat = pd.Categorical(['a', 'a', 'c'], categories=['a', 'b', 'c'])
      >>> codes, uniques = pd.factorize(cat)
      >>> codes
      array([0, 0, 1])
      >>> uniques
      ['a', 'c']
      Categories (3, object): ['a', 'b', 'c']
  
      Notice that ``'b'`` is in ``uniques.categories``, despite not being
      present in ``cat.values``.
  
      For all other pandas objects, an Index of the appropriate type is
      returned.
  
      >>> cat = pd.Series(['a', 'a', 'c'])
      >>> codes, uniques = pd.factorize(cat)
      >>> codes
      array([0, 0, 1])
      >>> uniques
      Index(['a', 'c'], dtype='object')
  
      If NaN is in the values, and we want to include NaN in the uniques of the
      values, it can be achieved by setting ``use_na_sentinel=False``.
  
      >>> values = np.array([1, 2, 1, np.nan])
      >>> codes, uniques = pd.factorize(values)  # default: use_na_sentinel=True
      >>> codes
      array([ 0,  1,  0, -1])
      >>> uniques
      array([1., 2.])
  
      >>> codes, uniques = pd.factorize(values, use_na_sentinel=False)
      >>> codes
      array([0, 1, 0, 2])
      >>> uniques
      array([ 1.,  2., nan])
      """
      # Implementation notes: This method is responsible for 3 things
      # 1.) coercing data to array-like (ndarray, Index, extension array)
      # 2.) factorizing codes and uniques
      # 3.) Maybe boxing the uniques in an Index
      #
      # Step 2 is dispatched to extension types (like Categorical). They are
      # responsible only for factorization. All data coercion, sorting and boxing
      # should happen here.
      if isinstance(values, (ABCIndex, ABCSeries)):
          return values.factorize(
              sort=sort, use_na_sentinel=use_na_sentinel
          )
  
      values = _ensure_arraylike(values, func_name="factorize")
      original = values
  
      if (
          isinstance(values, (ABCDatetimeArray, ABCTimedeltaArray))
          and values.freq is not None
      ):
          # The presence of 'freq' means we can fast-path sorting and know there
          #  aren't NAs
          codes, uniques = values.factorize(sort=sort)
          return codes, uniques
  
      elif not isinstance(values, np.ndarray):
          # i.e. ExtensionArray
          codes, uniques = values.factorize(
              use_na_sentinel=use_na_sentinel
          )
  
      else:
          values = np.asarray(values)  # convert DTA/TDA/MultiIndex
  
          if not use_na_sentinel and values.dtype == object:
              # factorize can now handle differentiating various types of null values.
              # These can only occur when the array has object dtype.
              # However, for backwards compatibility we only use the null for the
              # provided dtype. This may be revisited in the future, see GH#48476.
              null_mask = isna(values)
              if null_mask.any():
                  na_value = na_value_for_dtype(
                      values.dtype, compat=False
                  )
                  # Don't modify (potentially user-provided) array
                  values = np.where(null_mask, na_value, values)
  
          codes, uniques = factorize_array(
              values,
              use_na_sentinel=use_na_sentinel,
              size_hint=size_hint,
          )
  
      if sort and len(uniques) > 0:
          uniques, codes = safe_sort(
              uniques,
              codes,
              use_na_sentinel=use_na_sentinel,
              assume_unique=True,
              verify=False,
          )
  
      uniques = _reconstruct_data(uniques, original.dtype, original)
  
      return codes, uniques
  
imports: from __future__ import annotations
  import decimal
  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, ArrayLikeT, 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, np_find_common_type
  from pandas.core.dtypes.common import ensure_float64, ensure_object, ensure_platform_int, is_array_like, is_bool_dtype, is_complex_dtype, is_dict_like, is_extension_array_dtype, is_float, is_float_dtype, is_integer, is_integer_dtype, is_list_like, is_object_dtype, is_signed_integer_dtype, needs_i8_conversion
  from pandas.core.dtypes.concat import concat_compat
  from pandas.core.dtypes.dtypes import BaseMaskedDtype, CategoricalDtype, ExtensionDtype, NumpyEADtype
  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 11 for calling a global function with example usage: factorize(values, sort, use_na_sentinel, size_hint) and returns: codes,  uniques, values, codes,  uniques