pandas-dev
diff --git a/‎doc/source/whatsnew/v0.24.0.rst
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diff --git a/‎pandas/core/groupby/groupby.py
Lines changed: 2 additions & 1 deletion b/‎pandas/core/groupby/groupby.py
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diff --git a/‎pandas/core/indexes/base.py
Lines changed: 13 additions & 7 deletions b/‎pandas/core/indexes/base.py
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diff --git a/‎pandas/core/indexes/interval.py
Lines changed: 6 additions & 2 deletions b/‎pandas/core/indexes/interval.py
Lines changed: 6 additions & 2 deletions
diff --git a/‎pandas/core/indexes/multi.py
Lines changed: 19 additions & 3 deletions b/‎pandas/core/indexes/multi.py
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diff --git a/‎pandas/tests/groupby/test_nth.py
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diff --git a/‎pandas/tests/indexes/common.py
Lines changed: 6 additions & 5 deletions b/‎pandas/tests/indexes/common.py
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diff --git a/‎pandas/tests/indexes/datetimes/test_setops.py
Lines changed: 21 additions & 13 deletions b/‎pandas/tests/indexes/datetimes/test_setops.py
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diff --git a/‎pandas/tests/indexes/interval/test_interval.py
Lines changed: 12 additions & 5 deletions b/‎pandas/tests/indexes/interval/test_interval.py
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@@ -288,6 +288,7 @@ Other Enhancements
 - Added :meth:`Interval.overlaps`, :meth:`IntervalArray.overlaps`, and :meth:`IntervalIndex.overlaps` for determining overlaps between interval-like objects (:issue:`21998`)
 - :func:`~DataFrame.to_parquet` now supports writing a ``DataFrame`` as a directory of parquet files partitioned by a subset of the columns when ``engine = 'pyarrow'`` (:issue:`23283`)
 - :meth:`Timestamp.tz_localize`, :meth:`DatetimeIndex.tz_localize`, and :meth:`Series.tz_localize` have gained the ``nonexistent`` argument for alternative handling of nonexistent times. See :ref:`timeseries.timezone_nonexistent` (:issue:`8917`)
+- :meth:`Index.difference` now has an optional ``sort`` parameter to specify whether the results should be sorted if possible (:issue:`17839`)
 - :meth:`read_excel()` now accepts ``usecols`` as a list of column names or callable (:issue:`18273`)
 - :meth:`MultiIndex.to_flat_index` has been added to flatten multiple levels into a single-level :class:`Index` object.
 - :meth:`DataFrame.to_stata` and :class:` pandas.io.stata.StataWriter117` can write mixed sting columns to Stata strl format (:issue:`23633`)
@@ -1417,6 +1418,7 @@ Groupby/Resample/Rolling
 - Bug in :meth:`DataFrame.resample` and :meth:`Series.resample` when resampling by a weekly offset (``'W'``) across a DST transition (:issue:`9119`, :issue:`21459`)
 - Bug in :meth:`DataFrame.expanding` in which the ``axis`` argument was not being respected during aggregations (:issue:`23372`)
 - Bug in :meth:`pandas.core.groupby.DataFrameGroupBy.transform` which caused missing values when the input function can accept a :class:`DataFrame` but renames it (:issue:`23455`).
+- Bug in :func:`pandas.core.groupby.GroupBy.nth` where column order was not always preserved (:issue:`20760`)
 
 Reshaping
 ^^^^^^^^^
 
@@ -494,7 +494,8 @@ def _set_group_selection(self):
 
         if len(groupers):
             # GH12839 clear selected obj cache when group selection changes
-            self._group_selection = ax.difference(Index(groupers)).tolist()
+            self._group_selection = ax.difference(Index(groupers),
+                                                  sort=False).tolist()
             self._reset_cache('_selected_obj')
 
     def _set_result_index_ordered(self, result):
 
@@ -2944,17 +2944,20 @@ def intersection(self, other):
             taken.name = None
         return taken
 
-    def difference(self, other):
+    def difference(self, other, sort=True):
         """
         Return a new Index with elements from the index that are not in
         `other`.
 
         This is the set difference of two Index objects.
-        It's sorted if sorting is possible.
 
         Parameters
         ----------
         other : Index or array-like
+        sort : bool, default True
+            Sort the resulting index if possible
+
+            .. versionadded:: 0.24.0
 
         Returns
         -------
@@ -2963,10 +2966,12 @@ def difference(self, other):
         Examples
         --------
 
-        >>> idx1 = pd.Index([1, 2, 3, 4])
+        >>> idx1 = pd.Index([2, 1, 3, 4])
         >>> idx2 = pd.Index([3, 4, 5, 6])
         >>> idx1.difference(idx2)
         Int64Index([1, 2], dtype='int64')
+        >>> idx1.difference(idx2, sort=False)
+        Int64Index([2, 1], dtype='int64')
 
