自顶向下的归并排序代码

自顶向下的归并排序是一种经典的排序算法，它采用分治的思想将待排序的数组不断地二分，然后将分割后的子数组进行合并，最终得到有序的数组。以下是一个示例的自顶向下的归并排序代码：

def merge_sort(arr):
    if len(arr) <= 1:
        return arr
    
    mid = len(arr) // 2
    left = arr[:mid]
    right = arr[mid:]
    
    left = merge_sort(left)
    right = merge_sort(right)
    
    return merge(left, right)

def merge(left, right):
    result = []
    i = j = 0
    
    while i < len(left) and j < len(right):
        if left[i] < right[j]:
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    
    while i < len(left):
        result.append(left[i])
        i += 1
    
    while j < len(right):
        result.append(right[j])
        j += 1
    
    return result