How to write Hill sorting algorithm in Python?

How to write Hill sorting algorithm in Python?

Hill sort (Shell Sort) is an improved insertion sort algorithm. It moves elements by comparing elements at a certain interval, thereby reducing the number of moves. The core idea of ​​Hill sorting is to group the elements to be sorted according to a certain interval, and then perform insertion sort on each group, continuously reducing the interval until it is 1, and finally perform a complete insertion sort.

Below we will introduce in detail how to use Python to write the Hill sorting algorithm.

First, we need to write a function to implement insertion sort. The core idea of ​​insertion sort is to insert the current element into the already sorted previous sequence.

def insertion_sort(arr):
    n = len(arr)
    for i in range(1, n):
        key = arr[i]
        j = i - 1
        while j >= 0 and key < arr[j]:
            arr[j + 1] = arr[j]
            j -= 1
        arr[j + 1] = key

Next, we write a Hill sort function that receives a list to be sorted as a parameter.

def shell_sort(arr):
    n = len(arr)
    gap = n // 2  # 初始间隔设置为列表长度的一半
    while gap > 0:
        for i in range(gap, n):
            temp = arr[i]
            j = i
            while j >= gap and arr[j - gap] > temp:
                arr[j] = arr[j - gap]
                j -= gap
            arr[j] = temp
        gap = gap // 2  # 缩小间隔

Finally, we write a test function to verify the correctness of Hill sorting.

def test_shell_sort():
    arr = [12, 34, 55, 23, 8, 17, 45, 91]
    shell_sort(arr)
    assert arr == [8, 12, 17, 23, 34, 45, 55, 91]
    print("希尔排序测试通过！")

if __name__ == "__main__":
    test_shell_sort()

After running the test function, if no error is reported and the prompt "Hill sort test passed!" is output, it means that the implementation of Hill sort is correct.

The time complexity of Hill sorting is related to the selected interval sequence. The best interval sequence has not been found yet. The average time complexity of Hill sort is about O(n^1.3), and the worst-case time complexity is about O(n^2).

Hill sorting is an efficient sorting algorithm. Compared with insertion sorting, it can partially order the elements of insertion sorting at the beginning, thus reducing subsequent comparison and move operations and improving efficiency. Sorting efficiency. If you want to sort a list quickly, try using the Hill sort algorithm.

The above is the detailed content of How to write Hill sorting algorithm in Python?. For more information, please follow other related articles on the PHP Chinese website!