         """
         self._assert_can_do_setop(other)
@@ -2985,10 +2990,11 @@ def difference(self, other):
         label_diff = np.setdiff1d(np.arange(this.size), indexer,
                                   assume_unique=True)
         the_diff = this.values.take(label_diff)
-        try:
-            the_diff = sorting.safe_sort(the_diff)
-        except TypeError:
-            pass
+        if sort:
+            try:
+                the_diff = sorting.safe_sort(the_diff)
+            except TypeError:
+                pass
 
         return this._shallow_copy(the_diff, name=result_name, freq=None)
 
 
@@ -1037,7 +1037,7 @@ def overlaps(self, other):
         return self._data.overlaps(other)
 
     def _setop(op_name):
-        def func(self, other):
+        def func(self, other, sort=True):
             other = self._as_like_interval_index(other)
 
             # GH 19016: ensure set op will not return a prohibited dtype
@@ -1048,7 +1048,11 @@ def func(self, other):
                        'objects that have compatible dtypes')
                 raise TypeError(msg.format(op=op_name))
 
-            result = getattr(self._multiindex, op_name)(other._multiindex)
+            if op_name == 'difference':
+                result = getattr(self._multiindex, op_name)(other._multiindex,
+                                                            sort)
+            else:
+                result = getattr(self._multiindex, op_name)(other._multiindex)
             result_name = get_op_result_name(self, other)
 
             # GH 19101: ensure empty results have correct dtype
 
@@ -2798,10 +2798,18 @@ def intersection(self, other):
             return MultiIndex.from_arrays(lzip(*uniq_tuples), sortorder=0,
                                           names=result_names)
 
-    def difference(self, other):
+    def difference(self, other, sort=True):
         """
         Compute sorted set difference of two MultiIndex objects
 
+        Parameters
+        ----------
+        other : MultiIndex
+        sort : bool, default True
+            Sort the resulting MultiIndex if possible
+
+            .. versionadded:: 0.24.0
+
         Returns
         -------
         diff : MultiIndex
@@ -2817,8 +2825,16 @@ def difference(self, other):
                               labels=[[]] * self.nlevels,
                               names=result_names, verify_integrity=False)
 
-        difference = sorted(set(self._ndarray_values) -
-                            set(other._ndarray_values))
+        this = self._get_unique_index()
+
+        indexer = this.get_indexer(other)
+        indexer = indexer.take((indexer != -1).nonzero()[0])
+
+        label_diff = np.setdiff1d(np.arange(this.size), indexer,
+                                  assume_unique=True)
+        difference = this.values.take(label_diff)
+        if sort:
+            difference = sorted(difference)
 
         if len(difference) == 0:
             return MultiIndex(levels=[[]] * self.nlevels,
 
@@ -390,3 +390,27 @@ def test_nth_empty():
                                           names=['a', 'b']),
                          columns=['c'])
     assert_frame_equal(result, expected)
+
+
+def test_nth_column_order():
+    # GH 20760
+    # Check that nth preserves column order
+    df = DataFrame([[1, 'b', 100],
+                    [1, 'a', 50],
+                    [1, 'a', np.nan],
+                    [2, 'c', 200],
+                    [2, 'd', 150]],
+                   columns=['A', 'C', 'B'])
+    result = df.groupby('A').nth(0)
+    expected = DataFrame([['b', 100.0],
+                          ['c', 200.0]],
+                         columns=['C', 'B'],
+                         index=Index([1, 2], name='A'))
+    assert_frame_equal(result, expected)
+
+    result = df.groupby('A').nth(-1, dropna='any')
+    expected = DataFrame([['a', 50.0],
+                          ['d', 150.0]],
+                         columns=['C', 'B'],
+                         index=Index([1, 2], name='A'))
+    assert_frame_equal(result, expected)
@@ -666,12 +666,13 @@ def test_union_base(self):
                 with pytest.raises(TypeError, match=msg):
                     first.union([1, 2, 3])
 
-    def test_difference_base(self):
+    @pytest.mark.parametrize("sort", [True, False])
+    def test_difference_base(self, sort):
         for name, idx in compat.iteritems(self.indices):
             first = idx[2:]
             second = idx[:4]
             answer = idx[4:]
-            result = first.difference(second)
+            result = first.difference(second, sort)
 
             if isinstance(idx, CategoricalIndex):
                 pass
@@ -685,21 +686,21 @@ def test_difference_base(self):
                 if isinstance(idx, PeriodIndex):
                     msg = "can only call with other PeriodIndex-ed objects"
                     with pytest.raises(ValueError, match=msg):
-                        first.difference(case)
+                        first.difference(case, sort)
                 elif isinstance(idx, CategoricalIndex):
                     pass
                 elif isinstance(idx, (DatetimeIndex, TimedeltaIndex)):
                     assert result.__class__ == answer.__class__
                     tm.assert_numpy_array_equal(result.sort_values().asi8,
                                                 answer.sort_values().asi8)
                 else:
-                    result = first.difference(case)
+                    result = first.difference(case, sort)
                     assert tm.equalContents(result, answer)
 
             if isinstance(idx, MultiIndex):
                 msg = "other must be a MultiIndex or a list of tuples"
                 with pytest.raises(TypeError, match=msg):
-                    first.difference([1, 2, 3])
+                    first.difference([1, 2, 3], sort)
 
     def test_symmetric_difference(self):
         for name, idx in compat.iteritems(self.indices):
 
