```
"""
https://en.wikipedia.org/wiki/Shellsort#Pseudocode
"""
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]
>>> shell_sort([])
[]
>>> shell_sort([-2, -5, -45])
[-45, -5, -2]
"""
# Marcin Ciura's gap sequence
gaps = [701, 301, 132, 57, 23, 10, 4, 1]
for gap in gaps:
for i in range(gap, len(collection)):
insert_value = collection[i]
j = i
while j >= gap and collection[j - gap] > insert_value:
collection[j] = collection[j - gap]
j -= gap
if j != i:
collection[j] = insert_value
return collection
if __name__ == "__main__":
from doctest import testmod
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))
```

Given an unsorted array of n elements, write a function to sort the array

- start with the initial gap, g
- go through the first (n - g) elements in the array
- compare the element with the next element that is g distance away
- swap the two elements if the first element is bigger
- decrease the gap and repeat until gap = 1

Time complexity is dependent on the gap sequences. Below time complexities are based on the gap sequences of n/2^k.

`O(n^2)`

Worst case performance

`O(n)`

Best-case performance

`O(n^2)`

Average performance

`O(1)`

Worst case

Donald Shell

```
arr[] = {61, 109, 149, 111, 34, 2, 24, 119}
Initial Gap: 4
1. Index = 0, Next element index = 4
2. 61 > 34, swap 61 and 34
3. The array is now {34, 109, 149, 111, 61, 2, 24, 119}
4. Index = 1, Next element index = 5
5. 109 > 2, swap 109 and 2
6. The array is now {34, 2, 149, 111, 61, 109, 24, 119}
7. Index = 2, Next element index = 6
8. 149 > 24, swap 149 and 24
9. The array is now {34, 2, 24, 111, 61, 109, 149, 119}
10. Index = 3, Next element index = 7
11. 111 < 119, do nothing and continue
12. Divide the gap by 2 and repeat until gap = 1
```

A video explaining the Shell Sort Algorithm

Shell sort is also known as diminishing increment sort.