DOC: Corrected Out-of-date list of sort algorithms

Reference Issues/PRs
Fixes: #38287

Implemented changes:
Changed the docstring of all the methods using np.sort as it now includes one additional stable algorithm

pandas/core/arrays/base.py

@@ -561,7 +561,7 @@ def argsort(
         ascending : bool, default True
             Whether the indices should result in an ascending
             or descending sort.
-        kind : {'quicksort', 'mergesort', 'heapsort'}, optional
+        kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
             Sorting algorithm.
         *args, **kwargs:
             Passed through to :func:`numpy.argsort`.

pandas/core/arrays/categorical.py

@@ -1452,7 +1452,7 @@ def argsort(self, ascending=True, kind="quicksort", **kwargs):
         ascending : bool, default True
             Whether the indices should result in an ascending
             or descending sort.
-        kind : {'quicksort', 'mergesort', 'heapsort'}, optional
+        kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
             Sorting algorithm.
         **kwargs:
             passed through to :func:`numpy.argsort`.

pandas/core/frame.py

@@ -5536,9 +5536,9 @@ def sort_index(
             sort direction can be controlled for each level individually.
         inplace : bool, default False
             If True, perform operation in-place.
-        kind : {'quicksort', 'mergesort', 'heapsort'}, default 'quicksort'
-            Choice of sorting algorithm. See also ndarray.np.sort for more
-            information.  `mergesort` is the only stable algorithm. For
+        kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, default 'quicksort'
+            Choice of sorting algorithm. See also :func:`numpy.sort` for more
+            information. `mergesort` and `stable` are the only stable algorithms. For
             DataFrames, this option is only applied when sorting on a single
             column or label.
         na_position : {'first', 'last'}, default 'last'

pandas/core/generic.py

@@ -4369,9 +4369,9 @@ def sort_values(
              the by.
         inplace : bool, default False
              If True, perform operation in-place.
-        kind : {'quicksort', 'mergesort', 'heapsort'}, default 'quicksort'
-             Choice of sorting algorithm. See also ndarray.np.sort for more
-             information.  `mergesort` is the only stable algorithm. For
+        kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, default 'quicksort'
+             Choice of sorting algorithm. See also :func:`numpy.sort` for more
+             information. `mergesort` and `stable` are the only stable algorithms. For
              DataFrames, this option is only applied when sorting on a single
              column or label.
         na_position : {'first', 'last'}, default 'last'

pandas/core/series.py

@@ -3067,9 +3067,9 @@ def sort_values(
             If True, sort values in ascending order, otherwise descending.
         inplace : bool, default False
             If True, perform operation in-place.
-        kind : {'quicksort', 'mergesort' or 'heapsort'}, default 'quicksort'
+        kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, default 'quicksort'
             Choice of sorting algorithm. See also :func:`numpy.sort` for more
-            information. 'mergesort' is the only stable  algorithm.
+            information. 'mergesort' and 'stable' are the only stable  algorithms.
         na_position : {'first' or 'last'}, default 'last'
             Argument 'first' puts NaNs at the beginning, 'last' puts NaNs at
             the end.
@@ -3280,9 +3280,9 @@ def sort_index(
             sort direction can be controlled for each level individually.
         inplace : bool, default False
             If True, perform operation in-place.
-        kind : {'quicksort', 'mergesort', 'heapsort'}, default 'quicksort'
+        kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, default 'quicksort'
             Choice of sorting algorithm. See also :func:`numpy.sort` for more
-            information.  'mergesort' is the only stable algorithm. For
+            information. 'mergesort' and 'stable' are the only stable algorithms. For
             DataFrames, this option is only applied when sorting on a single
             column or label.
         na_position : {'first', 'last'}, default 'last'
@@ -3421,9 +3421,9 @@ def argsort(self, axis=0, kind="quicksort", order=None) -> "Series":
         ----------
         axis : {0 or "index"}
             Has no effect but is accepted for compatibility with numpy.
-        kind : {'mergesort', 'quicksort', 'heapsort'}, default 'quicksort'
-            Choice of sorting algorithm. See np.sort for more
-            information. 'mergesort' is the only stable algorithm.
+        kind : {'mergesort', 'quicksort', 'heapsort', 'stable'}, default 'quicksort'
+            Choice of sorting algorithm. See :func:`numpy.sort` for more
+            information. 'mergesort' and 'stable' are the only stable algorithms.
         order : None
             Has no effect but is accepted for compatibility with numpy.
 

pandas/core/sorting.py

@@ -54,7 +54,7 @@ def get_indexer_indexer(
     target : Index
     level : int or level name or list of ints or list of level names
     ascending : bool or list of bools, default True
-    kind : {'quicksort', 'mergesort', 'heapsort'}, default 'quicksort'
+    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, default 'quicksort'
     na_position : {'first', 'last'}, default 'last'
     sort_remaining : bool, default True
     key : callable, optional