REGR: concat materializing index even if sort is not necessary (pandas-dev#47508)

* REGR: concat materializing index even if sort is not necessary

* Add check for index

* Add exact

Author: phofl

doc/source/whatsnew/v1.4.4.rst

@@ -14,7 +14,7 @@ including other versions of pandas.
 
 Fixed regressions
 ~~~~~~~~~~~~~~~~~
--
+- Fixed regression in :func:`concat` materializing :class:`Index` during sorting even if :class:`Index` was already sorted (:issue:`47501`)
 -
 
 .. ---------------------------------------------------------------------------

pandas/core/indexes/api.py

@@ -157,7 +157,7 @@ def _get_combined_index(
         index = union_indexes(indexes, sort=False)
         index = ensure_index(index)
 
-    if sort:
+    if sort and not index.is_monotonic_increasing:
         index = safe_sort_index(index)
     # GH 29879
     if copy:

pandas/tests/reshape/concat/test_index.py

@@ -387,3 +387,14 @@ def test_concat_with_levels_with_none_keys(self, levels):
         msg = "levels supported only when keys is not None"
         with pytest.raises(ValueError, match=msg):
             concat([df1, df2], levels=levels)
+
+    def test_concat_range_index_result(self):
+        # GH#47501
+        df1 = DataFrame({"a": [1, 2]})
+        df2 = DataFrame({"b": [1, 2]})
+
+        result = concat([df1, df2], sort=True, axis=1)
+        expected = DataFrame({"a": [1, 2], "b": [1, 2]})
+        tm.assert_frame_equal(result, expected)
+        expected_index = pd.RangeIndex(0, 2)
+        tm.assert_index_equal(result.index, expected_index, exact=True)