code: def factorize(
      values, sort=False, order=None, na_sentinel=-1, size_hint=None
  ):
      # Implementation notes: This method is responsible for 3 things
      # 1.) coercing data to array-like (ndarray, Index, extension array)
      # 2.) factorizing labels and uniques
      # 3.) Maybe boxing the output 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.
  
      values = _ensure_arraylike(values)
      original = values
  
      if is_extension_array_dtype(values):
          values = getattr(values, "_values", values)
          labels, uniques = values.factorize(na_sentinel=na_sentinel)
          dtype = original.dtype
      else:
          values, dtype, _ = _ensure_data(values)
  
          if (
              is_datetime64_any_dtype(original)
              or is_timedelta64_dtype(original)
              or is_period_dtype(original)
          ):
              na_value = na_value_for_dtype(original.dtype)
          else:
              na_value = None
  
          labels, uniques = _factorize_array(
              values,
              na_sentinel=na_sentinel,
              size_hint=size_hint,
              na_value=na_value,
          )
  
      if sort and len(uniques) > 0:
          from pandas.core.sorting import safe_sort
  
          if na_sentinel == -1:
              # GH-25409 take_1d only works for na_sentinels of -1
              try:
                  order = uniques.argsort()
                  order2 = order.argsort()
                  labels = take_1d(
                      order2, labels, fill_value=na_sentinel
                  )
                  uniques = uniques.take(order)
              except TypeError:
                  # Mixed types, where uniques.argsort fails.
                  uniques, labels = safe_sort(
                      uniques,
                      labels,
                      na_sentinel=na_sentinel,
                      assume_unique=True,
                  )
          else:
              uniques, labels = safe_sort(
                  uniques,
                  labels,
                  na_sentinel=na_sentinel,
                  assume_unique=True,
              )
  
      uniques = _reconstruct_data(uniques, dtype, original)
  
      # return original tenor
      if isinstance(original, ABCIndexClass):
          uniques = original._shallow_copy(uniques, name=None)
      elif isinstance(original, ABCSeries):
          from pandas import Index
  
          uniques = Index(uniques)
  
      return labels, uniques
  
imports: from __future__ import division
  from textwrap import dedent
  from warnings import catch_warnings, simplefilter, warn
  import numpy
  from pandas._libs import algos, hashtable, lib
  from pandas._libs.tslib import iNaT
  from pandas.util._decorators import Appender, Substitution, deprecate_kwarg
  from pandas.core.dtypes.cast import construct_1d_object_array_from_listlike, maybe_promote
  from pandas.core.dtypes.common import ensure_float64, ensure_int64, ensure_object, ensure_platform_int, ensure_uint64, is_array_like, is_bool_dtype, is_categorical_dtype, is_complex_dtype, is_datetime64_any_dtype, is_datetime64tz_dtype, is_datetimelike, is_extension_array_dtype, is_float_dtype, is_integer_dtype, is_interval_dtype, is_list_like, is_numeric_dtype, is_object_dtype, is_period_dtype, is_scalar, is_signed_integer_dtype, is_sparse, is_timedelta64_dtype, is_unsigned_integer_dtype, needs_i8_conversion
  from pandas.core.dtypes.generic import ABCIndex, ABCIndexClass, ABCSeries
  from pandas.core.dtypes.missing import isna, na_value_for_dtype
  from pandas.core import common
label_desc: Use image node_id 10 for calling a global function with example usage: factorize(values, sort, order, na_sentinel, size_hint) and returns: labels,  uniques