@@ -209,47 +209,55 @@ def test_intersection_bug_1708(self):
         assert len(result) == 0
 
     @pytest.mark.parametrize("tz", tz)
-    def test_difference(self, tz):
-        rng1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+    @pytest.mark.parametrize("sort", [True, False])
+    def test_difference(self, tz, sort):
+        rng_dates = ['1/2/2000', '1/3/2000', '1/1/2000', '1/4/2000',
+                     '1/5/2000']
+
+        rng1 = pd.DatetimeIndex(rng_dates, tz=tz)
         other1 = pd.date_range('1/6/2000', freq='D', periods=5, tz=tz)
-        expected1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+        expected1 = pd.DatetimeIndex(rng_dates, tz=tz)
 
-        rng2 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+        rng2 = pd.DatetimeIndex(rng_dates, tz=tz)
         other2 = pd.date_range('1/4/2000', freq='D', periods=5, tz=tz)
-        expected2 = pd.date_range('1/1/2000', freq='D', periods=3, tz=tz)
+        expected2 = pd.DatetimeIndex(rng_dates[:3], tz=tz)
 
-        rng3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+        rng3 = pd.DatetimeIndex(rng_dates, tz=tz)
         other3 = pd.DatetimeIndex([], tz=tz)
-        expected3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+        expected3 = pd.DatetimeIndex(rng_dates, tz=tz)
 
         for rng, other, expected in [(rng1, other1, expected1),
                                      (rng2, other2, expected2),
                                      (rng3, other3, expected3)]:
-            result_diff = rng.difference(other)
+            result_diff = rng.difference(other, sort)
+            if sort:
+                expected = expected.sort_values()
             tm.assert_index_equal(result_diff, expected)
 
-    def test_difference_freq(self):
+    @pytest.mark.parametrize("sort", [True, False])
+    def test_difference_freq(self, sort):
         # GH14323: difference of DatetimeIndex should not preserve frequency
 
         index = date_range("20160920", "20160925", freq="D")
         other = date_range("20160921", "20160924", freq="D")
         expected = DatetimeIndex(["20160920", "20160925"], freq=None)
-        idx_diff = index.difference(other)
+        idx_diff = index.difference(other, sort)
         tm.assert_index_equal(idx_diff, expected)
         tm.assert_attr_equal('freq', idx_diff, expected)
 
         other = date_range("20160922", "20160925", freq="D")
-        idx_diff = index.difference(other)
+        idx_diff = index.difference(other, sort)
         expected = DatetimeIndex(["20160920", "20160921"], freq=None)
         tm.assert_index_equal(idx_diff, expected)
         tm.assert_attr_equal('freq', idx_diff, expected)
 
-    def test_datetimeindex_diff(self):
+    @pytest.mark.parametrize("sort", [True, False])
+    def test_datetimeindex_diff(self, sort):
         dti1 = DatetimeIndex(freq='Q-JAN', start=datetime(1997, 12, 31),
                              periods=100)
         dti2 = DatetimeIndex(freq='Q-JAN', start=datetime(1997, 12, 31),
                              periods=98)
-        assert len(dti1.difference(dti2)) == 2
+        assert len(dti1.difference(dti2, sort)) == 2
 
     def test_datetimeindex_union_join_empty(self):
         dti = DatetimeIndex(start='1/1/2001', end='2/1/2001', freq='D')
 
@@ -801,19 +801,26 @@ def test_intersection(self, closed):
         result = index.intersection(other)
         tm.assert_index_equal(result, expected)
 
-    def test_difference(self, closed):
-        index = self.create_index(closed=closed)
-        tm.assert_index_equal(index.difference(index[:1]), index[1:])
+    @pytest.mark.parametrize("sort", [True, False])
+    def test_difference(self, closed, sort):
+        index = IntervalIndex.from_arrays([1, 0, 3, 2],
+                                          [1, 2, 3, 4],
+                                          closed=closed)
+        result = index.difference(index[:1], sort)
+        expected = index[1:]
+        if sort:
+            expected = expected.sort_values()
+        tm.assert_index_equal(result, expected)
 
         # GH 19101: empty result, same dtype
-        result = index.difference(index)
+        result = index.difference(index, sort)
         expected = IntervalIndex(np.array([], dtype='int64'), closed=closed)
         tm.assert_index_equal(result, expected)
 
         # GH 19101: empty result, different dtypes
         other = IntervalIndex.from_arrays(index.left.astype('float64'),
                                           index.right, closed=closed)
-        result = index.difference(other)
+        result = index.difference(other, sort)
         tm.assert_index_equal(result, expected)
 
     def test_symmetric_difference(self, closed):