希尔排序
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"""
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))
关于此算法
问题陈述
给定一个包含 n 个元素的未排序数组，编写一个函数来对该数组进行排序
方法
- 从初始间隔 g 开始
- 遍历数组中前 (n - g) 个元素
- 将元素与间隔为 g 的下一个元素进行比较
- 如果第一个元素更大，则交换这两个元素
- 减小间隔并重复，直到间隔 = 1
时间复杂度
时间复杂度取决于间隔序列。 以下时间复杂度基于 n/2^k 的间隔序列。
O(n^2) 最坏情况性能
O(n) 最佳情况性能
O(n^2) 平均性能
空间复杂度
O(1) 最坏情况
创始人姓名
唐纳德·希尔
示例
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
视频解释
其他
希尔排序也称为递减增量排序。
