Add Shell Sort algorithm (fixes #13887)

Author: rachit-27

sorts/shell_sort.py

@@ -1,40 +1,51 @@
 """
-https://en.wikipedia.org/wiki/Shellsort#Pseudocode
+Shell Sort Algorithm
+--------------------
+
+Issue: #13887
+Implements the Shell Sort algorithm which is a generalization of insertion sort.
+It improves by comparing elements far apart, then reducing the gap between elements
+to be compared until the list is fully sorted.
+
+Time Complexity:
+    Worst case: O(n^2)
+    Best case:  O(n log n)
+    Average:    O(n^(3/2))
+
+Space Complexity: O(1)
 """
 
+from __future__ import annotations
 
-def shell_sort(collection: list[int]) -> list[int]:
-    """Pure implementation of shell sort algorithm in Python
-    :param collection:  Some mutable ordered collection with heterogeneous
-    comparable items inside
-    :return:  the same collection ordered by ascending
 
-    >>> shell_sort([0, 5, 3, 2, 2])
-    [0, 2, 2, 3, 5]
+def shell_sort(arr: list[int]) -> list[int]:
+    """
+    Sorts the given list using Shell Sort and returns the sorted list.
+
+    >>> shell_sort([5, 2, 9, 1])
+    [1, 2, 5, 9]
     >>> shell_sort([])
     []
-    >>> shell_sort([-2, -5, -45])
-    [-45, -5, -2]
+    >>> shell_sort([3])
+    [3]
+    >>> shell_sort([1, 2, 3])
+    [1, 2, 3]
+    >>> shell_sort([4, 3, 3, 1])
+    [1, 3, 3, 4]
     """
-    # Marcin Ciura's gap sequence
+    n = len(arr)
+    gap = n // 2
 
-    gaps = [701, 301, 132, 57, 23, 10, 4, 1]
-    for gap in gaps:
-        for i in range(gap, len(collection)):
-            insert_value = collection[i]
+    # Keep reducing the gap until it becomes 0
+    while gap > 0:
+        for i in range(gap, n):
+            temp = arr[i]
             j = i
-            while j >= gap and collection[j - gap] > insert_value:
-                collection[j] = collection[j - gap]
+            while j >= gap and arr[j - gap] > temp:
+                arr[j] = arr[j - gap]
                 j -= gap
-            if j != i:
-                collection[j] = insert_value
-    return collection
-
+            arr[j] = temp
+        gap //= 2
 
-if __name__ == "__main__":
-    from doctest import testmod
+    return arr
 
-    testmod()
-    user_input = input("Enter numbers separated by a comma:\n").strip()
-    unsorted = [int(item) for item in user_input.split(",")]
-    print(shell_sort(unsorted))

tests/sorts/test_shell_sort.py

@@ -0,0 +1,21 @@
+from sorts.shell_sort import shell_sort
+
+
+def test_shell_sort_basic():
+    assert shell_sort([5, 2, 9, 1]) == [1, 2, 5, 9]
+
+
+def test_shell_sort_empty():
+    assert shell_sort([]) == []
+
+
+def test_shell_sort_one_element():
+    assert shell_sort([3]) == [3]
+
+
+def test_shell_sort_sorted():
+    assert shell_sort([1, 2, 3, 4]) == [1, 2, 3, 4]
+
+
+def test_shell_sort_duplicates():
+    assert shell_sort([4, 3, 3, 1]) == [1, 3, 3, 4]