Backport PR #49776 on branch 1.5.x (REGR: arithmetic ops recursion error with midx with different dtypes) (#49782)

Backport PR #49776: REGR: arithmetic ops recursion error with midx with different dtypes

Co-authored-by: Patrick Hoefler <61934744+phofl@users.noreply.github.com>

Author: meeseeksmachine

doc/source/whatsnew/v1.5.2.rst

@@ -15,6 +15,7 @@ Fixed regressions
 ~~~~~~~~~~~~~~~~~
 - Fixed regression in :meth:`MultiIndex.join` for extension array dtypes (:issue:`49277`)
 - Fixed regression in :meth:`Series.replace` raising ``RecursionError`` with numeric dtype and when specifying ``value=None`` (:issue:`45725`)
+- Fixed regression in arithmetic operations for :class:`DataFrame` with :class:`MultiIndex` columns with different dtypes (:issue:`49769`)
 - Fixed regression in :meth:`DataFrame.plot` preventing :class:`~matplotlib.colors.Colormap` instance
   from being passed using the ``colormap`` argument if Matplotlib 3.6+ is used (:issue:`49374`)
 - Fixed regression in :func:`date_range` returning an invalid set of periods for ``CustomBusinessDay`` frequency and ``start`` date with timezone (:issue:`49441`)

pandas/core/ops/__init__.py

@@ -334,7 +334,9 @@ def should_reindex_frame_op(
         left_uniques = left.columns.unique()
         right_uniques = right.columns.unique()
         cols = left_uniques.intersection(right_uniques)
-        if len(cols) and not (cols.equals(left_uniques) and cols.equals(right_uniques)):
+        if len(cols) and not (
+            len(cols) == len(left_uniques) and len(cols) == len(right_uniques)
+        ):
             # TODO: is there a shortcut available when len(cols) == 0?
             return True
 

pandas/tests/frame/test_arithmetic.py

@@ -1135,6 +1135,26 @@ def test_binop_other(self, op, value, dtype, switch_numexpr_min_elements):
                 expected = op(df, value).dtypes
             tm.assert_series_equal(result, expected)
 
+    def test_arithmetic_midx_cols_different_dtypes(self):
+        # GH#49769
+        midx = MultiIndex.from_arrays([Series([1, 2]), Series([3, 4])])
+        midx2 = MultiIndex.from_arrays([Series([1, 2], dtype="Int8"), Series([3, 4])])
+        left = DataFrame([[1, 2], [3, 4]], columns=midx)
+        right = DataFrame([[1, 2], [3, 4]], columns=midx2)
+        result = left - right
+        expected = DataFrame([[0, 0], [0, 0]], columns=midx)
+        tm.assert_frame_equal(result, expected)
+
+    def test_arithmetic_midx_cols_different_dtypes_different_order(self):
+        # GH#49769
+        midx = MultiIndex.from_arrays([Series([1, 2]), Series([3, 4])])
+        midx2 = MultiIndex.from_arrays([Series([2, 1], dtype="Int8"), Series([4, 3])])
+        left = DataFrame([[1, 2], [3, 4]], columns=midx)
+        right = DataFrame([[1, 2], [3, 4]], columns=midx2)
+        result = left - right
+        expected = DataFrame([[-1, 1], [-1, 1]], columns=midx)
+        tm.assert_frame_equal(result, expected)
+
 
 def test_frame_with_zero_len_series_corner_cases():
     # GH#28600