BUG: fix memory_usage method with deep of StringArray

doc/source/whatsnew/v1.1.0.rst

@@ -758,6 +758,7 @@ ExtensionArray
 - Fixed bug where :meth:`Series.value_counts` would raise on empty input of ``Int64`` dtype (:issue:`33317`)
 - Fixed bug in :class:`Series` construction with EA dtype and index but no data or scalar data fails (:issue:`26469`)
 - Fixed bug that caused :meth:`Series.__repr__()` to crash for extension types whose elements are multidimensional arrays (:issue:`33770`).
+- Fixed bug where :meth:`StringArray.memory_usage` was not implemented (:issue:`33963`)
 
 
 Other

pandas/core/arrays/string_.py

@@ -292,6 +292,12 @@ def value_counts(self, dropna=False):
 
         return value_counts(self._ndarray, dropna=dropna).astype("Int64")
 
+    def memory_usage(self, deep=False):
+        result = self._ndarray.nbytes
+        if deep:
+            return result + lib.memory_usage_of_objects(self._ndarray)
+        return result
+
     # Override parent because we have different return types.
     @classmethod
     def _create_arithmetic_method(cls, op):

pandas/tests/arrays/string_/test_string.py

@@ -303,3 +303,10 @@ def test_value_counts_na():
     result = arr.value_counts(dropna=True)
     expected = pd.Series([2, 1], index=["a", "b"], dtype="Int64")
     tm.assert_series_equal(result, expected)
+
+
+def test_memory_usage():
+    # GH 33963
+    series = pd.Series(["a", "b", "c"], dtype="string")
+
+    assert 0 < series.nbytes <= series.memory_usage() < series.memory_usage(deep=True)