code: import numpy as np
  
  from pandas import DatetimeIndex, Index, date_range, factorize
  import pandas._testing as tm
  
  
  class TestDatetimeIndexFactorize:
      def test_factorize(self):
          idx1 = DatetimeIndex(
              ["2014-01", "2014-01", "2014-02", "2014-02", "2014-03", "2014-03"]
          )
  
          exp_arr = np.array([0, 0, 1, 1, 2, 2], dtype=np.intp)
          exp_idx = DatetimeIndex(["2014-01", "2014-02", "2014-03"])
  
          arr, idx = idx1.factorize()
          tm.assert_numpy_array_equal(arr, exp_arr)
          tm.assert_index_equal(idx, exp_idx)
          assert idx.freq == exp_idx.freq
  
          arr, idx = idx1.factorize(sort=True)
          tm.assert_numpy_array_equal(arr, exp_arr)
          tm.assert_index_equal(idx, exp_idx)
          assert idx.freq == exp_idx.freq
  
          # tz must be preserved
          idx1 = idx1.tz_localize("Asia/Tokyo")
          exp_idx = exp_idx.tz_localize("Asia/Tokyo")
  
          arr, idx = idx1.factorize()
          tm.assert_numpy_array_equal(arr, exp_arr)
          tm.assert_index_equal(idx, exp_idx)
          assert idx.freq == exp_idx.freq
  
          idx2 = DatetimeIndex(
              ["2014-03", "2014-03", "2014-02", "2014-01", "2014-03", "2014-01"]
          )
  
          exp_arr = np.array([2, 2, 1, 0, 2, 0], dtype=np.intp)
          exp_idx = DatetimeIndex(["2014-01", "2014-02", "2014-03"])
          arr, idx = idx2.factorize(sort=True)
          tm.assert_numpy_array_equal(arr, exp_arr)
          tm.assert_index_equal(idx, exp_idx)
          assert idx.freq == exp_idx.freq
  
          exp_arr = np.array([0, 0, 1, 2, 0, 2], dtype=np.intp)
          exp_idx = DatetimeIndex(["2014-03", "2014-02", "2014-01"])
          arr, idx = idx2.factorize()
          tm.assert_numpy_array_equal(arr, exp_arr)
          tm.assert_index_equal(idx, exp_idx)
          assert idx.freq == exp_idx.freq
  
      def test_factorize_preserves_freq(self):
          # GH#38120 freq should be preserved
          idx3 = date_range("2000-01", periods=4, freq="M", tz="Asia/Tokyo")
          exp_arr = np.array([0, 1, 2, 3], dtype=np.intp)
  
          arr, idx = idx3.factorize()
          tm.assert_numpy_array_equal(arr, exp_arr)
          tm.assert_index_equal(idx, idx3)
          assert idx.freq == idx3.freq
  
          arr, idx = factorize(idx3)
          tm.assert_numpy_array_equal(arr, exp_arr)
          tm.assert_index_equal(idx, idx3)
          assert idx.freq == idx3.freq
  
      def test_factorize_tz(self, tz_naive_fixture, index_or_series):
          tz = tz_naive_fixture
          # GH#13750
          base = date_range("2016-11-05", freq="H", periods=100, tz=tz)
          idx = base.repeat(5)
  
          exp_arr = np.arange(100, dtype=np.intp).repeat(5)
  
          obj = index_or_series(idx)
  
          arr, res = obj.factorize()
          tm.assert_numpy_array_equal(arr, exp_arr)
          expected = base._with_freq(None)
          tm.assert_index_equal(res, expected)
          assert res.freq == expected.freq
  
      def test_factorize_dst(self, index_or_series):
          # GH#13750
          idx = date_range("2016-11-06", freq="H", periods=12, tz="US/Eastern")
          obj = index_or_series(idx)
  
          arr, res = obj.factorize()
          tm.assert_numpy_array_equal(arr, np.arange(12, dtype=np.intp))
          tm.assert_index_equal(res, idx)
          if index_or_series is Index:
              assert res.freq == idx.freq
  
          idx = date_range("2016-06-13", freq="H", periods=12, tz="US/Eastern")
          obj = index_or_series(idx)
  
          arr, res = obj.factorize()
          tm.assert_numpy_array_equal(arr, np.arange(12, dtype=np.intp))
          tm.assert_index_equal(res, idx)
          if index_or_series is Index:
              assert res.freq == idx.freq
  