PERF: MultiIndex.memory_usage shouldn't trigger the index engine

Ignore the index engine when it isn't already cached.

doc/source/whatsnew/v3.0.0.rst

@@ -342,6 +342,7 @@ Performance improvements
 - Performance improvement in ``DataFrameGroupBy.__len__`` and ``SeriesGroupBy.__len__`` (:issue:`57595`)
 - Performance improvement in indexing operations for string dtypes (:issue:`56997`)
 - Performance improvement in unary methods on a :class:`RangeIndex` returning a :class:`RangeIndex` instead of a :class:`Index` when possible. (:issue:`57825`)
+- Performance improvement in :meth:`MultiIndex.memory_usage` to ignore the index engine when it isn't already cached. (:issue:`58385`)
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_300.bug_fixes:

pandas/core/indexes/base.py

@@ -4841,8 +4841,9 @@ def _from_join_target(self, result: np.ndarray) -> ArrayLike:
     def memory_usage(self, deep: bool = False) -> int:
         result = self._memory_usage(deep=deep)
 
-        # include our engine hashtable
-        result += self._engine.sizeof(deep=deep)
+        # include our engine hashtable, only if it's already cached
+        if "_engine" in self._cache:
+            result += self._engine.sizeof(deep=deep)
         return result
 
     @final

pandas/core/indexes/multi.py

@@ -1391,8 +1391,9 @@ def _nbytes(self, deep: bool = False) -> int:
         names_nbytes = sum(getsizeof(i, objsize) for i in self.names)
         result = level_nbytes + label_nbytes + names_nbytes
 
-        # include our engine hashtable
-        result += self._engine.sizeof(deep=deep)
+        # include our engine hashtable, only if it's already cached
+        if "_engine" in self._cache:
+            result += self._engine.sizeof(deep=deep)
         return result
 
     # --------------------------------------------------------------------

pandas/tests/base/test_misc.py

@@ -142,6 +142,31 @@ def test_memory_usage_components_narrow_series(any_real_numpy_dtype):
     assert total_usage == non_index_usage + index_usage
 
 
+def test_memory_usage_doesnt_trigger_engine(index):
+    index._cache.clear()
+    assert "_engine" not in index._cache
+
+    res_without_engine = index.memory_usage()
+    assert "_engine" not in index._cache
+
+    # explicitly load and cache the engine
+    _ = index._engine
+    assert "_engine" in index._cache
+
+    res_with_engine = index.memory_usage()
+
+    # the engine doesn't affect the result even when initialized with values, because
+    # index._engine.sizeof() doesn't consider the content of index._engine.values
+    assert res_with_engine == res_without_engine
+
+    if len(index) == 0:
+        assert res_without_engine == 0
+        assert res_with_engine == 0
+    else:
+        assert res_without_engine > 0
+        assert res_with_engine > 0
+
+
 def test_searchsorted(request, index_or_series_obj):
     # numpy.searchsorted calls obj.searchsorted under the hood.
     # See gh-12238