Type recursive quick sort for any comparable items (#15490)

* Type recursive quick sort for any comparable items

Part of #15234

* Cover recursive quick sort in the comparison-sort battery

Part of #15234

* Replace placeholder test file with comparison-sort coverage

Part of #15234

* Document the comparison operators recursive quick sort actually uses

The partition uses <= and >, so the Comparable protocol should declare __le__ and __gt__ as well as __lt__.

* Apply batched suggestions from code review

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update recursive_quick_sort.py

---------

Co-authored-by: Christian Clauss <cclauss@me.com>

Author: HarshRajSinghania

sorts/recursive_quick_sort.py

@@ -1,19 +1,60 @@
-def quick_sort(data: list) -> list:
-    """
-    >>> for data in ([2, 1, 0], [2.2, 1.1, 0], "quick_sort"):
+"""
+A pure Python implementation of a recursive quick sort.
+
+For doctests run the following command:
+    python3 -m doctest -v recursive_quick_sort.py
+
+For manual testing run:
+    python3 recursive_quick_sort.py
+"""
+
+from typing import Any, Protocol
+
+
+class Comparable(Protocol):
+    def __ge__(self, other: Any, /) -> bool: ...
+    def __le__(self, other: Any, /) -> bool: ...
+
+
+def quick_sort[T: Comparable](data: list[T]) -> list[T]:
+    """Sort a list of mutually comparable items with recursive quick sort.
+
+    Returns a new list. Items must be mutually orderable. Mixing types that
+    cannot be compared raises ``TypeError`` instead of returning a silently
+    wrong order.
+
+    Examples:
+    >>> quick_sort([2, 1, 0])
+    [0, 1, 2]
+    >>> quick_sort([2.2, 1.1, 0])
+    [0, 1.1, 2.2]
+    >>> quick_sort(["c", "a", "b"])
+    ['a', 'b', 'c']
+    >>> quick_sort([])
+    []
+    >>> quick_sort([0])
+    [0]
+    >>> quick_sort([2.5, -1, 0.0]) == sorted([2.5, -1, 0.0])
+    True
+    >>> quick_sort(list("quick_sort")) == sorted("quick_sort")
+    True
+    >>> quick_sort([1, "a"])
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'str' and 'int'
+    >>> for data in ([2, 1, 0], [2.2, 1.1, 0], list("quick_sort")):
     ...     quick_sort(data) == sorted(data)
     True
     True
     True
     """
     if len(data) <= 1:
         return data
-    else:
-        return [
-            *quick_sort([e for e in data[1:] if e <= data[0]]),
-            data[0],
-            *quick_sort([e for e in data[1:] if e > data[0]]),
-        ]
+    return [
+        *quick_sort([item for item in data[1:] if item <= data[0]]),
+        data[0],
+        *quick_sort([item for item in data[1:] if item > data[0]]),
+    ]
 
 
 if __name__ == "__main__":

tests/test_sorts.py

@@ -48,6 +48,7 @@
 from sorts.quick_sort_3_partition import three_way_radix_quicksort
 from sorts.recursive_insertion_sort import rec_insertion_sort
 from sorts.recursive_mergesort_array import merge
+from sorts.recursive_quick_sort import quick_sort as recursive_quick_sort
 from sorts.reverse_selection import reverse_selection_sort
 from sorts.reversort import reversort
 from sorts.selection_sort import selection_sort
@@ -117,6 +118,7 @@ def test_intro_sort_heap_fallback_preserves_surrounding_items(max_depth: int) ->
     pancake_sort,
     patience_sort,
     quick_sort,
+    recursive_quick_sort,
     reverse_selection_sort,
     reversort,
     selection_sort,
@@ -196,6 +198,7 @@ def test_rec_insertion_sort(case) -> None:
         odd_even_transposition,
         pancake_sort,
         patience_sort,
+        recursive_quick_sort,
         reverse_selection_sort,
         reversort,
         selection_sort,